RES2DINV ver. 3.55
for Windows 98/Me/2000/NT/XP
Rapid 2-D Resistivity & IP inversion
using the least-squares method
Wenner (α,β,γ), dipole-dipole, inline pole-pole, poledipole,
equatorial dipole-dipole, Wenner-Schlumberger
and non-conventional arrays
On land, underwater and cross-borehole surveys
Geoelectrical Imaging 2-D & 3D
GEOTOMO SOFTWARE
June 2005
This software is distributed by :
Geotomo Software,
5 Cangkat Minden Lorong 6,
Minden Heights, 11700 Gelugor,
Penang,
MALAYSIA
Tel : +60 4 6574525, Fax : +60 4 6588437
email : geotomo@tm.net.my
Internet : www.geoelectrical.com
Table of Contents
Topic Page No.
1 Introduction 1
2 Computer system requirements and installation 3
3 Copy protection 7
4 Theory 7
5 Disc contents 9
6 Using the program 10
7 Data file operations and data format 11
8 Editing the data 16
9 Changing the program settings 19
10 Inversion options 25
11 Topographical modelling 33
12 Display the inversion results 36
13 Program settings 41
14 Help 41
15 Printing the pseudosections 41
16 Other useful programs 42
17 Pitfalls in 2-D inversion 43
18 Some field examples 45
19 Trouble shooting 49
Acknowledgements 50
References 51
Appendix A : Dipole-dipole and pole-dipole surveys 54
Appendix B : The Wenner-Schlumberger array 57
Appendix C : Fixing Resistivities 59
Appendix D : The Equatorial Dipole-Dipole array 61
Appendix E : Underwater surveys 62
Appendix F : IP data inversion 68
Appendix G : New batch mode options 72
Appendix H : Speed of graphics display 73
Appendix I : Cross-borehole data inversion 74
Appendix J : Remote electrodes 84
Appendix K : Robust data and model inversion 88
Appendix L : Non-conventional or general arrays 90
Appendix M : Array types in RES2DINV 96
Appendix N : Saving results in SURFER format 98
Appendix O : Model refinement 101
Appendix P : Combining 2-D files 104
Appendix Q : Bedrock edge detection 108
Appendix R : Time-lapse resistivity inversion 111
Appendix S : Incorporating data noise estimates 119
Appendix T : Incorporating boundaries of known layers 121
Appendix U : Special topography information
for mineral exploration 124
Appendix V : Plotting methods for the gradient array 125
Special OhmMapper Note 129
Disclaimer 130
Support 130
Notice of Copyright
RES2DINV is copyrighted by © Geotomo Software, 2000-2004. All rights
reserved. No part of this document may be reproduced without written
permission of Geotomo Software.
1
1 Introduction
RES2DINV is a computer program that will automatically determine a twodimensional
(2-D) resistivity model for the subsurface for the data obtained
from electrical imaging surveys (Griffiths and Barker 1993). Since it is a
Windows based program, all Windows compatible graphics cards and printers
are automatically supported. It has been tested with video screen modes of up
to 1600 by 1200 pixels and 256 colours.
Figure 1 shows an example of the electrodes arrangement and measurement
sequence that can be used for a 2-D electrical imaging survey. This program is
designed to invert large data sets (with about 200 to 21000 data points)
collected with a system with a large number of electrodes (about 25 to 16000
electrodes).
The 2-D model used by the inversion program, which consists of a number of
rectangular blocks, is shown in Figure 2. The arrangement of the blocks is
loosely tied to the distribution of the data points in the pseudosection. The
distribution and size of the blocks is automatically generated by the program
using the distribution of the data points as a rough guide. The depth of the
bottom row of blocks is set to be approximately equal to the equivalent depth
of investigation (Edwards 1977) of the data points with the largest electrode
spacing. The survey is usually carried out with a system where the electrodes
are arranged along a line with a constant spacing between adjacent electrodes.
However, the program can also handle data sets with a non-uniform electrode
spacing.
A forward modelling subroutine is used to calculate the apparent resistivity
values, and a non-linear least-squares optimisation technique is used for the
inversion routine (deGroot-Hedlin and Constable 1990, Loke and Barker
1996a). The program supports both the finite-difference and finite-element
forward modelling techniques. This program can be used for surveys using the
Wenner, pole-pole, dipole-dipole, pole-dipole, Wenner-Schlumberger and
equatorial dipole-dipole (rectangular) arrays. In addition to these common
arrays, the program even supports non-conventional arrays with an almost
unlimited number of possible electrode configurations! You can process
pseudosections with up to 16000 electrodes and 21000 data points at a single
time on a computer with 1 GB RAM. The largest electrode spacing can be up
to 36 times the smallest spacing used in a single data set. The program data
limits will be extended in the future as larger field data sets are encountered.
Besides normal surveys carried out with the electrodes on the ground surface,
the program also supports underwater and cross-borehole surveys!
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Figure 1. Sequence of measurements to build up a pseudosection using a
computer controlled multi-electrode survey setup.
Figure 2. Arrangement of the blocks used in a model together with the data
points in the pseudosection.
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2 Computer system requirements and installation
This program is designed to run on IBM PC compatible microcomputers using
the Windows 95/98/Me/2000/NT/XP operating systems. Due to the
computational power required for the 2-D forward modelling and least-squares
subroutines, it is written for 32-bit computer systems with at least 32
megabytes of RAM. On a Pentium computer, it will take a few minutes to
invert the data set obtained from a survey with about 50 electrodes.
Minimum requirements : Hard disc with at least 64 megabytes free space, and
motherboard with at least 32 megabytes RAM. SVGA colour graphics system
with screen resolution of at least 800 by 600 pixels and 256 colours. Windows
95/98/2000/NT/XP operating system. Pentium, Pentium Pro, Pentium II,
Pentium III or Pentium 4 CPU (or compatible CPUs).
However, it is recommended that you use it on a system with 64 (or more)
megabytes of memory if you want to process very large data sets with more
than 400 electrodes and 3000 data points. You should be able to process the
largest example data set, DUFUYA.DAT that has 297 electrodes, on a system
with 32 megabytes of RAM and 64 megabytes free hard disc space. However,
it is recommended that your system has at least 128 megabytes free hard disc
space. This is a 32-bit Windows program that can access up to 4 gigabytes of
memory. The more RAM and free hard disc space you have, the larger is the
data set that you can process with this program.
It is also recommended that you use the 800 by 600 (for 14 and 15 inch
monitors) or the 1024 by 768 (for 17 and 19 inch monitors) or the 1280 by
1024 (for 21 inch monitors) with 256 colours SVGA graphics mode. You can
change the graphics mode by clicking 'Start', and then 'Settings' followed by
'Control Panel' and then 'Display'. If you are using SVGA modes with 16-bit or
24-bit colours, please switch the display mode to 256 (i.e. 8-bit) colours if you
encounter problems. Graphics operations with the 256 colours mode can be
significantly faster, and more memory will be available to your programs.
There should preferably not be too many background programs running before
executing this program. The active background programs are usually shown on
the 'Start' bar at the bottom of the screen. By shutting down the other programs,
more memory will be available to this program. This will reduce memory to
hard disc swapping that slows down the program.
The RES2DINV package comes in a single compressed installation file
SETUP.EXE which is a Windows based installation program. To install the
program, click Start, and then Settings followed by the Control Panel, and then
Add/Remove Programs.
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After installing the RES2DINV.EXE program, you should run the
JACOBWIN.EXE program to create several support files. You only have to
run the JACOBWIN.EXE program once after installing the RES2DINV
program.
Practically all computers have an in-built power management system that slows
down and eventually shuts down the computer system if the keyboard/mouse
or hard disc is not accessed after a certain time limit. This can interfere with the
operation of the RES2DINV program if you are inverting a large data set since
this program spends most of the time calculating using the CPU and
coprocessor only. Windows also has an in-built screen saver functions which
replaces the contents of the screen with a screen saver program. Before running
the RES2DINV program, you will need to disable both the power management
and screen saver programs. To disable them, you need to take the following
steps.
1). Shortly after the computer is switched on, it usually runs a memory check.
During this time, you need to go to the CMOS Setup program in the computer
BIOS. For most computers, this is done by pressing the "Del" key. The CMOS
setup screen will next be shown. Go to the section which concerns power
management, and disable the power management options for the computer.
2). After Windows starts up, go to the Control Panel. Click the Power
Management icon. Here it will probably show the number of minutes after
which Windows will automatically shut down the computer if the mouse or
keyboard is not used. Disable this feature.
3). Next, still within the Control Panel, click the Display icon. In the Display
program, click the Screen Saver option and disable the screen saver. This will
ensure that Windows does not automatically run a screen saver.
After disabling the power management and screen saver options, you can
physically switch off the monitor if the computer is left running overnight.
Before carrying out the inversion of a large data set with more than a thousand
data points, please close down other active programs to free the system
resources to RES2DINV alone. Also, using the “Set program priority” suboption
in the “File” option of the main menu, set the program priority to High
or Highest to ensure that it is not interrupted by other programs while inverting
the data set.
In Windows 95/98/Me/2000/NT/XP, it is necessary to install a system driver
for the dongle.
a). For users with the Rainbow Technologies Sentinel SuperPro key
Run the RainbowSSD5.39.2.exe file in the RAINBOW_SYSTEM_DRIVER
subdirectory in the CDROM. This program will automatically install the
system driver for the dongle. If you are using a Toshiba Laptop with the Win
5
XP operating system, there are special instructions together with a patch file
Sentinel.sys in the Toshiba_XP.zip file. After installing the driver, restart the
computer for the driver to take effect. In case of problems, use the
SuperProMedic.exe program to check the condition of the dongle. More
information about the system drivers can be obtained at the following web site.
www.rainbow.com.
b). For users with the Keylok key (parallel port or USB)
Please run the INSTALL.EXE program in the KEYLOK_SYSTEM_DRIVER
subdirectory for the Keylok drivers. This program will install the appropriate
driver for your operating system into your computer hard-disk..
If you are using the Keylok USB key, please follow the steps below.
1). If the RES2DINV and RES3DINV software are already installed in your
computer, you will need to replace the RES2DINV.EXE and RES3DINV.EXE
files with the latest USB versions in the CD. You need to copy the
RES2DINV.EXE and RES3DINV.EXE files from the Win_Updates
subdirectory to the appropriate folders in you computer (usually
C:\RES2DINV and C:\RES3DINV).
2). If the RES2DINV and RES3DINV software have not yet been installed, run
the SETUP.EXE files found in the RES2DINV and RES3DINV folders in the
CD.
3). First, make sure that the USB dongle is not attached to the computer. You
will now need to install the software driver for the Keylok dongle by running
the INSTALL.EXE program in the KEYLOK_SYSTEM_DRIVER folder in
the CD. Please note that in Windows NT/2000/XP you must have
Administrator privileges in order to install the driver.
4). After installing the driver, switch off the computer and attach the USB
dongle. It is recommended that you attach the USB dongle to the first USB port
on the computer. Some older computer systems have trouble detecting it on the
second USB port. Now switch on the computer. Windows will display a
message saying that it has found a new hardware and it should then
automatically copy the driver for the dongle.
5). Try running the RES2DINV and RES3DINV program, and they should be
able to detect the dongle. If the programs still cannot detect the dongle, you
will need to install the driver manually. Click the Control Panel under Settings,
and then select the “Add New Hardware” option. Windows then searches for
new Plug and Play devices. Click the “No the device isn’t in the list” and then
the “No I want to select the hardware from a list” options. Near the near bottom
of hardware list, the “USB Dongle” will probably be displayed. Click it, and
then the “Have Disk” option in the next dialog box. Then click “Browse” and
change the folder to the KEYLOK_SYSTEM_DRIVER folder in the CD. A
list of files with the “inf” extension will then be displayed. For Windows
6
98/Me select the “usbkey98.inf” file, for Windows NT/2000/XP select the
“Usbkey2K.inf” file. After that click “OK”, and a “Copying files” dialog box
should be shown, and Windows should copy the drivers.
After copying the drivers, you need to restart the computer, and the
RES2DINV/RES3DINV programs should then be able to detect the dongle.
More information about the system drivers can be obtained at the following
web site : www.keylok.com
In Windows 95/98/2000/NT/XP, a Recycle Bin program is sometimes used to
save recently deleted files. This feature might prove to be a nuisance when
inverting very large data sets as the program uses a number of temporary files.
Although the program deletes the files, they might end up in the Recycle Bin,
and quickly fill up your hard disc! The RES2DINV program will, by default,
use the hard disc drive with the largest amount of free space as the buffer drive.
It is recommended that you disable the Recycle Bin for this drive. This can be
done by clicking the Recycle Bin icon with the right mouse button, followed by
the Properties option. You can then configure the settings for each hard disc
drive.
For both operating systems it is recommended that you remove the CDROM
disc, if present, from the CD-ROM drive when using this program. Due
to the multi-tasking nature of these systems, sometimes the program on the disc
might be launched while RES2DINV is busy inverting a large data set! For all
versions of Windows, it is recommended that you run the SCANDISK program
occasionally to check the condition of the hard disc, and also the DEFRAG
program to reduce file fragmentation.
3 Copy protection
A hardware key (dongle) is supplied with the registered version of the
program. Attach this key to the parallel printer port of your computer. You can
attach the 25-pin connector of the printer to the other end of the key. The
demonstration version of the program does not require a hardware key but
some important features of the program cannot be used.
The program should be able to detect the dongle if the parallel printer port
follows the IBM PC specifications. If it is unable to find the dongle, the printer
port might not completely IBM PC compatible. In this case, after connecting
the dongle to the computer, connect a printer to the other end of the dongle.
Turn on the printer and print out something to confirm that the printer port is
working. Leave the printer on, and then try to run the RES2DINV.EXE
program again. If the program is not able to detect the dongle, you will need a
special adapter from Rainbow Technologies to use the dongle without a printer
7
(particularly for older laptop computers). If the computer is a desktop model,
you could change the adapter card with the printer port, or set up a second
printer port with another card. If you are using Windows NT, it is necessary to
install a system driver for the dongle (please refer to previous section). If you
are still not able to solve the problem, please contact the Rainbow
Technologies or Keylok company by email.
A more common problem is that the printer port was assigned to another
device, such as a scanner port, and not as LPT1 which is the default printer
port. In this case, you will need to reassign the parallel port as a printer port. In
Windows 95/98/Me/2000/NT, you have to select the Settings option on the
Start menu bar to access the Control Panel or the Printers folder.
4 Theory
The inversion routine used by the program is based on the smoothnessconstrained
least-squares method (deGroot-Hedlin and Constable 1990, Sasaki
1992). The smoothness-constrained least-squares method is based on the
following equation
(JTJ + uF)d = JTg (1)
where F = fxfx
T
+ fzfz
T
fx = horizontal flatness filter
fz = vertical flatness filter
J = matrix of partial derivatives
u = damping factor
d = model perturbation vector
g = discrepancy vector
One advantage of this method is that the damping factor and flatness filters can
be adjusted to suit different types of data. A detailed description of the different
variations of the smoothness-constrained least-squares method can be found in
the free tutorial notes by Loke (2001).
The program supports a new implementation of the least-squares method based
on a quasi-Newton optimisation technique (Loke and Barker 1996a). This
technique is more than 10 times faster than the conventional least-squares
method for large data sets and requires less memory. You can also use the
conventional Gauss-Newton method in this program. It is much slower than the
quasi-Newton method, but in areas with large resistivity contrasts of greater
than 10:1, it gives slightly better results. A third option in this program is to use
the Gauss-Newton method for the first 2 or 3 iterations, after which the quasi-
8
Newton method is used. In many cases, this provides the best compromise
(Loke and Dahlin 2002).
The 2-D model used by this program divides the subsurface into a number of
rectangular blocks (Figure 2). The purpose of this program is to determine the
resistivity of the rectangular blocks that will produce an apparent resistivity
pseudosection that agrees with the actual measurements. For the Wenner and
Schlumberger arrays, the thickness of the first layer of blocks is set at 0.5 times
the electrode spacing. For the pole-pole, dipole-dipole and pole-dipole arrays,
the thickness is set to about 0.9, 0.3 and 0.6 times the electrode spacing
respectively. The thickness of each subsequent deeper layer is normally
increased by 10% (or 25%). The depths of the layers can also be changed
manually by the user.
The optimisation method basically tries to reduce the difference between the
calculated and measured apparent resistivity values by adjusting the resistivity
of the model blocks. A measure of this difference is given by the root-meansquared
(RMS) error. However the model with the lowest possible RMS error
can sometimes show large and unrealistic variations in the model resistivity
values and might not always be the "best" model from a geological perspective.
In general the most prudent approach is to choose the model at the iteration
after which the RMS error does not change significantly. This usually occurs
between the 3rd and 5th iterations.
More information about the inversion method can be found in the free
“Tutorial Notes” on electrical imaging (Tutorial : 2-D and 3-D electrical
imaging surveys) that is available on the www.geoelectrical.com web site.
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5 Disc contents
The Res2dinv folder in the CD contains the main setup file SETUP.EXE. After
installing this setup file, you should have the following files in the subdirectory
containing the RES2DINV program.
RES2DINV.EXE Main inversion program
JACOBWIN.EXE Program to create some support files.
REGISTER.TXT Registration file
LANDFILL.DAT An example field data file for the Wenner array obtained
by a survey with 50 electrodes. This example shows an
interesting application of 2-D electrical imaging to map
a pollution plume from a landfill site (Niederleithinger,
1994).
GRUNDFOR.DAT Another field example for the Wenner array, but with a
more irregular distribution of the data points.
ODARSLOV.DAT A fairly large data set collected over a high resistivity
dyke (Wenner array).
ROMO.DAT Another fairly large data set (Wenner array).
DUFUYA.DAT This is a large data set with nearly 300 electrodes and
more than 1200 data points (Wenner array). On a 266
Mhz Pentium II it took about 23 minutes to invert this
data set where the Jacobian matrix was recalculated after
each iteration.
GLADOE2.DAT An example data file with topographical information.
BLOCKWEN.DAT Input test data file for Wenner array with a few bad data
points.
BLOCKDIP.DAT Example input data file for dipole-dipole array.
BLOCKTWO.DAT Example input data file for pole-pole array.
RATHCRO.DAT Wenner array data file from an archaeological survey
which also contains topographical information.
PIPESCHL.DAT Example field data set for the Wenner-Schlumberger
array.
WATER.DAT Example data file for an underwater survey.
MODEL101.DAT A very large test data set for computer systems with at
least 64 MB RAM.
DIPOLEN5.DAT Example dipole-dipole data file with non-integer values
for the “n” factor.
BLUERIDGE.DAT Example dipole-dipole data set with different “a” and
“n” combinations.
WENSCHN5.DAT Example Wenner-Schlumberger data set with noninteger
values for the “n” factor.
PDIPREV.DAT Example pole-dipole data file with the "forward" and
"reverse" arrangement of the electrodes.
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POLDPIN5.DAT Example pole-dipole data set with non-integer values for
the “n” factor.
OHMMAPPER.DAT Example field data set from a mobile surveying system
KNIVSAS.DAT Example data set using the gradient array
ITALY_CAVE.DAT Example data set in general array data format but with
the topography in a separate list
IPMODEL.DAT IP with data set with chargeability values
IPSHAN.DAT Field survey IP data set with PFE values
IPMAGUSI.DAT Field survey IP data set with metal factor values.
IPKENN.DAT Field survey IP data set with phase angle values
BOREHOLE.DAT Example cross-borehole data set.
BOREHIP.DAT Example cross-borehole data set with IP measurements.
BORELANC.DAT Cross-borehole field data set.
BOREDIFF.DAT Example cross-borehole data set where the electrodes in
the two borehole are not at the same depths.
BORERES.DAT Example cross-borehole data set with measurements
given as resistance values.
BOREHOLE_TOPO.
DAT
Example borehole data set with topography
RES2DINV.HLP Help file for this program.
RES2DINV.CNT A support file for the help file.
RES2DINV.INI Configuration file for the RES2DINV program.
RES2DINV.IN2 Alternative configuration file.
README.TXT Latest information about the current version of the 2-D
inversion program.
RESIS.BTH Example file for the batch processing mode option
6 Using the program
After running the SETUP.EXE installation program, and the JACOBWIN.EXE
program, the main program RES2DINV.EXE and the support files
(GRADWEN, GRADTWO and GRADDIP) and example data files should be
in the same subdirectory in the hard disc. Please check the condition of the
hard disc using the CHKDSK and SCANDISK programs, or similar programs
in software utility packages such as Norton Utilities.
To run the resistivity inversion program, click the RES2DINV icon. The
program will first check the computer system to ensure that it has the necessary
resources that this program requires. It will check for the available memory and
hard disc space. If the program displays a warning, you should quit from the
program and make the necessary changes. After checking the computer
configuration, the program will then display the following Main Menu bar near
the top of the screen.
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You can select an option by clicking it with the mouse cursor. If this is the first
time you are using the program, try reading in the resistivity data file
LANDFILL.DAT provided with the program. Then select the inversion option
to carry out an inversion of the data set. Figure 3 shows an example of the
results from the inversion of this data set. After reading a data set, you should
generally check for bad data points using the “Edit data” option. In the
following sections, a more detailed description of each item in the above menu
is given.
7 Data file operations and data format
When you select the “File” option, the following menu choices are displayed.
Read data file - When you select this option, the list of files in the current
directory that has an extension of .DAT will be displayed. You can use the
mouse or keyboard to select the appropriate file, or to change the subdirectory.
12
The apparent resistivity values must first be typed into a text file. You can use
any general purpose text editor, such as the Windows NOTEPAD program.
The data are arranged in an ASCII delimited manner where a comma or blank
space or a LF/CR is used to separate different numerical data items. The
program requires the data to be arranged in a certain format. If there is a
problem in running this program, one possible cause is that the input data was
arranged in a wrong format. An example of an input data set is given in the file
LANDFILL.DAT. The initial section of this file with a description of the data
format is given in the 'Comments' section below.
LANDFILL.DAT file Comments
LANDFILL SURVEY | Line 1- Name of survey line
3.0 | Line 2 - Smallest electrode spacing
1 | Line 3 - Array type (Wenner = 1, Pole-pole = 2,
| Dipole-dipole = 3, Pole-dipole = 6, Schlumberger = 7
| Equatorial dipole- dipole - 8 )
334 | Line 4 - Total number of data points
1 | Line 5 - Type of x-location for data points.
| Enter 0 if location of first electrode in array used to
| indicate the x-location. Enter 1 if mid-point of the
| array (i.e. location of data point in pseudosection)
| is used.
0 | Line 6 - Flag for IP data (enter 0 for resistivity data
| only)
4.50 3.0 84.9 | Line 7 - The x-location, electrode spacing and
| measured apparent resistivity value for the first
| data point.
7.50 3.0 62.8 |Line 8 - The x-location, electrode spacing and
| measured apparent resistivity value for the second
| data point.
Subsequent lines give similar information for the other data points. This is
followed by four 0's that are reserved flags for other features.
Subsequent lines give similar information for the other data points. This is
followed by four 0's that are reserved flags for other features.
The dipole-dipole, pole-dipole and Schlumberger array data sets have a
slightly different format since an extra parameter, the dipole separation factor,
is needed. Please refer to Appendices A and B for a description of the data
formats for these arrays. The file DIPOLEN5.DAT is an example data set for
the dipole-dipole array.
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Figure 3 : The observed and calculated apparent resistivity pseudosection for
the LANDFILL.DAT data set together with a model obtained by the inversion
program.
Note that the program assumes that the x-location of the data points increases
from the left to the right side of the pseudosection. If the x-locations in your
data set are arranged in the other way, the pseudosection will appear to have
undergone a left-to-right reversal when displayed on the screen!
The file GLADOE2.DAT is an example with topographical data. The bottom
section of this file with a description of the format for topographical data is as
follows :GLADOE2.DAT
file Comments
237 2 39.207 | Last four data points
203 2 14.546 | with x-location of the data point,
227 2 31.793 | electrode spacing and
233 2 30.285 | measured apparent resistivity values
2 | Topography data flag. If no topography data, place 0 here.
26 | Number of topography data points
-100 33 | Horizontal and vertical coordinates of 1st,
-40 34.5 | 2nd topography data point
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-20 35.0 | This is followed by similar data for
0 35.209 | the remaining topography data points
10 34.904 |
20 33.678 |
30 32.264 |
40 31.191 |
50 30.560 |
60 29.905 |
70 29.200 |
80 28.774 |
90 28.569 |
100 28.473 |
110 28.553 |
120 28.462 |
130 28.486 |
140 28.601 |
150 28.652 |
160 28.825 |
170 28.996 |
180 29.284 |
190 29.643 |
200 29.563 |
270 30.0 |
300 33 | Last topography data point
2 | The topography data point number with the first electrode
0 | Enter four 0s at the
0 | end of the file
0 |
0 |
Note that the topography data is placed immediately after the apparent
resistivity data points. The first item is a flag to indicate whether the file
contains topography data. If there is no topography data, its value is 0. Enter 1
or 2 if topographical data is present. In the case where the actual horizontal and
vertical coordinates of points along the survey line are given, enter 1. Even if
the actual horizontal distances are given in the topography data section, you
must still use the x-distance along the ground surface in the apparent resistivity
data section. In most surveys the distances of the points along the ground
surface, and not true horizontal distances, are actually measured with a tape. In
this case, enter a value of 2 for the topography data flag. This is followed by
the number of topographical data points.
It is not necessary to measure the elevation for each electrode. For example, the
data in the GLADOE2.DAT file involves 161 electrodes but only the
15
elevations at 26 points are given. The maximum number of topographical data
points you can have is 500. For each data point, the horizontal location and the
elevation is entered into the data file. After the last topographical data point,
the number of the topographical data point where the first electrode is located
is given. In the above example, the first electrode was located at -40 metres,
which corresponds to the 2nd topographical data point. Note that the elevation
of the first electrode is required. If this was not measured in the field, you can
estimate it from the elevations of the neighbouring data points. For data sets
with IP measurements as well, please refer to Appendix F.
One common problem encountered in using this program is mistakes in the
input data file. If the program stops with an error message it could be due to a
mistake in the input data file. First check that the data in the file is arranged
according to the format described above. The program will try to detect
common mistakes, such zero or negative apparent resistivity values, but there
might be some new exotic mistakes that the current version of this program
cannot detect. Other possible problems are discussed in the "Pitfalls in 2-D
inversion" section of this manual.
Import data in ..... format : This program also allows you to run other
programs to convert data arranged in a propriety format into the format
required by this program. This program is usually supplied by the manufacturer
of the multielectrode resistivity meter system you are using.
Collate data into RES3DINV format – Please refer to Appendix P for the
details.
Run JACOBWIN program - This is a utility program that generates a number
of support file required by the RES2DINV program. You should run this
program after installing the RES2DINV program. You only need to run the
JACOBWIN program once.
Change buffer drive - The program will automatically use the hard disc drive
with the largest amount of free disc space as the buffer drive to store temporary
files which it uses while inverting a data set. This option allows you to change
the buffer drive used by the program.
16
8 Editing the data
This option enables you to make some changes to the data you have read from
the input data file described in the previous option. It will enable you to
remove bad data points, and to select a portion of the data set to invert for very
large data sets. When you select this option, the following submenu will be
displayed:
Exterminate bad datum points - In this option, the apparent resistivity data
values are displayed in the form of profiles for each data level. You can use the
mouse to remove any bad data point. The main purpose of this option is to
remove data points that have resistivity values which are clearly wrong. Such
bad data points could be due to the failure of the relays at one of the electrodes,
poor electrode ground contact due to dry soil, or shorting across the cables due
to very wet ground conditions. These bad data points usually have apparent
resistivity values that are obviously too large or too small compared to the
neighboring data points. The best way to handle such bad points is to drop
them so that they do not influence the model obtained. Figure 4 shows an
example of a data set with a few bad points. To remove a bad data point, move
the cross-shaped cursor with the mouse to the data point and click the left
mouse button. The colour of the data point should change from black to purple.
If you click the same data point again, it will not be removed from the data set.
To quit from this option, just press the Q key or click the Exit option.
Splice large data set - This option enables you to choose a section of the full
data set (which is too large to be processed at a single time) to invert. After
choosing this option, the distribution of the data points in a pseudosection will
be displayed. You can select a section of the data set to invert by using the
arrow keys. Full instructions on the keys to use are displayed on the screen.
The data points selected will be marked by purple crosses or dots, whereas the
remaining data points are black. At the top of the display, the left and right
limits of the section selected are marked by yellow vertical lines. If there are
17
too many data points in the lower levels, you can reduce the number of data
points by selecting only odd or even points in a level. To do this, move the
horizontal yellow marker on the left side of the display up or down to the level
you want to decimate using the up and down arrow keys. Then press D to
decimate the data points in that level. The program allows you to read in a file
which involves up to 15000 electrodes. Using this option, you can select a
section of the data set (which covers up to a maximum of 500 electrodes and
8000 data points for a system with 64 megabytes RAM) to invert. The entire
data set can then be inverted by inverting successive subsections of the data set.
After selecting the data set subsection you want invert, you should select the
"Exterminate bad data points" option to check for bad data points. In general, it
is recommended that you try to invert the entire data set at one go. In most
cases, this can be easily done by adding more RAM and free hard disc space to
your computer.
Reverse pseudosection - This option flips the pseudosection horizontally from
left to right. This is helpful when you have parallel survey lines but the surveys
were started from different ends.
Figure 4 : Example of a data set with a few bad data points. The data is
displayed using the "Exterminate bad data points" option.
Change location of first electrode - This allows you to change the location of
the first electrode in the survey line. It is basically intended for plotting
18
purposes, so that overlapping survey lines have the same x-locations for
electrodes which coincide.
Edit data file - When you select this option, the text editor (by default
NOTEPAD) will start up. To return to the RES2DINV program, you must first
exit from the text editor program.
Run another program - This option enables you to run another program. It is
mainly intended for cases where the program had not been installed and thus
not in the list of programs recorded in the Windows Start and Program option.
Choose font - In this option, you can choose the type of font used by the
program when it draws the pseudosections. The default font is an Arial font.
The other choice is the system font. With the default Arial font the program
should be able to fit everything into the screen when drawing the
pseudosections, even with the 800x600 graphics mode. The system font usually
has bolder characters when might be better when making printouts of the
images. It is recommended that you use the 1024x768 or higher resolution
graphics mode when you use the system font.
Restore colours - This option restores the default colour scheme used by the
program.
19
9. Changing the program settings
The program has a set of predefined settings for the damping factors and other
variables that generally give satisfactory results for most data sets. However, in
some situations, you might get better results by modifying the parameters that
control the inversion process. When you select the "Change Settings" option,
the following list of menu options is displayed.
To change a particular setting, move the mouse cursor to the appropriate line
and then just click it. A message will then appear which gives some
information about the values you can use, and the type of information you need
to enter.
20
INVERSION DAMPING PARAMETERS
The following options modify the use of the damping factor u in equation (1).
Damping factors - In this option, you can set the initial value for the damping
factor in equation (1), as well as the minimum damping factor. If the data set is
very noisy, you should use a relatively larger damping factor (for example 0.3).
If the data set is less noisy, use a smaller initial damping factor (for example
0.1). The inversion subroutine will generally reduce the damping factor in
equation (1) after each iteration. However, a minimum limit for the damping
factor must be set to stabilise the inversion process. The minimum value should
usually set to about one-fifth the value of the initial damping factor.
Change of damping factor with depth - Since the resolution of the resistivity
method decreases exponentially with depth, the damping factor used in the
inversion least-squares method is normally also increased with each deeper
layer. This in done in order to stabilise the inversion process. Normally, the
damping factor is increased by 1.05 times with each deeper layer, but you can
change it. Use a larger value if the model shows unnatural oscillations in the
resistivity values in the lower sections. This will help to suppress the
oscillations. You can also select the choice to allow the program to determine
the value to increase the damping factor with depth automatically. This might
be a good choice if the thickness of the layers is much thinner than the default
values, for example if you had reduced the unit electrode spacing by half in the
data file in order to produce a model with smaller model blocks.
Optimise damping factor - If you select this option, the program will attempt to
find the optimum damping factor u in equation (1) that gives the lowest RMS
error in each iteration. By optimising the damping factor, the number of
iterations the program requires to converge can be significantly reduced.
However, the time taken per iteration will be increased. For small to medium
size data sets, this can significantly reduce the overall computer time needed to
invert the data set. For very large data sets with more than 1000 data points, the
time taken in each iteration could be significantly increased as it is necessary to
solve the least-squares equation more than once per iteration. Use this option
with care as the model with the lowest RMS error is not always the “best”
model, particularly for very noisy data sets (see the “Theory” section). In
practice, the improvement in the results by optimising the damping factor for
most data sets is rather small.
21
Limit range of model resistivity - When you select this option, the following
dialog box will be shown.
This option allows you to limit the range of resistivity values that the inversion
subroutine will give. In the above example, the upper limit for is 20 times the
average model resistivity value for the previous iteration while the lower limit
is 0.05 times (i.e. 1/20 times). The program uses “soft” limits that allow the
actual resistivity model values to exceed the limits to a certain degree.
However, this option will avoid extremely small or large model resistivity
values that are physically unrealistic. The user can also choose to use the
inversion model obtained at the first iteration as the reference model.
Vertical to horizontal flatness filter ratio - You can select the ratio of the
damping factor for the vertical flatness filter (fz) to the horizontal flatness filter
(fx). By default, the same damping factor is used for both. However, if the
anomalies in the pseudosection are elongated vertically, you can force the
program to produce models that are also elongated vertically by selecting a
higher value (for example 2.0) for the ratio of the vertical to horizontal flatness
filter. For anomalies that are elongated horizontally, choose a smaller value
(e.g. 0.5).
MESH PARAMETERS
These set of options change the finite-difference or finite-element mesh used in
the forward modelling subroutine.
Finite mesh grid size - You can choose a mesh grid used by the forward
modelling program to have 2 or 4 nodes between adjacent electrodes. With 4
nodes per electrode spacing, the calculated apparent resistivity values would be
more accurate (particularly for large resistivity contrasts). However, the
computer time and memory required are correspondingly larger. By default, the
22
program will use the 2 nodes option if the data set involves more than 90
electrodes.
Use finite-element method - This program allows you to use either the finitedifference
or finite-element method to calculate the apparent resistivity values.
By default, the program will use the finite-difference method, which is faster, if
the data set does not contain topography. If the data set contains topography,
the default choice is the finite-element method.
Mesh refinement - This option allows you to use a finer mesh (in the vertical
direction) for the finite-difference or finite-element method. The apparent
resistivity values calculated by either method will be more accurate with a finer
mesh, but the computer time and memory required will be greater. The use of a
finer mesh can give better results for cases where subsurface resistivity
contrasts of greater than 20:1 is expected. This is particularly useful in areas
where a low resistivity layer lies below a high resistivity layer.
INVERSION PROGRESS
The following set of options control the path the inversion subroutine takes
during the inversion of a data set.
Line search - The inversion routine determines the change in the model
parameters by solving equation (1). Normally the parameter change vector d
will result in a model with a lower RMS error. In the event that the RMS error
increases, you have two options. One option is to perform a line search using
quartic interpolation to find the optimum step size for the change in the
resistivity of the model blocks. The program will attempt to reduce the RMS
error, but it can also be trapped in a local minimum. The alternative is to ignore
the increase in the RMS error, and hope that the next iteration will lead to a
smaller RMS error. This might enable you to jump out of a local minimum, but
it could also lead a further increase in the RMS error. A third alternative is to
perform a line search at each iteration. This will usually give the optimum step
size, but will require at least one forward computation per iteration. In some
cases, the extra forward computations could be worthwhile if it reduces the
number of iterations needed to bring the RMS error down to an acceptable
level. To select a particular setting, just click the appropriate button. This
setting will only affect the inversion process for the third iteration onwards. For
the first two iterations, where the largest changes in the RMS error usually
occurs, the program will always carry out a line search to find the optimum
step size to further reduce the RMS error.
Percentage change for line search - The line search method used can estimate
the expected change in the apparent resistivity RMS error. If the expected
change in the RMS error is too small, it might not be worthwhile to proceed
23
with the line search to determine the optimum step size for the model
parameter change vector. Normally a value between 0.1 and 1.0 % is used.
Convergence limit - This sets the lower limit for the relative change in the
RMS error between 2 iterations. By default, a value of 5% is used. In this
program the relative change in the RMS error, rather than an absolute RMS
value, is used to accommodate different data sets with different degrees of
noise present.
RMS convergence limit – This sets the percentage RMS error in the inversion
of the apparent resistivity data where the program will stop after the model
produce has an RMS error less than this limit. Normally a value of between 2%
and 5% should be used, depending on the quality of the data.
Number of iterations - This allows the user to set the maximum number of
iterations for the inversion routine. By default the maximum number of
iterations is set to 5. For most data sets, this is probably sufficient. When the
inversion routine reaches this maximum limit, it will ask the user for the
number of additional iterations if you wish to continue with the inversion
process. It is usually not necessary to use more than 10 iterations.
Model resistivity values check - The program will display a warning if after an
iteration in the inversion of the data set, a model resistivity value becomes too
large (more than 20 times the maximum apparent resistivity value) or too small
(less than 1/20 the minimum apparent resistivity value). This option allows you
to disable the warning.
DATA/DISPLAY SELECTION
Minor options for pre-processing of data files and display of the sections
during the inversion.
Cutoff limit for borehole resistance readings - In cross-borehole measurements,
certain combinations of the current and potential electrodes could result in
extremely low potential values. This could result in readings with very low
signal to noise ratios. To filter out such potentially noisy readings, the program
estimates the potential per a unit input current, that would be measured by each
electrode configuration used in the data set. If the estimated potential falls
below a certain limit, compared with the combination which gives the
maximum potential, the reading is rejected. For example, if you choose a value
of 0.001, this means configurations which will result in potential values that are
a thousand times smaller than the maximum potential measured will be
rejected. Normally a value of between 0.008 and 0.0007 is used. The program
also allows you to enter the measurements as resistance values, and carry out
the inversion with the resistance (rather than apparent resistivity) values. In this
24
case, the cutoff limit option is not used. For more details, please refer to
Appendix I.
Option for contour intervals - By default, the program will use logarithmic
contour intervals for the pseudosections and model sections when displaying
the results in the “Inversion” option in the Main Menu. This is usually the best
choice for most data sets. However, you can choose to use the linear or the user
defined contour intervals options if you wish.
Show pseudosections during inversion - You can choose to display the
pseudosections during the data inversion, or just display the model RMS
values. It is recommended that you display the sections unless the Windows
driver for your graphics card is extremely slow. In the long run, it is
recommended that you download a new version of the Windows driver.
Save inversion parameters – This option saves the inversion parameters into a
file RES2DINV.IVP.
Read inversion parameters –This option reads back the parameters stored in the
RES2DINV.IVP files and uses them in the program. RES2DINV_NEW.IVP is
an example file that contains more inversion parameters. These files can also
be used by the ‘Batch mode” option. Please refer to Appendix G for the new
format for the ‘Batch mode’ script file.
25
10. Inversion options
This option enables you to carry out the inversion of the data set that you had
read in using the "File" option. You can also display the arrangement of the
blocks used by the inversion model, as well as to change some of the
parameters that control the inversion process. On selecting this option the
following menu will be displayed.
Least-squares inversion - This option will start the least-squares inversion
routine. You will be asked for the name of the output data file in which to store
the results, and the contour intervals for the pseudosections if you had chosen
the user defined option for the contour intervals. You can stop the inversion by
pressing the Q key, and then wait for a short while.
INVERSION METHODS
These set of options allow you to select the type of regularised inversion
method to use.
26
Include smoothing of model resistivity values - The least-squares formulation
used in equation (1) applies a smoothness constraint on the model perturbation
vector d only, and not directly on the model resistivity values. In most cases, it
will produce a model with a reasonably smooth variation in the resistivity
values. In some cases, particularly for very noisy data sets, better results might
be obtained by applying a smoothness constraint on the model resistivity
values as well. The resulting least-squares equation is given by
(JTJ + uF)d = JTg - uFr (2)
where r is a vector containing the logarithm of the model resistivity values.
While for the same damping factors this will usually produce a model with a
larger apparent resistivity RMS error, this modification will ensure that the
resulting model shows a smooth variation in the resistivity values.
Use combined inversion method - This option is intended for use in unusual
situations where the data sensitivity values of the model blocks are
significantly distorted by large resistivity variations. In some situations, such as
a survey over a very low resistivity body, the current paths could be distorted
such that parts of the subsurface are not well mapped and have very low data
sensitivity values in the inversion model. This could lead to large distortions
just below the low resistivity body. By combining the Marquardt (or ridge
regression) and Occam (or smoothness-constrained) inversion methods, the
distortions in some cases might be reduced. This option should be used as a last
resort if everything else fails! It seems to give better results in resolving
compact structures where the width and thickness are slightly smaller than the
depth, such as a cave or ore-body whose size is just slightly less than its depth.
In theory, it is possible to just use the Marquardt (or ridge regression) method
alone. However, it has been found that this method is unstable when the data
contains noise if a model with a relatively large number of model parameters is
used.
Select robust inversion – This allows you to select the robust or blocky
inversion method. It should be used when sharp boundaries are expected to be
present. Please refer to Appendix K for further details.
Choose logarithm of apparent resistivity - By default, the program will use the
logarithm of the apparent resistivity values as the data parameter when carrying
out the inversion. For most cases, this gives the best results. In some cases, for
example with negative or zero apparent resistivity, this is not possible. This
option enables the apparent resistivity value by itself to be used for such
situations.
Jacobian matrix calculation - In this program you have three options in the
calculation of the Jacobian matrix J in equation (1). The fastest method is to
use the quasi-Newton method to estimate the Jacobian matrix (Loke and
Barker 1996a). This might be a good alternative to use in the field where a
27
slower laptop computer with more limited memory is frequently used. The
most accurate and slowest method is to recalculate the Jacobian matrix for all
iterations. This requires a fast computer with preferably at least 32 megabytes
of RAM, and about 64 megabytes free hard disc space for very large data sets.
A third alternative is to recalculate the Jacobian matrix for the first 2 iterations
only, and use the quasi-Newton updating method for subsequent iterations. The
largest changes in the Jacobian matrix usually occurs in the first few iterations.
So in many cases, a limited recalculation of the Jacobian matrix gives the best
compromise between speed and accuracy. By default, the program will choose
the limited recalculation option for the Jacobian matrix. However, the default
settings can be changed by the user in this menu option. The quasi-Newton
option is useful to get a quick look at the results, particularly in the field during
the course of a survey using a laptop computer. For the final model, it is best to
use the limited recalculation option on a faster desktop computer with more
RAM and free hard disc space. In areas with large resistivity contrasts, where
the largest apparent resistivity value is more than 10 times the smallest value,
recalculating the Jacobian matrix for all iterations produces models with
boundaries which are a shade sharper than those produced by the quasi-Newton
method.
Type of optimisation method – This option allows you to choose two different
methods to solve the least-squares equation (1). On selecting this menu option,
the following dialog box will be shown.
By default the program uses the ‘Standard Gauss-Newton’ least-squares
method, particularly if the number of data points and/or model cells is small
(less than a few thousand), where an exact solution of the least-squares
equation is calculated. If the number of data points and/or model cells is large
(more than 2000), the time taken to solve the least-squares equation could be
28
the most time-consuming part of the inversion process. To reduce the inversion
time, an alternative method that calculates an approximate solution of the leastsquares
equation using the ‘Incomplete Gauss-Newton’ method can be used.
The user can set the accuracy of the solution. For most data sets, an accuracy of
about 0.5% (i.e. a convergence limit of 0.005 in the above dialog box) seems
to provide a solution that is almost the same as that obtained by the ‘Standard
Gauss-Newton’ method. Setting a higher accuracy, for example 0.1%, will in
theory give a result that is even closer to the ‘Standard Gauss-Newton’ method
but this is at the expense of a longer inversion time. For very large data sets
and models (usually over 10000 data points/model cells), a “data compression”
option is provided with the ‘Incomplete Gauss-Newton’ method. This can
significantly reduce the computer memory required.
For data sets from very long survey lines (over 2000 electrode positions), a
“sparse inversion” option is provided that can greatly reduce the computer time
and memory required. For example, the inversion of an underwater survey data
set with nearly 7500 electrode positions was reduced by a factor of 10 (to about
101 minutes hours on a 3.2GHz P4 computer) with the sparse inversion option.
This method inverts the entire data set and model at a single time to produce a
continuous and seamless model.
MODEL DISCRETIZATION
These option allows you to modify the way the program subdivides the
subsurface into cells that is used as the inversion model.
Display model blocks - This option will display the distribution of the model
blocks and data points. The data points will be plotted at the median depth of
investigation (Edwards 1977) for the array used. The program has a maximum
limit of 24 model layers. If you had chosen the 10% option for the increase in
the layers thickness, and the bottom layer is above the bottom row of data
points, you should change to the 25% option.
Change thickness of layers - In this option you can choose a model where the
thickness of the layers increase by 10% or by 25% with each deeper layer.
Choose the 10% option if there are only a small number (8 or less) of data
levels. If there are a large number of sparse data levels, the 25% option might
be better. Within this option, you can also allow the number of model blocks to
exceed the number of data points. The program normally uses a model where
the depth to the deepest layer does not exceed the maximum pseudodepth in
the data set. To use a model that spans a deeper depth range, you can change
the factor to increase model depth range, for eg. from 1.0 to 1.30 to increase
the model depth range by 30%.
29
Modify depths to layers - This option allows you to change the depth of the
layers used by the inversion model. You can adjust the depths so that some of
the boundaries coincide with known depths from borehole and other data.
Use extended model – This option extends the model cells to the edges of the
survey line (Figure 5c).
Allow number of model blocks to exceed datum points - By default, the
program will try to arrange the position and size of the model cells such that
they do not exceed the number of data points. This is probably the best option
for large and medium size data sets collected with more than about 50
electrodes, particularly where the distribution of the data points with the larger
spacings is more sparse. In some cases, the width of the model cells in the
lower layers might be larger than those in the upper layers. However, for
smaller data sets, it might be useful to relax this constrain, and allow the
number of model parameters to exceed the number of data points. This will
produce a model where the interior cells in all layers have a uniform width that
is equals to the smallest electrode spacing (Figure 5b).
Make sure model blocks have same widths –The model shown in Figure 5b
have model cells that are wider at the edges. This option will ensure that all the
cells have the same width that is equal to the unit electrode spacing.
Reduce effect of side blocks – This option affects the calculation of the
Jacobian matrix values for the model blocks located at the sides and bottom of
the model section. Normally, for a block located at the side, the contributions
by all the mesh elements associated with the model block are added up right to
the edge of the mesh. This gives a greater weight to the side block compared to
the interior blocks. In some cases, particularly when the robust inversion option
is used, this can result in unusually a high or low resistivity value for the side
block. This option leaves out the contribution of the mesh elements outside the
limits of the survey line to the Jacobian matrix values for the side blocks.
Change width of blocks – This option allows the user to force the program to
use model cells which are wider than one unit electrode spacing for all the
layers.
Use model refinement – Please refer to Appendix P for the details.
Type of cross-borehole model - There are two choices for the type of model
you can use for the inversion of cross-borehole data. You can choose to use the
Standard Model where the dimensions of the model blocks are the same as the
spacing between the electrodes on the ground surface and in the boreholes.
Alternatively, you can use a model with smaller blocks where the size of the
blocks is half that of the Standard Model (see Figure 20 in Appendix I).
30
Figure 5. Different methods to subdivide the subsurface into 2-D rectangular
cells. Models obtained with (a) the default algorithm, (b) by allowing the
number of model blocks to exceed the number of data points, (c) a model
which extends to the edges of the survey line and (d) using the sensitivity
values for a homogeneous earth model.
31
MODEL SENSITIVITY OPTIONS
Display blocks sensitivity - This will show a plot of the sensitivity of the
blocks used in the inversion model. The sensitivity value is a measure of the
amount of information about the resistivity of a model block contained in the
measured data set. The higher the sensitivity value, the more reliable is the
model resistivity value. In general, the blocks near the surface usually have
higher sensitivity values because the sensitivity function has very large values
near the electrodes. The blocks at the sides and bottom also have high
sensitivity values due to the much larger size of these blocks that are extended
to the edges of the finite-difference or finite-element mesh. If you had carried
out an inversion of the data set before calling this option, the program will
make use of the Jacobian matrix of the last iteration. Otherwise, it will
calculate the Jacobian matrix for a homogenous earth model.
Display subsurface sensitivity - This shows a plot of the sensitivity of the
subsurface for blocks of equal size. This basically eliminates the effect of
changes in the model block size so that it shows more clearly the change of the
subsurface sensitivity with depth and location.
Normalise sensitivity values – By default, the calculated sensitivity values are
normalised by dividing with the average sensitivity value. In this option, you
can choose not to normalise the sensitivity values.
Generate model blocks – This option generates the model cells by making use
of the model sensitivity values. Please refer to Appendix L for a description of
this option.
IP OPTIONS
Type of IP inversion method - To invert a combined resistivity and IP dataset,
you can choose to invert both data sets concurrently in each iteration or to
invert the IP data sequentially after the inversion of the resistivity data.
IP damping factor – The damping factor used in the inversion of IP is usually
smaller than that used in the inversion of the corresponding resistivity data set.
If a value of 1.0 is used, then the same damping factors will be used for both
the resistivity and IP inversion routines. Normally a much smaller value of
about 0.05 to 0.25 is used. Alternatively, you can choose the option to let the
program automatically calculate the damping factor.
Batch mode - In this option, you can invert a number of data sets automatically.
The name of the input data files, and other information, is provided through a
file. It must be emphasised that before inverting the data sets, you should check
the data for bad data points using the Edit Data option discussed earlier. When
32
you select the batch mode suboption, you will first be asked for the name of the
data file containing the information required. An example file provided is
RESIS.BTH which enables the inversion of 3 data sets using the batch mode.
The format of this file is as follows :Line
1 - Number of data files to process.
Lines 2 to 16 - This contains the information for the first data file in the
following format. The corresponding values used in the example RESIS.BTH
for the first data file is also listed below to help clarify matters.
Type of information Value in RESIS.BTH
Header DATA FILE 1
Name of input data file RATHCRO.DAT
Name of output data file RATHCRO.INV
Starting damping factor 0.15
Minimum damping factor 0.03
Line Search option to be used ALWAYS
Convergence limit 5.0
Percentage change for line search 0.4
Number of iterations 6
Vertical/Horizontal flatness filter ratio 1.00
Thickness of model layers increase 10
Finite-difference grid size 4
Include smoothing of model resistivity NO
Reduce number of topographical datum points YES
Carry out topographical correction YES
Type of linear trend to remove END-TO-END
Type of Jacobian matrix calculation LIMITED RECALCULATION
If you do not wish to carry out the topographical corrections, just enter “No” at
the appropriate line. To remove a linear least-squares or average trend, enter
Linear or Average in the file. Even if the data set does not contain
topographical data, you still must enter the topographical processing
information. Although in this case the topographical processing information
will be ignored by the program, you must still type in something at the
appropriate lines or else the program cannot read in the parameters for the
following data files in the correct sequence. The other options for the type of
Jacobian matrix calculation are “Quasi-Newton” and “Recalculate”. The
information for the other data files to be processed follow the same format.
Please refer to the example file RESIS.BTH. An example of an extended batch
file that includes more inversion parameters is the file RESIS_NEW.BTH.
A new ‘Batch mode’ script file format is also described in Appendix G which
makes use of the IVP files that are created by the RES2DINV program. It is
easier to use since the user does not need to deal with the details about the
format of file containing the inversion parameters.
33
11. Topographical modelling
If there is significant topographical relief along the survey line, the effect of the
topographical effects can be accounted for if the horizontal and vertical
coordinates of a number of points along the survey line are known. When the
program reads in a data file with topography data (please refer to section 7 for
the data format), it will automatically select the finite-element method that
incorporates the topography into the modelling mesh used. In this case, the
topographic modelling will be automatically carried out by the program when
you invert the data set. When you select the “Topography Option” menu, the
following submenu will be displayed:
Display topography - This option simply plots the topography, such as in
Figure 6.
Select type of trend removal - You can choose to remove the average elevation,
a least-squares linear trend, or a straight line joining the first and last
topography data points. If the ground surface along the survey line is generally
flat except for a few points, use the option to subtract a constant value from the
heights of the electrodes locations. If the survey points are on a slope, choose
either a least-squares or an end-to-end straight line for the linear trend. Figure 6
shows an example with topography where the end-to-end straight line trend
was removed.
Type of topographic modelling - Selecting this option will show the following
dialog box where you can choose 3 different topographic modelling methods.
Distorted finite-element grid with uniform distortion : This method, and the
next two methods, use a distorted finite-element grid such that the surface
34
nodes of the mesh match the actual topography. This gives more accurate
results than the older method of using the correction factors for a homogeneous
earth model calculated with the finite-element method (Fox et al. 1980) which
can cause distortions in cases where large resistivity variations occur near the
surface (Tong and Yang 1990, Loke 2000). In this particular option, the nodes
below the surface (and thus also the model layers) are shifted to the same
extent as the surface nodes.
Distorted finite-element grid with damped distortion : In this option, the
subsurface nodes are shifted to a lesser extent compared with the surface
nodes, i.e. the effect of the topography is “damped” with depth. This option is
probably a reasonable choice if the amplitude of the curvature of the
topography is less than the depth of the deepest model layer. A damping factor
that controls the degree of damping with depth (Figure 7) can be modified by
the user.
S-C transformation with distorted finite-element grid : This method uses the
Schwarz-Christoffel transformation method to calculate the distortion in the
subsurface layers. It is probably the best method that produces a more ‘natural’
looking model section in cases with a comparatively large topography
curvature. In such cases, the damped topography approach might produce
unusually thick model layers under areas where the topography curves
upwards. In some unusual cases where the topography has very sharp acute
peaks and sparse topography data points, the Schwarz-Christoffel
transformation method might not work. If this happens, add a few extra
topography data points near the peak.
Figure 6. Topography linear trend removal for the Rathcroghan mound data
set.
35
Figure 7. Different methods to incorporate topography into a 2-D inversion
model. (a) Schematic diagram of a typical 2-D inversion model with no
topography. A finite-element mesh with four nodes in the horizontal direction
between adjacent electrodes is normally used. The near surface layers are also
subdivided vertically by several mesh lines. Models with a distorted grid to
match the actual topography where (b) the subsurface nodes are shifted
vertically by the same amount as the surface nodes, (c) the shift in the
subsurface nodes are gradually reduced with depth or (d) rapidly reduced with
depth, and (e) the model obtained with the inverse Schwartz-Christoffel
transformation method.
36
12. Displaying the inversion results
In this option, you can read in a data file or the output file produced by the
inversion subroutine and display the measured and calculated apparent
resistivity pseudosections and the model section. Within this option, you can
change the contour interval used for drawing the pseudo and model sections,
the vertical scale of the sections, and include topography in the model section.
You can also change the colour scheme used by the program. If you had earlier
read in an input data file or used the inversion option in the Main Menu, the
program will first read the last file used. After selecting this option on the Main
Menu bar, the program will switch to the Window for displaying the
pseudosections and model section. To return to the Main menu, you will need
to Exit from this window. This window has the following top menu bar.
The “File” option will bring up the following submenu.
Read data file with inversion results - You can read in the output data file
produced by the inversion subroutine or an input data file.
Save data in XYZ format - You can save the inversion results into a disc file
with a format used by many contouring programs, such as Geosoft. This is a
separate program sold by GEOSOFT Inc. which enables you to use more
sophisticated contouring techniques than those used by the RES2DINV
program.
Save data in SURFER format – This saves the data and model sections in
SURFER format. Please refer to Appendix N for the details.
Model output in LUND format - This is a data format used by the LUND
Imaging System produced by ABEM. You can save the model resistivity
values in the .RHO and .RMS files used by the MODSEC program.
Save contour values - This option saves the values used to draw the contours in
the pseudo and model sections.
37
Figure 8. The observed apparent resistivity pseudosection from the
Rathcroghan mound survey together with the model section. The topography
has been incorporated in the model section.
Clicking the “Display sections” option on the top menu bar will bring up the
following submenu.
Display data and model sections - Select this option to plot the model and
apparent resistivity pseudosections on the screen.
Include topography in model display - For inversion results where topographic
modelling were earlier carried out, you can incorporate the topography into the
model section by calculating that the true depth and location of the model
blocks below the surface. Figure 8 shows an example of a model section with
the topography. The field data for this survey (as well as the Landfill example
in Figure 3) was measured using a Campus Geopulse resistivity imaging
system manufactured by Campus Geophysical Instruments Ltd.
38
For both display options, you will be asked to enter the iteration number and
the contour intervals. After the section is displayed, you can display the results
for the next iteration by pressing the PgDn key. Similarly, pressing the PgUp
key will display the results for the previous iteration.
Choose resistivity or IP display - If the data set has IP data as well, this option
allows you to choose to display the resistivity or IP sections. You can also
display both the resistivity and IP model sections at the same time.
Type of pole-dipole display - This option is only relevant for pole-dipole data
sets with measurements with the “forward” and “reverse” pole-dipole arrays
(see Appendix A). Here you can choose to display the apparent resistivity
values measured with the array in the “forward” or “reverse” configuration.
The “Change display settings” option enables you to change the parameters
that control the way the apparent resistivity pseudosections and the model
section are displayed. The following submenu will be displayed when you click
this option.
Default colour scheme - This will reset the colour scheme used for colouring
the sections to a default system used by the program.
39
Customise colour scheme - This enables the user to change the colours used for
the sections.
Read customise colour scheme - You can change the colour scheme to a set of
customise colours that was earlier saved in a disk file.
Number of sections to display - You can choose to display 1, 2 or 3 sections on
the screen. By default, all the 3 sections (the observed and calculated apparent
resistivity pseudosections and the model section) are displayed.
Apparent resistivity difference - You can choose to display either the
calculated apparent resistivity pseudosection itself, or the percentage difference
between the logarithms of the calculated and observed apparent resistivity
values.
Vertical display scaling factor - This option allows you to specify the ratio of
the vertical scale to the horizontal scale, i.e. the vertical exaggeration factor, in
the display. Convenient values to use are 2.0, 1.5 and 1.0. If you enter a value
of 0.0, the program will use a default scaling factor so that the display can fit
into the display screen.
Horizontal plotting scale - This allows you to change the horizontal scale, in
terms of number of pixels per unit electrode spacing. This option is useful
when you want to plot the results from different survey lines with different
numbers of electrodes, with the same scale.
Show locations of datum points - By default, the location of the data points
(and centres of the model blocks) will be shown by white dots in the colour
pseudosection display. You can choose not to display the dots with this option.
Resistivity or conductivity display - The resistivity pseudosections and model
sections are normally displayed. However, you can display the sections using
conductivity values (i.e. the reciprocal of the resistivity) which is more
commonly used in certain fields, such as hydrogeology.
Display pseudodepth values - For the apparent resistivity pseudosections, you
can display the pseudodepth values on the vertical scale, or display the
electrode spacing and “n” factors (where applicable).
Colour/Black-White display - By default, the program will display the
pseudosections and model section in colour. This option allows you to display
the sections in black and white, possibly for making printouts on normal laser
printers. The program provides two choices for the black and white display.
The first choice is to use pure black and white colours together with a dithering
40
method to provide the different tones. Such screen images can be printed on
almost any printer. The second choice is to use a grey scale where different
shades of grey, ranging from pure white to pure black, is used. You will
probably need a laser printer to make reasonably good printouts of the grey
scale images.
Type of model display - In this option, you can display the resistivity values in
the model section in the form of contours (the default choice), or in the form of
rectangular blocks which constitute the inversion model. The contoured section
makes it easier to visualise geological structures, while finer features might be
more easily detected in the rectangular blocks section.
When the “Edit data” option is selected, the following “RMS error statistics”
submenu is displayed. This option provides another means of removing bad
data points from the data set. In fact, for cross-borehole or certain types of nonconventional
arrays data where the apparent resistivity values cannot be
conveniently displayed in the form of a pseudosection or profiles, this is the
primary method to remove the bad data points.
RMS error statistics - This suboption just displays the distribution of the
percentage difference between the logarithms of the observed and calculated
apparent resistivity values. It can only be used after carrying out a trial
inversion of the data set. To save some time, you could use the quasi-Newton
method to carry out the trial inversion (see section 10). On selecting this
suboption, the distribution of the RMS errors will be displayed in the form of a
bar chart. It is expected the “bad” data points will have relatively large
“errors”, for example above 100 percent. To remove the points with large
errors, just move the green cursor line to set the cut-off error limit to remove
the “bad” data points.
The “Print” option on the main menu bar enables you to save the screen image
as a BMP or PCX graphics file, or to make a direct printout with a printer by
using the Windows Paintbrush program. On selecting this option, the following
submenu will be displayed.
41
Saving the screen image into the form of a BMP or PCX graphics file allows
you to edit the picture with a bit-mapped graphics program, such as the
Windows PaintBrush program, before printing it (see section 15).
13. Progam settings
By default, the Windows Paintbrush is used as the program to manipulate and
print the BMP or PCX graphics file, and the NOTEPAD program is used as the
text editor. You can change these default choices by changing the appropriate
lines in the RES2DINV.INI file which should be located in the same
subdirectory as the RES2DINV.EXE program.. For example, a configuration
file with the following contents :-
[programs]
paint=c:\psp\psp.exe
editor=c:\gwd\gwd.exe
[files]
extension=*.lok
input=c:\res2dinv\
output=c:\res2dinv\
will use the Paint Shop Pro graphics program (located in the subdirectory
C:\PSP) and the GWD text editor (in the C:\GWD subdirectory). It will also
look for files with the extension LOK when you choose the option to read in a
data file. The default subdirectory with the data files is C:\RES2DINV, and the
same subdirectory is used for the output files.
14. Help
If you click the “Help” option, the Windows help file for the program will be
displayed. Clicking the “Info” option will display the copyright notice.
15. Printing the pseudosections
Besides displaying the pseudosections on the screen, you can make a printout
of the model sections. There are three methods of making a printout.
The simplest method is to use the RES2DINV.EXE to display the
pseudosection and model sections that you want to print by using the “Display
inversion results” option in the Main Menu. After the program has completed
drawing the pseudosection, click the Print option. This will display options to
save the screen as a BMP file, a PCX file or to call up the PaintBrush program
to print the file. If you need to print the screen image together with some text, it
might be more convenient to save the screen image as a BMP or PCX file. You
42
can later insert the picture directly into the document if the word processor,
such as Microsoft Word for Windows or Lotus Amipro or WordPerfect, allows
you to import graphics files.
Another method is to save the information into a XYZ file (see “File” section),
which is a general format supported by a number of dedicated graphics
contouring/plotting program. With such a program, you can redraw the model
sections and print them. This is particularly useful if you want to combine the
results from different survey lines within the same area to make a pseudo 3-D
plot of the structures. If you want to include topography in the model values
saved in the XYZ file, you will need to first run the “Include topography in
model section” option before saving the XYZ file. In this case, the XYZ file
will contain the model values without the topography, followed by a section
with the model after incorporating the topography.
The third method is to save the model information into SURFER format, and
use the SURFER for Windows program to draw and print the sections. Please
refer to Appendix N for details about this option.
16 Other useful programs
Two shareware programs that have been found to be useful are the Paint Shop
Pro image processing program, and the GWD text editor program. Both are
Windows based programs. The Paint Shop Pro program enables you to carry
out a number of sophisticated processing to enhance the BMP and PCX bitmapped
graphics files. For example, you can convert the files to a GIF format
which takes up much less space compared to the BMP and PCX files. The
GWD text editor is a professional level editor which enables you to carry out
many operations not possible with the NOTEPAD program. You can make use
of these programs, instead of the default Microsoft Paintbrush and NOTEPAD
program, by modifying the appropriate lines in the RES2DINV.INI file. The
file RES2DINV.IN2 gives such an example.
There are also a number of fine shareware paint programs and text editors
which you can download directly from Internet shareware sites. Besides Paint
Shop Pro, the paint programs I have tested are Lview Pro, VuePrint and
Graphics Workshop for Windows. All of these programs allow you to change
the BMP and PCX files to the GIF format which can dramatically reduce the
size of the graphics files. You can download these shareware programs from
most Internet shareware sites, such as www.softseek.com.
The SURFER 2-D drawing program from Golden Software Inc.
(www.golden.com) has a large variety of useful options for drawing sections.
43
The RES2DINV program has an option to export the data to the SURFER
format.
17 Pitfalls in 2-D inversion
If the program still does not give a satisfactory model (assuming that the input
data is in the correct format), it could be due to one of the following problems.
Garbage In - Garbage Out : One common problem is bad data points. Check
for unusually low or high apparent resistivity values. These anomalous values
can be caused by instrumentation errors during the field survey, poor electrode
contact in dry, sandy or stony ground, shorting of electrodes due to very wet
conditions or metal objects (such as fences, pipes etc.) or mistakes such as
attaching electrodes to the wrong connectors. You can easily pick out these
anomalous values using the "Edit data" option described earlier. Remember, a
good model requires good data.
Non-uniqueness : It is well known in the inversion of resistivity sounding data
that it is possible for the calculated apparent resistivity values for slightly
different models to be almost the same. The same thing holds for 2-D inversion
of resistivity data. However, while the finer features in the different models
obtained for a single data set can be different, the major features should be
similar. Also, bear in mind that the resolving power of the resistivity method
itself decreases exponentially with depth. This program allows you to modify
some of the parameters, such as the damping factor and the flatness filters, that
will influence the inversion process. By using different inversion parameters,
you will probably end up with slightly different models.
Unusual ground conditions : If the top ground layer is very dry, you might not
be able to pump enough current into the ground. In this case, the resistivity
technique itself might not be suitable and you should consider alternative
geophysical methods (such as EM). Another similar situation is a very
conductive top layer. In this case, the voltage difference measured by the
potential electrodes might be too small (perhaps even below the background
noise level). In this situation, try to get more current into the ground and check
the actual voltage difference measured. If you are using the dipole-dipole array,
try again with another array such as the Wenner-Schlumberger that gives larger
potential values. If this still does not work, try using another geophysical
method such as seismic refraction!
3-D geology : It should be noted that a basic limitation of this program is the
assumption of a 2-D subsurface model. For surveys carried out across the strike
of elongated geological structures, this assumption is reasonably accurate.
However, if there are significant variations in the subsurface resistivity in a
44
direction perpendicular to the survey line (i.e. the geology is 3-D), this could
cause distortions in the lower sections of the model obtained. Measurements
made with larger electrode spacings are not only affected by the deeper
sections of the subsurface, they are also affected by structures at a larger
horizontal distance from the survey line. This effect is most pronounced when
the survey line is placed near a steep contact with the line parallel to the
contact.
A 3-D resistivity inversion (Loke and Barker 1996b) program, RES3DINV, is
now available. To invert a 3-D data set with a reasonable number of data
points, a fast Pentium microcomputer with at least 64 megabytes of RAM is
recommended! With 64 megabytes of RAM, the 3-D inversion program can
handle surveys grids of up to 32 by 32 electrodes and a maximum of about
11,000 data points. A free 3-D resistivity and IP forward modelling program
RES3DMOD is also available. You can use this program to calculate the
apparent resistivity and IP values for a variety of 3-D structures for different
electrode arrays. This will give you an idea of the extent of the 3-D effects.
There is a discussion on other interesting pitfalls in the free “Tutorial notes” on
electrical imaging that is available on the www.geoelectrical.com web site.
45
18 Some field examples
Some examples of field data sets that were inverted with this program are
given below :Grundfor
Line 2 - This survey was carried out by the Department of Earth
Sciences, University of Aarhus, Denmark to map the lithology of the nearsurface
unconsolidated sediments and aquifers in the Grundfor area
(Christensen and Sorensen 1994). The low resistivity zones in the inversion
model (Figure 9) consist of more clayey Quaternary glacial deposits while the
high resistivity areas consist of more sandy deposits. The model obtained was
confirmed by a number of boreholes along this line. This is a moderately large
data set with 447 data points and 141 electrodes. On a 90 MHz Pentium it took
about 1033 seconds (17.2 minutes) to invert this data set, while on a 266 MHz
Pentium II it took about 158 seconds (2.6 minutes).
Odarslov Dyke - The dyke causes a prominent high apparent resistivity zone
near the middle of the pseudosection (Dahlin 1996) in the upper part of Figure
10. This is a particularly difficult data set to invert as the width of the high
resistivity dyke is smaller than the depth to the lower section of the dyke. Thus
the lower part of the dyke is not well resolved. If the damping factor used is too
small, this will result in oscillations in the resistivity values in the model
section. To invert this data set, the weight of the vertical flatness filter was set
at twice that of the horizontal filter since the dyke has a predominantly vertical
direction. The robust data inversion option (see Appendix K) was used to
reduce the effect of a few data points that might be more noisy on the inversion
results. Since there is a sharp and distinct contrast between the resistivity of
igneous dyke and the surrounding sedimentary rocks, the robust model
inversion option (Appendix K) was also used. In the model section, the dyke
shows up as a prominent high resistivity body with vertical sides. This data set
has 701 data points and 181 electrodes. The Grundfor and Odarslov dyke
surveys were carried out using the LUND Automatic Resistivity Imaging
System produced by ABEM Instrument AB.
46
Figure 9 : The observed apparent resistivity pseudosection for the Grundfor
Line 2 survey together with an inversion model.
Figure 10: The observed apparent resistivity pseudosection for the Odarslov
dyke survey together with an inversion model.
47
Figure 11. Mapping of holes in a clay layer, U.S.A. (a) Apparent resistivity
pseudosection for the survey to map holes in the lower clay layer. (b) Inversion
model and (c) sensitivity values of the model cells used by the inversion
program.
Holes in clay layer - U.S.A.
This survey was carried out for the purpose of mapping holes in a clay layer
that underlies 8 to 20 feet of clean sand (Cromwell pers. comm.). The results
from the electrical imaging survey were subsequently confirmed by boreholes.
The pseudosection from one line from this survey is shown in Figure 11a. The
data in the pseudosection was built up using data from horizontally overlapping
survey lines. One interesting feature of this survey is that it demonstrates the
misleading nature of the pseudosection, particularly for the dipole-dipole array.
In the inversion model, a high resistivity anomaly is detected below the 200 ft.
mark, which is probably a hole in the lower clay layer (Figure 11b). This
feature falls in an area in the pseudosection where there is an apparent gap in
the data. However, a plot of the sensitivity value of the cells used in the
inversion model shows that the model cells in the area of the high resistivity
48
body have higher sensitivity values (i.e. more reliable model resistivity values)
than adjacent areas at the same depth with more data points in the
pseudosection plot (Figure 11c). This phenomenon is due to the shape of the
contours in the sensitivity function of the dipole-dipole array, where the areas
with the highest sensitivity values are beneath the C1C2 and P1P2 dipoles, and
not at the plotting point below the center of the array. If the model cells are
placed only at the location of the data points, the high resistivity body will be
missing from the inversion model, and an important subsurface feature would
not be detected!
Bauchi groundwater survey - A groundwater survey using the Wenner
Alpha, Beta and Wenner arrays was carried in the Bauchi area of Nigeria
(Acworth 1987). In this region, groundwater is frequently found in the
weathered layer above the crystalline bedrock. The weathered layer is thicker
in areas with fractures in the bedrock, and thus such fractures are good targets
for groundwater. The Wenner Gamma array data set is shown in Figure 12 as
an example. To emphasize the boundary between the soil layer and the
bedrock, the robust inversion option was used (Appendix K). The thickness of
the lower resistivity weathered layer is generally about 10 to 20 metres. There
is a narrow vertical low resistivity zone with a width of less than 20 metres
below the 190 metres mark that is probably a fracture zone in the bedrock. A
borehole well that was placed at the 175 metres mark that lies at the edge of the
fracture zone had yields that were lower than expected. The placement of the
well was largely based on resistivity and EM profiling measurements using the
Geonics EM34-3, and before fast 2-D resistivity inversion microcomputer
software was widely available.
Figure 12. Bauchi Wenner Gamma array survey. (a). Apparent resistivity
pseudosection. (b) The inversion model with topography.
49
19 Trouble shooting
A brief compilation of possible problems and their possible causes and
solutions is given in this section.
Insufficient memory : If the program cannot find sufficient memory, one
possible reason is that it has been reserved for other programs. In this case, you
will need to remove the other active programs. In Windows 95/98/NT, the
active programs are usually shown on the Start menu bar near the bottom of the
screen. If you have less than 64 megabytes RAM, it is recommended that you
buy some RAM.
Program stops when it tries to calculate the partial derivatives :
The partial derivative values are stored in the files GRADWEN.10,
GRADTWO.10, GRADDIP.10, GRADWEN.25, GRADTWO.25 and
GRADDIP.25. First check that these files are in the same sub-directory of your
hard disc as the RES2DINV.EXE files. If they are there, one possible problem
could be due to bad sectors in the hard disc. You need to scan the hard disk to
check for possible unmarked bad sectors. Also, check that the hard disc has at
least 64 megabytes of free space that the program needs to store temporary
files for large data sets.
Program crashes when it tries to invert the data set : This could be due to
data arranged in the wrong format or other errors in the data set. When the
program reads the data file, it will check for some common errors such as zero
or negative apparent resistivity values. However, there might be some new
unexpected errors. One preliminary check you could make is to view the data
using the "Edit data" option described in section 8. If you still cannot find the
error, please send a copy of the data set to the company who sold you this
program (or the author of this program) by email.
Program cannot find dongle : If the program cannot find the hardware key, it
will run as a demonstration program. If you had securely attached the dongle
provided to the printer port and the program still cannot detect it, please refer
to section 3 for a method to check for the source of the problem. The two most
likely causes are a faulty printer port, or one which is not completely IBM PC
compatible (this problem is more common in older laptop computers). Another
possibility is that the parallel port has been reconfigured by a program as
another port instead of as a printer port. If you are using Windows NT, it is
necessary to install a system driver for the dongle (please refer to sections 2
and 3). The system driver file provided (SYSDRVR.EXE for the Rainbow
Technologies dongle and INSTALL.EXE for the Keylok dongle) also contains
the drivers for Windows 95/98. Install this driver if the program is unable to
detect the dongle with 95/98.
50
If you are using the USB dongle, the Keylok system driver must be installed.
During the installation of the driver, the program will copy the necessary
system (SYS) files needed by Windows to detect the USB dongle. Please refer
to the installation note provided with the USB dongle for further details.
Acknowledgements
Dr. Torleif Dahlin of Lund University in Sweden provided the interesting and
challenging Odarslov Dyke, Gladkvarn and Knivsas data sets. The Grundfor
data set was kindly provided by Dr. Niels B. Christensen of the University of
Aarhus in Denmark and Dr. Torleif Dahlin. The Rathcroghan data set was
kindly provided by Dr. Kevin Barton and Dr. Colin Brown from data collected
by the Applied Geophysics Unit of University College Galway, Ireland. Dr.
Andrew Binley of Lancaster University kindly provided the cross-borehole
field data set. Mr. Ernst Neiderleithinger of Buro Fur Geophysik Lorenz
(Germany) supplied the Landfill data set that provided the initial motivation to
write this program to handle large 2-D data sets. I am also grateful to Prof.
Douglas Oldenburg of the University of British Columbia in Canada for
pointing out the some of the possible advantages of using equation (2). The
Bauchi data was provided by Dr. Ian Acworth of School of Civil and
Environmental Engineering, The Un. of New South Wales, Australia. Many
thanks to Richard Cromwell and Rory Retzlaff of Golder Assoc. (Seattle) for
the survey example to map holes in a clay layer. Bill Seaton of ATS, Virginia
kindly provided the BLUERIDGE.DAT data set. Dr. Fabrizio Cara of the
Instituto Nazionale di Geofisica e Vulcanologia, Italy generously supplied the
ITALY_CAVE.DAT data set. I would also like to thank Ron Kaufman of
Technos Inc. for his permission to use the Lake Lelia underwater field survey
example. I would like to acknowledge Michel Ritz of IRD, France for kindly
providing the BOREHOLE_TOPO.DAT example data set. Finally, a special
thanks to Rob Barker of The University of Birmingham (U.K.) for the
Birmingham time-lapse, Stud Farm bedrock survey and the Clifton (with
Julian Scott) data sets, and his advice through the years.
51
References
Acworth, R. I., 1987. The development of crystalline basement aquifers in a
tropical environment: Quarterly Journal Engineering
Geology, 20, 265-272.
Barker, R. and Moore, J., 1998. The application of time-lapse electrical
tomography in groundwater studies. The Leading Edge, 17, 1454-
1458.
Christensen N.B. and Sorensen K.I., 1994. Integrated use of electromagnetic
methods for hydrogeological investigations. Proceedings of the
Symposium on the Application of Geophysics to Engineering and
Environmental Problems, March 1994, Boston, Massachusetts, 163-
176.
Claerbout, J.F. and Muir, F., 1973. Robust modeling with erratic data.
Geophysics, 38, 826-844.
Dahlin, T., 1996. 2D resistivity surveying for environmental and engineering
applications. First Break, 14, 275-284.
Dahlin, T. and Zhou, B., 2004. A numerical comparison of 2D resistivity
imaging using ten electrode arrays. Geophysical Prospecting, 52, 379-
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Dahlin, T. and Zhou, B., 2005. Multiple gradient array measurements for
multi-channel 2D resistivity imaging. Near Surface Geophysics, in
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deGroot-Hedlin, C. and Constable, S., 1990, Occam's inversion to generate
smooth, two-dimensional models form magnetotelluric data.
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Edwards, L.S., 1977, A modified pseudosection for resistivity and inducedpolarization.
Geophysics, 42, 1020-1036.
Fox, R.C., Hohmann, G.W., Killpack,T.J. and Rijo, L., 1980, Topographic
effects in resistivity and induced polarization surveys. Geophysics, 45,
75-93.
Griffiths D.H. and Barker R.D. 1993, Two-dimensional resistivity imaging and
modelling in areas of complex geology. Journal of Applied
Geophysics, 29, 211-226.
Griffiths, D.H., Turnbull, J. and Olayinka, A.I., 1990, Two-dimensional
resistivity mapping with a computer-controlled array. First Break, 8,
121-129.
Hallof, P.G., 1990, Reconnaissance and detailed geophysical results, Granite
Mountain Area Pershing County, Nevada. in Fink, J.B., McAlister,
E.O., Sternberg, B.K., Wieduwilt, W.G. and Ward, S.H. (Eds), 1990,
Induced polarization : Applications and case histories : Investigations
in Geophysics No. 4, Soc. Expl. Geophys.
Keller G.V. and Frischknecht F.C.,1966. Electrical methods in geophysical
prospecting. Pergamon Press Inc., Oxford.
52
Loke, M.H., 1999. Time-lapse resistivity imaging inversion. 5th Meeting of the
Environmental and Engineering Geophysical Society European
Section Proceedings. Em1.
Loke, M.H., 2000. Topographic modelling in resistivity imaging inversion.
62nd EAGE Conference & Technical Exhibition Extended Abstracts,
D-2.
Loke, M.H., 2001. Tutorial : 2-D and 3-D electrical imaging surveys. Geotomo
Software, Malaysia.
Loke, M.H. and Barker, R.D., 1996a, Rapid least-squares inversion of apparent
resistivity pseudosections by a quasi-Newton method. Geophysical
Prospecting, 44, 131-152 .
Loke, M.H. and Barker, R.D., 1996b, Practical techniques for 3D resistivity
surveys and data inversion. Geophysical Prospecting, 44, 499-523.
Loke, M.H. and Dahlin, T., 2002. A comparison of the Gauss-Newton and
quasi-Newton methods in resistivity imaging inversion. Journal of
Applied Geophysics, 49, 149-162.
Loke, M.H., Acworth, I. and Dahlin, T., 2003. A comparison of smooth and
blocky inversion methods in 2D electrical imaging surveys.
Exploration Geophysics, 34, 182-187.
Nelson, G.D. and Van Voorhis, 1973, Letter to the editor regarding the paper
“Complex resistivity spectra of porphyry copper mineralization”.
Geophysics, 38, 984.
Niederleithinger, E., 1994, Use of high resolution geomagnetics, 2D-DCgeoelectrics
and induced polarisation in environmental investigations.
Paper presented at SAGEEP '94, Boston, USA.
Olivar, A., de Lime, L. and Sharma, M.M., 1990. A grain conductivity
approach to shaly sandstones. Geophysics, 55, 1347-1356.
Robain, H., Albouy, Y., Dabas, M., Descloitres, M., Camerlynck, C.,
Menchler, P. and Tabbagh, A., 1997, The location of infinite
electrodes in pole-pole electrical surveys: consequences for 2D
imaging. Journal of Applied Geophysics, 41, 313-333.
Sasaki, Y., 1992, Resolution of resistivity tomography inferred from numerical
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Scott, J.B.T., Barker, R.D. Peacock, S., 2000. Combined seismic refraction and
electrical imaging. Procs. 6th Meeting of the European Association for
Environmental and Engineering Geophysics, 3-7 Sept. 1997, Bochum,
Germany, EL05.
Seaton, W.J. and Burbey, T.J., 2000. Aquifer characterization in the Blue
Ridge physiographic province using resistivity profiling and borehole
geophysics : Geologic analysis. Journal of Environmental &
Engineering Geophysics, 5, no. 3, 45-58.
Silvester P.P. and Ferrari R.L., 1990, Finite elements for electrical engineers
(2nd. ed.) . Cambridge University Press.
53
Slater, L., Binley, A.M., Zaidman, M.D. and West, L.J., 1997, Investigation of
vadose zone flow mechanisms in unsaturated chalk using crossborehole
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Ward, S.H. (Eds), 1990, Induced polarization : Applications and case
histories : Investigations in Geophysics No. 4, Soc. Expl. Geophys.
54
Appendix A : Dipole-dipole and pole-dipole surveys
The format for the data points for a dipole-dipole survey is slightly different
from that used for the Wenner and pole-pole surveys. The arrangement of the
electrodes for the dipole-dipole survey is shown in the following figure.
Figure 13 : (a) Arrangement of the electrodes for the dipole-dipole array. (b)
Example of dipole-dipole array with non-integer “n” value. Arrangement of the
electrodes for (c) the “forward” and (d) “reverse” pole-dipole arrays.
The distance, a, between the two current electrodes, C1 and C2, is the same as
that between the potential electrodes. The distance between the current
electrode C1 and the potential electrode P1 (the dipole separation factor) is
usually an integer multiple, n, of the distance between the current or potential
electrode pair. Initially, the dipole separation factor (n) is set to 1. Then it is
increased to 2, 3 and so on until a maximum value of between 4 and 6. When
the dipole separation factor is increased, the potential measured between P1
and P2 decreases rapidly with increasing n. For this reason, it is not advisable
to use a value of n greater than 6. Using larger values of n could result in rather
noisy data. In some surveys, the distance (a) between the current and potential
55
electrode pairs is doubled or tripled (Edwards 1977) to increase the signal
strength. Thus both the dipole separation factor (n) and the spacing between the
current electrode pair (a) has to be recorded. Using the BLOCKDIP.DAT file
as an example, the data file format for the dipole-dipole array is as follows :BLOCKDIP.DAT
file Comments
TWO RECTANGULAR BLOCKS | Title
1.0 | Unit electrode spacing
3 | Array number (dipole-dipole=3)
356 | Number of data points
0 | x-location given in terms of first electrode
| use 1 if mid-point location is given
0 | 0 for no IP, use 1 if IP present
0.0 1.0 1 30.1 | For each data point; enter x-location, "a"
1.0 1.0 1 30.1 | spacing, "n" factor value, apparent
2.0 1.0 1 30.1 | resistivity
. |
. |
39.0 1.0 8 30.3 | Last 2 data points
40.0 1.0 8 30.4 |
0,0,0,0,0 | Put a few zero's at the end
The first value (in each line with the data point values) gives the x-location of
the data point. The second value gives the separation between the potential
electrode pair P1 and P2. This value is usually an integer multiple (of between
1 to 5 times) the unit electrode spacing. In some 2-D resistivity surveys, the
separation between the current electrode pair is fixed. In this case, this factor
will have a constant value (as in the file BLOCKDIP.DAT). The third value is
the dipole separation factor (n) with a maximum value of 8. The fourth value is
the measured apparent resistivity value.
The data filed BLUERIGDE.DAT is an example field data set where different
“a” and “n” combinations (Seaton and Burbey 2000) in order to increase the
depth of penetration without greatly reducing the signal strength.
The pole-dipole array has an array number of 6. The format of the data points
is similar to that for the dipole-dipole array. The file BLOCKPDI.DAT gives
an example of a pole-dipole data set. Compared to the dipole-dipole array, the
signal strength measured with the pole-dipole array decreases less rapidly when
the dipole separation factor (n) is increased. Unlike the other common arrays,
the pole-dipole is a non-symmetrical array which gives rise to somewhat more
complicated anomalies in the pseudosection. The centre point of this array is
defined as the mid-point between the C1 and P2 electrodes. This program
56
assumes that the x-location of C1 electrode is less than that of the P1 and P2
potential electrode pair (on the left side in Figure 13c). If the location of the
first electrode is given in the input data file, then the location of the C1
electrode is used.
The pole-dipole array is an asymmetrical array, and over symmetrical
structures the apparent resistivity anomalies in the pseudosection are also
asymmetrical. In some situations, the asymmetry in the measured apparent
resistivity values could influence the model obtained after inversion. One
method to eliminate the effect of this asymmetry is to repeat the measurements
with the electrodes arranged in the reverse manner (Figure 13d). By combining
the measurements with the “forward” and “reverse” pole-dipole arrays (Figures
13c and 13d), any bias in the model due to the asymmetrical nature of this
array would be removed. The file PDIPREV.DAT is an example field data set
that combines measurements made with the “forward” and “reverse” poledipole
arrays. For the reverse pole-dipole measurement, the location of the first
electrode is given by the position of the P2 electrode. A negative value for the
n factor is used to indicate that the reverse pole-dipole arrangement is used.
In this program, the maximum allowed dipole separation factor n is 10 while
the largest spacing between the P1-P2 electrode pair is 5 times the unit
electrode spacing for the dipole-dipole array. For the pole-dipole array, n can
have a maximum value of 10 while the P1-P2 spacing can be up to 5 times the
unit electrode spacing. In most cases, the n dipole separation factor is an
integer value. However it is possible for the n factor to have non-integer values
although all the electrodes still have a constant inter-electrode spacing. This
can occur when the spacing a between the C1-C2 pair is twice (or more) the
unit electrode spacing. For the example shown in Figure 13b, the unit electrode
spacing for the survey line is 1 metre. The a spacing has a value of 2 metres,
while the distance between the C1 and P1 electrodes is 3 metres. In this case,
the n factor has a value of 1.5. The data file, DIPOLEN5.DAT, gives an
example of a dipole-dipole data set with non-integer n values. For cases where
the fractional part of the n factor has is an infinite series in decimal notation,
the n value should be given to at least four decimal places. For example, if the
n value is one and one-third, it should be given as 1.3333.
57
Appendix B : The Wenner-Schlumberger array
In areas with limited open space for a long survey line, the conventional
Wenner array has a disadvantage in that there is a large reduction in horizontal
coverage when the electrode spacing is increased in order to achieve a deeper
depth of investigation. For example, in order to increase the depth of
investigation by two times, the electrode spacing a has to be increased to 2a
(Figure 14). In this case, the total length of the array is increased from 3a to 6a.
At the same time, the width of the pseudosection decreases by 3a with each
level of measurement (Figure 15). In comparison, the width of the
pseudosection decreases by 2a for the Wenner-Schlumberger array.
Figure 14 : The steps used by the (a) Wenner and the (b) WennerSchlumberger
arrays to increase the depth of investigation.
The apparent resistivity value for the Wenner-Schlumberger array is given by
ρ = pi n (n+1) a R
where R is the measured resistance, a is the spacing between the P1 and P2
electrodes and n is the ratio of the distances between the C1-P1 and the P1-P2
electrodes. This array effectively becomes the Schlumberger array when the n
factor is greater than 2. Thus it is actually a combination of the Wenner and
Schlumberger arrays adapted for use for an arrangement with a line of
electrodes with a constant spacing (as normally used in 2-D electrical imaging).
Besides better horizontal coverage, the maximum depth of penetration of this
array is about 15% larger than the Wenner array. Note that the normal Wenner
array is actually a special case of the Wenner-Schlumberger array where the n
factor is equals to 1.
In practice, since the potential between the P1 and P2 electrodes decreases
when the electrode spacing factor n is increased, the maximum value of n used
in actual field surveys is about 8. To increase the depth of investigation, the
spacing between the P1-P2 electrodes is increased to 2a and the measurements
58
are repeated for n equals to 1, 2, 3, 4, 5 and 6. Next, the P1-P2 spacing is
increased to 3a, and the same sequence of measurements is made. The file
PIPESCHL.DAT gives an example of a field data set using this array.
Figure 15 : Arrangement of data points in the pseudosections for the (a)
Wenner and the (b) Wenner-Schlumberger arrays.
While the n factor usually has integer values, the program can also accept noninteger
values for this factor. The data file, WENSCHN5.DAT, is an example
with non-integer values for the n factor.
One advantage of the normal Wenner array is that it has the highest signal-tonoise
ratio among the conventional arrays. To be on the safe side, you should
include all the normal Wenner array measurements when carrying out a survey
with the Wenner-Schlumberger array. The resulting pseudosection might look
a little messy with overlapping data measurement levels, but RES2DINV can
handle such a data set. In very noisy areas, the Wenner array measurements
should be the most reliable.
59
Appendix C : Fixing Resistivities
In some cases, the true resistivity of a section of the subsurface might be
known, for example from borehole resistivity measurements. This program
allows you to fix the resistivity of up to 256 sections of the subsurface. The
shape of the section to be fixed must be rectangular or triangular. The data to
fix the model resistivity values are entered into the input data file after section
with the topography information. As an example, part of the example data file
MODELFIX.DAT is listed below.
0 | Topography flag
2 | Number if regions to fix, put 0 if none
R | Type of first region, R for rectangular
24,0.7 | X and Z coordinates of top-left corner of rectangle
28,2.3 | X and Z coordinates of bottom-right corner of rectangle
2.0 | Resistivity value of rectangular region
2.0 | Damping factor weight
T | Type of second region, T for triangular
30,0.0 | X and Z coordinates of first corner of triangle
30,3.0 | X and Z coordinates of second corner of triangle
45,3.0 | Coordinates of third corner of triangle
10.0 | Resistivity value of triangular region
2.0 | Damping factor weight
The first item after the topography data section is the number of regions where
the resistivity is to be specified. In the example above, 2 regions are specified.
If a value of 0 is given (default value), then there are no regions where the
resistivity is specified by the user. Next, the shape of the region is given, R for
rectangular or T for triangular. If a rectangular region is specified, then the X
and Z coordinates of the top-left and bottom-right corners of the rectangle are
given, as shown in Figure 16.
If a triangular region is chosen, the X and Z coordinates of the 3 vertices of the
triangle must be given in an anti-clockwise order. After the coordinates of the
region to be fixed are given, the next data item is the resistivity of the region.
After that, the damping factor weight for the resistivity of the region is needed.
This parameter allows you control the degree in which the inversion subroutine
can change the resistivity of the region. There is usually some degree of
uncertainty in resistivity of the region. Borehole measurements can only give
the resistivity of a very limited zone near the borehole. Thus, it is advisable that
the program should be allowed (within limits) to change the resistivity of the
region. If a damping factor weight of 1.0 is used, the resistivity of the region is
allowed to change to the same extent as other regions of the subsurface model
60
The larger the damping factor weight is used, the smaller is the change that is
allowed in the resistivity of the "fixed" region. Normally, a value of about 1.5
to 2.5 is used. If a relatively large value is used, for example 10.0, the change
in the resistivity of the region would be very small during the inversion
process. Such a large value should only be used if the resistivity and shape of
the region is accurately known.
Figure 16 : Fixing the resistivity of rectangular and triangular regions of the
inversion model.
61
Appendix D : The Equatorial Dipole-Dipole array
The arrangement of the electrodes for this array is shown in the following
figure.
Figure 17 : The arrangement of the electrodes for the equatorial dipole-dipole
array.
The apparent resistivity value for this array is given by
ρ = 2 pi a s R / ( s - a )
where
s = ( a2
+ b2
)0.5
and R is the measured resistance. This array differs from the other arrays where
the electrodes are arranged in a single line. Each reading is characterised by
two spacings. The first spacing, a, is the distance between the current
electrodes pair C1-C1 and the potential pair P1-P2. The second spacing, b, is
the spacing between the C1 and C2 electrodes. This program has a restriction
that the spacing between the P1-P2 pair must be the same as that between the
C1-C2 pair. An example of a data file for this array is the data file
FAULTEQU.DAT. The initial part of the file is shown below with comments :FAULTEQU.DAT
file Comments
Equatorial dipole-dipole array | Title
1.00 | The unit electrode spacing
8 | Array number 8 for this array
1.50 | The spacing b between the C1-C2 pair
285 | The number of data points
1 | Flag for mid-point of array
0 | No IP data
0.50 1.00 2.74 | x-location, spacing a, app. resis.
1.50 1.00 2.74 | Repeat for all the other points
Note that for this array, it is necessary to include the spacing b between the C1C2
electrodes pair after the array number.
62
Appendix E : Underwater surveys
The possible situations for underwater surveys are shown in the following
figure.
Figure 18 : Three possible situations for underwater surveys, and a survey with
floating electrodes.
In the first situation, there is a water layer with a constant thickness over a flat
sediment surface (i.e. there is no topography). An example of such a data set is
given in the file WATER.DAT. The bottom section of this file with comments
is as follows :WATER.DAT
file Comments
39.00 1.00 16 51.36 | Last 3 data points
40.00 1.00 16 52.09 |
41.00 1.00 16 54.29 |
0 | 0 for no topography
0 | 0 for no fixed regions
1 | 1 to indicate water layer present
50.00, -100.00, 200.00 | Resistivity of water layer, left and right
| limits of water layer
4.00 | Thickness of water layer
63
1 | Surface geometric factor used to calculate
| apparent resistivities
0 |
While the left and right limits of the water layer are included in the data format,
this is at present not used by the program. It is included for future use for
surveys with some of the electrodes above the water layer, for example a
survey across a river. Note that a flag is included to indicate that the normal
geometric factor (as used for a surface survey) is used to calculate the apparent
resistivity values. If a value of 0 is used for this flag, the exact geometric factor
(which includes the thickness of the water layer) must be used to calculate the
apparent resistivity values. For actual field surveys, it is expected that the
normal surface geometric factor will be used.
If the river or sea bottom has topography, the topography information is
entered immediately after the data set as in a normal land surface survey. The
bottom section of the files is as follows :Underwater
survey file
wth topography Comments
39.00 1.00 16 51.36 | Last 3 data points
40.00 1.00 16 52.09 |
41.00 1.00 16 54.29 |
2 | 2 for topography with surface x|
distances
7 | Number of topography data points
0.0, 3.0 | The x-location and elevation of each
10.0, 4.0 | topography data point
15.0, 4.5 |
25.0, 5.0 |
30.0, 5.1 |
35.0, 4.5 |
45.0, 4.6 |
0 | 0 for no fixed regions
1 | 1 to indicate water layer present
50.00, -100.00, 200.00 | Resistivity of water layer, left and right
| limits of water layer
4.00 | Elevation of water surface with respect to
| local datum
1 | 1 to indicate normal surface geometric factor
| used
The program will automatically calculate the thickness of the water layer from
the elevation of the sea or river bottom and the elevation of the water surface.
Note that is format also allows for the where some of the electrodes are above
the water surface (i.e. on normal dry land) and some of the electrodes
64
underwater. In the example above, the electrodes between 0 and 10 meters are
above the water surface. A common situation where this occurs is a survey that
crosses a river. In this case, the program will assume that an electrode with an
elevation that is less than the elevation of the water surface is underwater. For
the case when some of the electrodes are above the water surface, the surface
geometric factor must be used for calculating the apparent resistivity values for
all the data points.
The topographic modelling is automatically carried out by the program when
you invert the data set. The program will automatically adjust the surface of the
finite-element grid used to model the subsurface so that it matches the surface
of the sediment below the water layer.
There is a fourth possible situation with a confined body of water that is so far
not supported. One possible situation is a river or lake with dykes. In this case,
some points with elevations below the water surface level are not underwater.
Support will probably be added in the future when such situations are more
frequently encountered.
Many underwater surveys are carried out by dragging a cable or streamer
behind a boat. In this case, the electrode locations are unlikely to be equally
spaced. This situation is best handled by entering the data in the general array
format that is described in Appendix L. The data file LAKELELIA.DAT is an
interesting field survey by Technos Inc. with data in the general array format
(Appendix L) and underwater topography. Parts of the file are highlighted
below to illustrate the data format used.
LAKELELIA.DAT file Comments
LAKE LELIA UNDERWATER SURVEY | Title
1.50 | Unit electrode spacing
11 | General array format
1 | Note Wenner sub-array type
Type of measurement (0=app. resistivity.1=resistance) | Header
0 | Data is in apparent resistivity
291 | Number of data points
2 | Surface x-distances
0 | No IP
4 82.37,0.0 91.37,0.0 85.37,0.0 88.37,0.0 43.137 | First four data points
4 89.55,0.0 98.55,0.0 92.55,0.0 95.55,0.0 36.599 | Note the electrode
4 96.74,0.0 105.74,0.0 99.74,0.0 102.74,0.0 36.458 | elevation is 0.0 here
4 103.92,0.0 112.92,0.0 106.92,0.0 109.92,0.0 37.019 | because it is given later
. | Other data points
. | Other data points
4 1050.25,0.0 1077.25,0.0 1059.25,0.0 1068.25,0.0 93.072 | Last two data
4 1056.35,0.0 1083.35,0.0 1065.35,0.0 1074.35,0.0 95.383 | points
Topography in separate list | Special header to indicate elevations
65
| are given separately from the main
| data section
2 | 2 to indicate surface x-distances
38 | Number of topography data points
26.12 999.09 | First two topography
30.48 999.09 | data points
. | Other topography
. | data points
1127.76 999.09 | Last topography data point
1 | First electrode coincides with first
| topography data point
0 | Put zero here in place of usual
| surface topography
0 | No fixed regions
1 | 1 to indicate water layer present
58.00,-2000.00,2000.00 | Resistivity of water layer, left and
| right limits of water layer
1000 | Elevation of water surface
1 | Surface geometric factor used to
| calculate apparent resistivities
0,0,0 | End with a few zeros
Figure 19 shows the apparent resistivity pseudosection and inversion model for
this data set. Mobile surveying systems typically produce survey lines that are
very long compared to the depth of investigation of the cable array system
used.
Surveys with floating electrodes
Another possible arrangement for a survey using a boat dragging a cable is
where the electrodes are floating on the water surface. The main disadvantage
of this arrangement is that a large part of the current flows within the water
layer, compared to the portion of the current that flows into the material below
the water bottom. The main advantage is that it is easier and faster to carry out
and avoids problems such as the cable being snagged by obstacles on the river
bottom. It could be an efficient method in shallow areas where the screening
effect due to the water layer is not too large. One possible way of interpreting
such a data set is to treat it as a standard surface data set where the water layer
is included as part of the model. This probably gives acceptable results where
there is a strong contrast between the water layer and the topmost layer of the
sub-bottom materials, and where the data has a low noise level. However if the
depth of the water bottom was measured during the course of the survey
(usually with an echo sounder), and the water resistivity was also measured, the
effect of the water layer could be calculated and included in the model. The file
WATER_FLOAT.DAT is a synthetic data set which gives an example of the
data format. The initial part of the file is identical with that used for normal
66
surface surveys or surveys with electrodes on the water bottom. The difference
is in the final section of the file where the water layer parameters are given.
WATER_FLOAT.DAT file Comments
Survey on water layer and floating electrodes | Title
2.0 | Unit electrode spacing
11 | General array format
0 | No sub-array type
Type of measurement (0=app.resistivity, 1=resistance) | Header
0 | Data is in apparent resistivity
942 | Number of data points
1 | True horizontal distances
0 | No IP
4 2.0,0.0 0.0,0.0 4.0,0.0 6.0,0.0 1.86738 | First three data points
4 4.0,0.0 2.0,0.0 6.0,0.0 8.0,0.0 1.86843 | Note water surface is assumed to be
4 6.0,0.0 4.0,0.0 8.0,0.0 10.0,0.0 1.87070 | at 0.0 metres
. | Other data points
. |
4 46.0,0.0 34.0,0.0 94.0,0.0 106.0,0.0 14.91776 | Last two data points
4 48.0,0.0 36.0,0.0 96.0,0.0 108.0,0.0 15.51526|
0 | No topography information
0 | No fixed regions
3 | 3 to indicate floating electrodes survey
Water resistivity | Header
1.5 | The water resistivity in ohm.m
Water elevation | Header
0.0 | Elevation of water surface
18 | Number of water bottom depth points
0 -1.5 | x-location and elevation of water bottom below water surface
10 -1.5 | Second depth point
20 -1.5 |
26 -1.5 |
28 -2.0 |
30 -2.5 |
. | Other bottom elevation data lines
. |
100 –1.5 |
108 –1.5 | Last depth point
1 | Indicates first electrode is at first depth point
0,0,0 | A few zeros to end the data file
While the above example gives the data in the general array format (Appendix
L), the program can also accept data in the index based format. For example,
the above data set is for the dipole-dipole array. An index based format (see
Appendix A) will give the location of the data point, the ‘a’ dipole length and
the ‘n’ dipole separation factor.
67
68
Appendix F : IP data inversion
The data collected from IP (Induced Polarization) surveys consists of two sets,
the normal apparent resistivity measurements and an apparent IP data set. So,
the number of data points is twice the number for a normal resistivity survey.
One possible method to invert such a joint data set is to treat the two data sets
as completely separate data sets. The inversion of the resistivity data is
completed before starting on the inversion of the IP data set. In this case, the
resistivity model obtained at the last iteration of the inversion of the resistivity
data set (which usually has the lowest RMS error) is used in the inversion of
the IP data set. This is probably the most efficient method if the resistivity
model is a good representation of the true subsurface resistivity. However, it
has been found that even in the inversion of computer generated data sets, the
model obtained can contain distortions particularly if a large number (more
than 5) of iterations is used in the inversion of the resistivity data set. This is
because the inversion is based on a finite number of data points. The distortion
becomes worse when the data contains noise. Many users tend to use a large
number of iterations together with small damping factors in an effort to reduce
the RMS error to the lowest possible value. If a resistivity model with
distortions is used in the inversion of the IP data, then the distortions will affect
the IP models for all iterations of the IP inversion.
The program provides two methods to invert the IP data. In the first method the
inversion of the resistivity and IP data are carried out concurrently.
Immediately after an iteration of the inversion of the resistivity data, an
iteration of the IP inversion is carried out. In the second method, the inversion
of the IP data is carried out only after the completion of the resistivity
inversion. In this case, only the resistivity of the model obtained at the last
resistivity iteration is saved.
The files IPMODEL.DAT, IPMAGUSI.DAT, IPSHAN.DAT and
IPKENN.DAT are example data files with both resistivity and IP data. This
program supports four different types of IP data; (i) time domain chargeability
measurements, (ii) frequency domain percent frequency effect measurements,
(iii) phase angle measurements and (iv) metal factor IP values. The file
IPMODEL.DAT has the IP data as chargeability values. The first part of the
files with comments are as follows :IPMODEL.DAT
file Comments
Fault and block model | Title
1.00 | Unit electrode spacing
3 | Array type
432 | Number of data points
1 | Location of centre of array given
1 | 1 to indicate IP present
69
Chargeability | Type of IP data
msec | IP unit
0.1,1.0 | Delay, integration time
1.50 1.00 1 12.04 7.2038 | x-loc., a, n, app. res., app. IP
2.50 1.00 1 12.03 7.1983 | 2nd data point
A value of “1”, instead of “0”, is entered into the sixth line to indicate that IP
data is present. This is followed by 3 data lines that gives information about the
nature of the IP data. The seventh line with the word Chargeability shows that
the IP data is given in terms of chargeability. Many IP instruments measured
the chargeability be integrating the area under the IP decay curve. In this case,
the unit is in msec (millisecond). The chargeability value obtained by this
method is normally calibrated to the Newmont M(331) standard (Summer 1976)
so that the chargeability value in msec has the same numerical value as the
chargeability given in mV/V. The chargeability in mV/V is defined as the ratio
of the secondary voltage immediately after the current is cut off to the primary
DC voltage.
IP surveys have traditionally been used in the mineral exploration industry,
particularly for metal sulfides, where generators producing high currents of the
order of 10 Amperes are used. The apparent IP values from such surveys are
usually less than 100 msec. (or mV/V). One recent development is the addition
of IP capability to battery based systems used in engineering and
environmental surveys where currents of 1 Ampere or less are normally used.
An accompanying phenomenon is the observation of IP values of over 1000
msec. (or less than -1000 msec.) in some data sets. Such values are almost
certainly caused by noise due to a very weak IP signal. To check whether such
high IP values are real, first check the apparent resistivity pseudosection. If it
shows unusually high and low values that vary in an erratic manner, the data is
noisy. If the apparent resistivity values are noisy, then the apparent IP values
are almost certainly unreliable. Next check the apparent IP pseudosection. If
the apparent IP values show an erratic pattern (frequently with anomalous
values lined up diagonally with an apex at a doubtful electrode), then the IP
values are too noisy to be interpretable.
IP values that are given in other units are converted into chargeability values
internally by the program during the inversion process. The relevant
conversion equations may be found in the papers by Van Voorhis et al. (1973)
and Nelson and Van Voorhis (1973).
For frequency domain measurements, the IP value is usually given in Percent
Frequency Effect (PFE). This is given as
PFE = 100 (ρDC - ρAC) / ρAC
where ρDC and ρAC are the apparent resistivity values measured at low and high
frequencies. The file IPSHAN.DAT is an example of a frequency domain IP
70
data set. In the seventh line, the type of IP data is given as “Percent Frequency
Effect”. The ninth data line contains the values of the low and high frequencies
used in the measurement. This data set is from a field survey in Burma where
the measurements were made with 20 metres and 40 metres dipoles (Edwards
1977). Like many field data sets, it has a very complex distribution of the data
points in the pseudosection. This is a relatively noisy data set. It is advisable to
use the option to “Include smoothing of model resistivity values” described in
section 9 for the inversion of this data set to avoid extremely large and small
model resistivity values. The survey target is a galena deposit in metasediments.
The geology is rather complex with massive galena deposits
together with quartz veins, silicified marbles and clay zones. There is a very
wide range of resistivity values.
IP values are also given as phase angles. In this case the unit normally used is
milli-radians (mrad). An example of an IP data set with phase angles is given
in the file IPKENN.DAT with values from the paper by Hallof (1990). In the
seventh line, the type of IP data type is given as “Phase Angle”. The second
parameter in the ninth data line contains the values of the frequency at which
the phase angles were measured. The first parameter is not used and is
normally set to 0. Many modern IP survey instruments can measure the phase
angle for several frequencies. In this case, the inversion of is repeated for the
phase angle data at each frequency. This will give an idea of the change of the
subsurface IP phase angle with frequency for complex resistivity studies.
IP data is sometimes given as a metal factor (MF) value. The MF value can be
calculated from either time domain or frequency domain measurements. In the
time domain, the metal factor is value is given by
MF = 1000 M / ρDC
where the chargeability M is given in terms of millisecond (Witherly and
Vyselaar, 1990). In the frequency domain, it is given as
MF = 100000 (ρDC - ρAC) / ρAC
2
The file IPMAGUSI.DAT is from a survey over the Magusi River ore body
(Edwards 1977) where the survey was conducted with 30.5 metres (100 feet),
61.0 metres (200 feet) and 91.4 metres (300 feet) dipoles. Again the resulting
pseudosection has a very complex distribution of the data points. The measured
apparent resistivity and IP pseudosections, together with the model sections
obtained are shown in Figure 20. The ore body shows up as a distinct low
resistivity body with high IP values near the middle of the survey line in the
model sections. In the inversion of this data set, the robust inversion method
was used (see Appendix K) to sharpen the boundary between ore body and the
surrounding rocks.
71
The inversion program tries to minimise the difference between the observed
and calculated equivalent apparent chargeability values. IP values in percent
frequency effect and phase angles are directly proportional to the equivalent
chargeability values. However, the metal factor value also involves a resistivity
value. The model that gives a minimum RMS error for the chargeability values
sometimes does not give a minimum RMS error for the metal factor values.
However, the actual effect on the inversion model is usually very small.
Figure 20. Magusi River ore body (a) Apparent resistivity pseudosection, (b)
resistivity model section, (c) apparent metal factor pseudosection and (d) metal
factor model section.
72
Appendix G : New batch mode options
This option is intended for users who might wish to invert a large number of
data sets at one go by remote control. It allows you to launch the batch mode
from another Windows program, or from a command line. In the batch mode
option a script file, for example RESIS.BTH, is used to inform the program of
the data files which need to be processed and the various inversion options
used. In Windows, you can access the command line option by clicking the
“Start” button, followed by the “Run” option. If the RES2DINV program is
located in the C:\R2DINV subdirectory, and the batch script file RESIS.BTH is
located in the D:\DATA subdirectory, the following command is typed into the
‘Run” dialog box.
C:\R2DINV\RES2DINV D:\DATA\RESIS.BTH
This command will launch the RES2DINV program that will automatically
process the list of data files in the RESIS.BTH. In the RESIS.BTH file, it is
recommended that you type in the full drive and path for all the files. After the
program has processed all the data files, it will automatically shut down. You
can process up to 40 data files using a single batch script file.
Starting with version 3.53, a new and simpler file format for the batch mode
option which makes use of the inversion parameters files (IVP) that are created
by the RES2DINV program itself. The file RESIS_IVP.BTH is an example,
with the following format.
RESIS_IVP.BTH file | Comments
-----------------------------------------------------------------------------------------------
3 | Number of files to invert
INVERSION PARAMETERS FILES USED | Header to indicate new batch mode
DATA FILE 1 | Header for first file
C:\RES2DINV\RATHCRO.DAT | Data file to invert
C:\RES2DINV\RATHCRO_L2.INV | Output file with inversion results
C:\RES2DINV\RES2DINV_L2.IVP | File containing the inversion settings
DATA FILE 2 | Header for second file
C:\RES2DINV\RATHCRO.DAT | Data file to invert
C:\RES2DINV\RATHCRO_L1.INV | Output file with inversion results
C:\RES2DINV\RES2DINV_L1.IVP | File with different inversion settings
DATA FILE 3 | Header for third file
C:\RES2DINV\LANDFILL.DAT | Third data file to invert
C:\RES2DINV\LANDFILL_L2.INV | Output file with inversion results
C:\RES2DINV\RES2DINV_L2.IVP | File containing the inversion settings
Since the IVP files are created by the RES2DINV program, it is not necessary
for the user to deal with the details about the file format. To create them, the
user just needs to click the appropriate inversion options within the
RES2DINV program, and then select the “Save inversion parameters’ option
under the “Change Settings” menu to save the parameters into an IVP file.
73
Appendix H : Speed of graphics display
As RES2DINV is a Windows based program, graphics operations by the
program are handled via the Windows display driver for the computer graphics
card. Thus the program will work with any graphics card as long as it has a
Windows driver. This is different from DOS based programs where
compatibility problems with the high resolution Super VGA graphics modes
are common. One big advantage of this program is that high resolution
graphics modes, such as the 1024 by 768 pixels with 256 colours graphics
mode, can be easily used by this program. This is important for data collected
from surveys with more than several hundred electrodes (a survey with about
650 electrodes and nearly 5200 data points now holds the record for land
surveys) where the standard VGA 640 by 480 pixels graphics mode is clearly
inadequate.
Since graphics operations are carried out via the display driver, the speed of the
graphics display is dependent on the efficiency of the display driver. For some
graphics cards, the earlier versions of the drivers are relatively inefficient
which results in painfully slow graphics operations such as in drawing the
pseudosections. If this happens on your computer, the cause is almost certainly
due to an early version graphics driver for the display card. The best way to
overcome this problem is to replace the Windows graphics card driver with a
newer version that should be more efficient. The drivers can be downloaded
via the Internet from many shareware sites or from the manufacturer’s web
site. Using the latest version of the display driver can result in significant
improvements in the speed of the graphics operations. This will affect not only
the speed of the graphics display in the RES2DINV program, but will also
improve the response of practically all graphics intensive Windows programs
(such as CAD and animation programs).
74
Appendix I : Cross-borehole data inversion
The resolution of electrical surveys carried out with electrodes on the ground
surface decreases exponentially with depth. One method to obtain reasonably
good resolution at depth is by making measurements with the electrodes in
boreholes. Cross-borehole surveys are much less frequently carried out
compared to surface based surveys, so unlike surface surveys, there are at
present no common standards with regards to the arrangement of the
electrodes. The cross-borehole option in this program is intended for shallow
surveys with the arrangement of the electrodes placed in a certain general
pattern (Sasaki 1992). The basic arrangement of the electrodes is shown in the
Figure 21.
The electrodes are divided into 3 sets with (i) the surface electrodes, (ii)
electrodes in borehole 1 and (ii) electrodes in borehole 2. It is assumed that the
boreholes do not have a metal casing which would severely alter the pattern of
the current flow. The program divides the subsurface into a number of
quadrilateral blocks (Figure 21). Note that the positions of the surface and
borehole electrodes control the manner in which the subsurface is divided into
the model blocks. The file BOREDIFF.DAT is an example data file with crossborehole
measurements. A description of the format used is given below in the
comments section. Note that in this example, the measurements are made with
the pole-dipole array where only the C1, P1 and P2 electrodes are used.
BOREDIFF.DAT file Comments
Borehole electrodes at different depths | Title
1.0 | Smallest electrode spacing
12 | Array number 12 for cross-borehole survey
840 | Number of data points
2 | 2 to indicate XYZ location format is used
0 | 0 for no IP data
Surface Electrodes | Header for surface electrodes
16 | Number of surface electrodes
0.0, 0.0 | x- and z-location of first surface electrode
1.0, 0.0 | location of second surface electrode
2.0, 0.0 | Note location values are given for the
3.0, 0.0 | electrodes in ascending order starting
4.0, 0.0 | from the left.
5.0, 0.0 | Note a zero value for the depth for the
6.0, 0.0 | surface electrodes.
7.0, 0.0 |
8.0, 0.0 |
9.0, 0.0 |
10.0, 0.0 |
11.0, 0.0 |
12.0, 0.0 |
13.0, 0.0 |
75
14.0, 0.0 |
15.0, 0.0 |
Borehole 1 Electrodes | Header for first borehole
10 | Number of electrodes in first borehole
4.0 1.0 | x- and z-location of first electrode
4.0 2.0 | x- and z-location of second electrode
4.0 3.0 | Note locations of electrodes
4.0 4.0 | are given from the topmost electrode
4.0 5.0 | below the surface.
4.0 6.0 | Also note a constant x-location for
4.0 7.0 | vertical borehole.
4.0 8.0 |
4.0 9.0 |
4.0 10.0 |
Borehole 2 Electrodes | Header for second borehole
10 | Number of electrodes in second borehole
11.0 1.5 | x- and z-location of first electrode
11.0 2.5 | location of other electrodes are then given.
11.0 3.5 |
11.0 4.5 |
11.0 5.5 |
11.0 6.5 |
11.0 7.5 |
11.0 8.5 |
11.0 9.5 |
11.0 10.5 |
Measured Data | Header for section with the measurements
3 0.00 0.00 1.00 0.00 2.00 0.00 101.5718 | The format for each data point is :-
3 0.00 0.00 2.00 0.00 3.00 0.00 99.5150 | Number of electrodes used in
3 0.00 0.00 3.00 0.00 4.00 0.00 99.2303 | measurement, x- and z-location of
3 0.00 0.00 4.00 0.00 5.00 0.00 99.1325 | C1 electrode, x- and z-location of
3 0.00 0.00 5.00 0.00 6.00 0.00 101.0616 | P1 electrode, x- and z-location of
3 0.00 0.00 6.00 0.00 7.00 0.00 105.7333 | P2 electrode, apparent resistivity
3 0.00 0.00 7.00 0.00 8.00 0.00 112.6745 | value.
3 0.00 0.00 8.00 0.00 9.00 0.00 118.5223 |
The array number is 12 for cross-borehole survey data with the measurements
given as apparent resistivity values. You can also enter the data as resistance
measurements, in which case the array number is 13. This might be more
convenient as most resistivity meters give the readings as a resistance value in
ohm, and furthermore the geometric factor for arrays with subsurface
electrodes is different from the geometric factor for conventional surface
arrays. The file BORERES.DAT gives an example where the measurements
are given as resistance values. An interesting field data set where the pole-pole
array was used, and the measurements are also given as resistance values, is
BORELUND.DAT from Lund University, Sweden.
76
Figure 21. Arrangement of the electrodes in a cross-borehole survey. (a) The
default Standard Model where the dimensions of the model blocks are equal to
the spacing between the electrodes. (b) An alternative model with finer blocks
with dimensions about half the spacing between the electrodes.
If only two electrodes are used in a measurement, only the x- and z-locations of
the C1 and P1 electrodes are given in the data file (see the file BOREHIP.DAT
77
which also contains IP measurements). However, if all four electrodes are used,
the x- and z-locations of the C1, C2, P1 and P2 electrodes must be given in this
order. You can combine measurements made with different numbers of
electrodes in the same data file.
When the programs reads in a file with resistance values, you have a choice of
inverting the data set using apparent resistivity values, or directly use the
resistance values. Using resistance values directly in the inversion has the
advantage of allowing you to use readings where the apparent resistivity value
does not exist, or is negative. After reading in a data file, the program will
attempt to filter out suspicious readings with potentially high noise levels if the
measurements are given as apparent resistivity values, or if you had chosen the
option to use apparent resistivity values in the inversion. If you choose to carry
out the inversion using resistance values, the readings are not filtered.
The geometric factor for subsurface electrodes is different from that used for
surface electrodes. As an example, the geometric factor for a measurement
where only two electrodes is used is as follows. If the C1 and P1 electrodes are
located at (x1,z1) and (x2,z2) respectively, the geometric factor k is then given by
k = 4 pi /(1/r1 + 1/r1')
where
r1 = sqrt (dx2
+ dz2
) r1'’
= sqrt (dx2
+ Dz2
)
dx = x1 - x2 dz = z1 - z2
Dz = z1 + z2
Similar equations for measurements with 3 or 4 electrodes can be easily
obtained by adding the appropriate terms.
The depth of the electrodes in Borehole 1 can be different from the
corresponding electrodes in Borehole 2. In practice, to get the best results the
depths should not differ too much.
This program requires that the number of electrodes in both boreholes must be
the same. In practice, this restriction is not a significant problem. You can be
easily overcome this restriction by inserting dummy electrodes into the data set
if the number of electrodes in one borehole is less (in the section where the xand
z-location of the electrodes in the borehole are given).
The program also requires that a surface electrode is located at the top of both
boreholes. If they do not physically exist, just insert dummy electrodes at the
appropriate locations in the data file. Also there should be at least a few surface
electrodes between the two boreholes, as well as at least two surface electrodes
to the left of borehole 1, and another two to the right of borehole 2. Again, if
78
the such electrodes were not used in the field survey, just insert dummy
electrodes into the data file to satisfy the requirements of this program. One
significant restriction of the present version of the program is that the boreholes
must be vertical, i.e. inclined boreholes are not allowed. If there is a significant
number of actual field surveys with inclined boreholes, this restriction might be
removed in future versions of the program.
By default, the program will subdivide the subsurface into quadrilateral blocks
such that the dimensions of the blocks are equal to the spacing between the
electrodes (Figure 21a). However, you can also choose to use a model where
the dimensions of the blocks is about half the spacing between the electrodes
(Figure 21b). Using the model with a finer discretisation could significantly
improve the inversion results in some cases (Sasaki 1992). To select the type of
model to use, click the ‘Change Settings’ options on the Main Menu top bar,
followed by ‘Type of cross-borehole model’. In theory, it is possible to further
subdivide the subsurface into even smaller blocks. However, since the
resolution of electrical measurements decreases rapidly with distance from the
measuring electrodes, this is unlikely to significantly improve the results. In
fact, it could result in unnatural oscillations in the model resistivity values,
particularly near the electrodes. This is as a result of the well known trade-off
between model resolution and model variance in geophysical inversion.
Figure 22 shows the model obtained after the inversion of the
BOREHOLE.DAT data set. This is a synthetic data set produced by a forward
modelling program with a high resistivity block in between the two boreholes.
The option to use finer blocks with half the size of the spacing between the
electrodes was used in the inversion of this data set.
Figure 23 shows the inversion results from an interesting field data set. This
data set is one from a number that were collected by a survey to study the flow
of fluids through the UK Chalk aquifer in east Yorkshire by using a saline
tracer (Slater et al 1997). There is a low resistivity zone near the surface where
the saline solution was irrigated onto the ground, and also prominent low
resistivity zones below a depth of 7 metres due to the saline tracer that had
flowed downwards. Another interesting feature of this data set is that no
surface electrodes were used. So all the surface electrodes given in the
BORELANC.DAT data file are dummy electrodes. The inversion of this data
set took about 15 minutes on a 200 Mhz Pentium Pro computer. the left of
borehole 1, and another two to the right of borehole 2. Again, if the such
electrodes were not used in the field survey, just insert dummy electrodes into
the data file to satisfy the requirements of this program. One significant
restriction of the present version of the program is that the boreholes must be
vertical, i.e. inclined boreholes are not allowed. If there is a significant number
79
of actual field surveys with inclined boreholes, this restriction might be
removed in future versions of the program.
If IP measurements were also made, you need to enter a value of 1 at the 6th
line in the data file, and two more data lines after that which gives the type of
IP measurement used and the two parameters associated with it (see Appendix
F). Next, enter the IP value after the apparent resistivity value for each data
point. The file BOREHIP.DAT is an example cross-borehole data file with IP
measurements.
Figure 22. The model obtained after the inversion of the BOREHOLE.DAT
data set. The option to use finer blocks with half the size of the spacing
between the electrodes was used.
80
Figure 23. Model obtained from the inversion of data from a cross-borehole
survey to map the flow of a saline tracer in between two boreholes. Note the
low resistivity zones near the surface (where the tracer was injected) and below
a depth of 7 metres. The locations of the borehole electrodes are shown by
small black dots.
81
The RES2DINV program supports up to 10 boreholes (20 boreholes if your
computer has at least 256 MB RAM) along a survey line. This limit might be
increased in future when the need arises. A possible situation where more than
2 “boreholes” exists is when a current electrode is placed at the end of a
borehole driller or penetrometer. The file BOREHOLE3.DAT gives an
example of the data format with more than 2 boreholes. A description of the
format is as follows.
BOREHOLE3.DAT file Comments
Pole-dipole borehole test | Title
1.0 | Smallest electrode spacing
12 | Array number 12 for cross-borehole survey
908 | Number of data points
2 | 2 to indicate XYZ location format is used
0 | 0 for no IP data
Surface Electrodes | Header for surface electrodes
16 | Number of surface electrodes
0.0, 0.0 | x- and z-location of first surface electrode
1.0, 0.0 | location of second surface electrode
2.0, 0.0 | Note location values are given for the
3.0, 0.0 | electrodes in ascending order starting
4.0, 0.0 | from the left.
5.0, 0.0 | Note a zero value for the depth for the
6.0, 0.0 | surface electrodes.
7.0, 0.0 |
8.0, 0.0 |
9.0, 0.0 |
10.0, 0.0 |
11.0, 0.0 |
12.0, 0.0 |
13.0, 0.0 |
14.0, 0.0 |
15.0, 0.0 |
Number of boreholes | New header for more than 2 boreholes
3 | Number of boreholes here
Borehole 1 Electrodes | Header for first borehole
11 | Number of electrodes in first borehole
4.0 1.0 | x- and z-location of first electrode
4.0 2.0 | x- and z-location of other electrodes
4.0 3.0 |
4.0 4.0 |
4.0 5.0 |
4.0 6.0 |
4.0 7.0 |
4.0 8.0 |
4.0 9.0 |
4.0 10.0 |
82
4.0 11.0 |
Borehole 2 Electrodes | Header for second borehole
11 |
11.0 1.0 |
11.0 2.0 |
11.0 3.0 |
11.0 4.0 |
11.0 5.0 |
11.0 6.0 |
11.0 7.0 |
11.0 8.0 |
11.0 9.0 |
11.0 10.0 |
11.0 11.0 |
Borehole 3 Electrodes |Header for third borehole
11 |
13.0 1.0 |
13.0 2.0 |
13.0 3.0 |
13.0 4.0 |
13.0 5.0 |
13.0 6.0 |
13.0 7.0 |
13.0 8.0 |
13.0 9.0 |
13.0 10.0 |
13.0 11.0 |
Measured Data | The apparent resistivity values start after this
3 0.00 0.00 1.00 0.00 2.00 0.00 101.5718 | Note 3 electrodes for
3 0.00 0.00 2.00 0.00 3.00 0.00 99.5150 | a pole-bipole array
.
.
3 11.00 11.00 11.00 5.00 11.00 4.00 110.7175 | Last two data
3 11.00 11.00 11.00 4.00 11.00 3.00 118.4761 | points
0,0,0,0,0 | End with 5 zeros
Note that the format is essentially the same as that used earlier for two
boreholes, except for the header after the list of surface electrodes and the
value for the number of boreholes.
The file BOREHOLE_TOPO.DAT is a field example of a cross-borehole data
set with topography. The initial part of this data file with a description of the
format is as follows.
83
BOREHOLE_TOPO.DAT file Comments
BOREHOLE WITH TOPOGRAPHY | Title
1.00000 | Smallest electrode spacing
12 | Array number 12 for cross-borehole survey
570 | Number of data points
2 | 2 to indicate XYZ location format is used
0 | 0 for no IP data
Topography Present | Header to indicate topography is present
Topography information mode (0=wrt to surface electrodes) | Header
0 | Indicates depths of borehole electrodes are given wrt
| the surface electrode at the top of the borehole
Type of x-distances | Header
2 | 2 to indicate x-distances are along the surface
Surface Electrodes | Header
31 | Number of surface electrodes
-14.0000 0.00 | x-location and elevation of first electrode
-13.0000 0.03 | x-location and elevation of second electrode
-12.0000 0.05 | Same for the rest
-11.0000 0.08 |
-10.000 0.11 |
-9.0000 0.13 |
. |
. |
15.0000 0.85 |
16.0000 0.95 | Last surface electrode
Borehole 1 electrodes | Header for first borehole
17 | Number of electrodes in borehole
-14.0000 1.0000 | x-location and depth of first borehole electrode
-14.0000 2.0000 | x-location and depth of first borehole electrode
. | Same for the rest
. | The format is the same as for normal borehole data files
Note that the topography information is given in the z-coordinates of the
surface electrodes.
84
Appendix J - Remote electrodes of the pole-pole and pole-dipole arrays
In theory, the pole-pole array has only 2 electrodes, the positive current
electrode C1 and the positive potential electrode P1. In practice such an array
does not exist since all field measurements are made using an array with 4
electrodes (Figure 24).
Figure 24. A schematic diagram of the arrangement of the electrodes in an
actual field pole-pole measurement.
To minimise the effects of the C2 and P2 electrodes, it is generally
recommended that the distance of these two electrodes from the C1 and P1
electrodes must be at least 10 times (and preferably 20 times) the C1-P1
spacing r1. In some cases, when large spacings between the C1 and P1
electrodes are used, this requirement is not met for all measurements. This
could lead to distortions in the inversion model (Robian et al. 1997). To
overcome this problem, the RES2DINV program allows the user to incorporate
the effects of the C2 and P2 electrodes in the inversion.
To calculate the apparent resistivity value measured with the non-ideal polepole
array, two possible geometric factors can be used. One method is to use
the same equation as the ideal pole-pole array. This gives an approximate
geometric factor since the resulting apparent resistivity value is not the same as
the true resistivity for a homogeneous half-space. Alternatively, the exact
85
geometric factor that takes into account the positions of the C2 and P2
electrodes can be used.
Approximate Geometric factor (ideal pole-pole array) = 2.pi.r1
Exact Geometric factor = 2 pi / [ (1/r1) - (1/r2) - (1/r3) + (1/r4) ]
The program supports both conventions.
A possible arrangement of the electrodes in a pole-pole survey is shown in
Figure 25. In this case, the C2 and P2 electrodes are fixed throughout the
survey. The measurements are made by using different pairs of electrodes
along the survey line as the C1 and P1 electrodes. For a survey line with n
electrodes, there are n(n+1)/2 possible combinations. For example, if there are
25 electrodes in the survey line, there are 300 possible combinations. In
practice, not all the possible measurements are made. Instead a maximum
distance between the C1 and P1 electrodes is set depending on the maximum
depth of investigation needed (Edwards 1977). In many cases, this maximum
distance is 6 to 10 times the unit electrode spacing along the survey line. To
avoid the possibility of negative or zero apparent resistivity values, the distance
of the C2 and P2 electrodes must be at least 2.5 times (and preferably 3 times)
the maximum C1 to P1 spacing used. For example, if the unit electrode spacing
is 1 metre, and the maximum C1-P1 spacing is 10 metres, then the C2 and P2
electrodes must be at least 25 metres from the survey line. Note that as the
distance of the C2 and P2 electrodes from the survey line decreases, the
effective maximum depth of investigation of the survey also decreases. It might
be significantly less than the depth of investigation for the ideal pole-pole array
(Edwards 1977).
Figure 25. A schematic diagram of the arrangement of the C2 and P2
electrodes and the electrodes along the survey line in a pole-pole survey. To
incorporate the effects of the C2 and P2 electrodes in the data inversion, their
x- and y-coordinates with respect to the survey line must be recorded.
86
The file POLPOLFX.DAT is an example data file with pole-pole
measurements where the locations of the C2 and P2 remote electrodes are
specified. A description of the format used is given below in the comments
section. Although the z-locations of the electrodes are also included in the file
data format for completeness, the values are presently not used by the program.
The program at present estimates the heights at the remote electrodes from the
heights of the electrodes along the survey line. However, in future, they might
be used to accommodate extreme cases where slope of the ground at the remote
electrodes is very different from that along the survey line.
POLPOLFX.DAT file Comments
Blocks Model | Title
2.00 | Smallest electrode spacing
2 | Array number 2 for pole-pole.
Remote electrodes included | Header to indicate position of remote
| electrodes included in data file
C2 remote electrode X, Y and | Header for second current electrode location
Z location |
-50.000,20.000,0.0 | x-, y- and z-location of C2 electrode
P2 remote electrode X, Y and | Header for second potential electrode
Z location | location
120.000,0.000,0.0 | x-, y- and z-location of P2 electrode
Exact Geometric factor used | Type of geometric factor used
295 | Number of data points
1 | 1 to indicate x-location of centre of array is
| given
0 | 0 for no IP
1.00 2.00 10.13 | The x-location, electrode spacing
| apparent resistivity for first data point
3.00 2.00 10.18 | Second data point
The data format is the same as that for normal pole-pole surveys except for the
section (after the array number) which contains information about the location
of the second current and potential electrodes. The data line “Exact Geometric
factor used” is used to indicate that the apparent resistivity values in the data
file were calculated used the exact geometric factor. If the approximate
geometric factor was used, this data line should be given as “Approximate
Geometric factor used”. The file POLDPLFA.DAT is an example data file for
a pole-dipole survey where the approximate geometric factor was used in
calculating the apparent resistivity values. Note that in this file, only the
location of the second current electrode C2 is given.
For the pole-pole array, the effect of the C2 electrode is approximately
proportional to the ratio of the C1-P1 distance to the C2-P1 distance. If the
effects of the C2 and P2 electrodes are not taken into account, the distance of
these electrodes from the survey line must be at least 20 times the largest C1-
87
P1 spacing used to ensure that the error is less than 5%. In surveys where the
inter-electrode spacing along the survey line is more than a few metres, there
might be practical problems in finding suitable locations for the C2 and P2
electrodes to satisfy this requirement. Thus the error in neglecting the effects of
the remote electrodes is greatest for the pole-pole array. As a general guide, if
the distances of the C2 and P2 electrodes from the survey line is more than 20
times the largest C1-P1 spacing used, the array can be treated as an ideal polepole
array for interpretation purposes. Otherwise, the coordinates of the C2 and
P2 electrodes should be recorded so that their effects can be determine by this
program. However, it should be noted that as the distance of the P2 electrode
from the survey line increases, the telluric noise picked up by the P1-P2 pair
also increases. This factor should also be taken into account when positioning
the P2 electrode.
For the pole-dipole array, the effect of the C2 electrode is approximately
proportional to the square of ratio of the C1-P1 distance to the C2-P1 distance.
Thus the pole-dipole array is less affected by the C2 remote electrode. If the
distance of the C2 electrode is more than 5 times the largest C1-P1 distance
used, the error caused by neglecting the effect of the C2 electrode is less than
5% (the exact error also depends on the location of the P2 electrode for the
particular measurement). So, as a general guide, if the distance of C2 electrode
from the survey line is more than 5 times the largest C1-P1 spacing, it can be
treated as an ideal pole-dipole array. Otherwise, enter the coordinates of the C2
electrode into the data file.
88
Appendix K : Robust data and model inversion
The conventional least-squares method will attempt to minimise the square of
difference between the measured and calculated apparent resistivity values.
This method normally gives reasonable results if the data contains random or
“Gaussian” noise. However if the data set contains “outlier” data points (where
the noise comes from non-random sources such mistakes or equipment
problems), this criteria is less satisfactory. Such “outlier” data points could
have a great influence on the resulting inversion model. To reduce the effect of
such “outlier” data points, an inversion method where the absolute difference
(or the first power) between the measured and calculated apparent resistivity
values is minimised can be used (Claerbout and Muir 1973).
In the RES2DINV program, this inversion method can be selected by clicking
the “Select robust inversion” option under the “Change settings” menu. In the
“Select robust inversion” dialog box, click the “Robust data constrain” option.
There is a cut-off factor which controls the degree in which this robust data
constrain is used. If a value of 0.05 is used, this means the effect of data points
where the differences in the measured and calculated apparent resistivity values
are much greater than 5 percent will be greatly reduced.
The conventional smoothness-constrained least squares method (deGrootHedlin
and Constable 1990) also attempts to minimise the square of the
changes in the model resistivity values. This will produce a model with a
smooth variation in the resistivity values. Such a model is most suitable where
subsurface resistivity also changes in a smooth manner, such as the pollution
plume example shown in Figure 3. However if the subsurface bodies have
sharp boundaries, such as the soil-bedrock interface or massive homogeneous
bodies, the conventional least-squares smoothness-constrain method tends to
smear the boundaries.
If the robust model constrain inversion method is used on the model resistivity
values, the program will attempt to minimise the absolute changes in the
resistivity values. This constrain tends to produce models with sharp interfaces
between different regions with different resistivity values, but within each
region the resistivity value is almost constant. This might be more suitable for
areas where such a geological situation exists, such as the soil-bedrock
interface over certain types of bedrock. As an example, Figure 26 shows the
inversion results for a synthetic model with a faulted block (with a resistivity of
50 ohm.m) and a small rectangular block (1 ohm.m) within a surrounding
medium with a resistivity of 10 ohm.m. The model produced by the standard
least-squares method has a gradational boundary for the faulted block. In
comparison, the model produced by the robust model inversion method has
sharper and straighter boundaries.
89
A field example with sharp boundaries was shown earlier in Figure 20 for the
Magusi River resistivity and IP data set. The main structure, the massive
sulphide ore body, by nature has a distinct and sharp resistivity/IP contrast with
the surrounding igneous/metamorphic country rocks.
In the RES2DINV program, this robust model option can be selected by
clicking the “Robust model constrain” option in the “Select robust inversion”
dialog box. There is a cut-off factor which controls the degree in which this
robust model constrain is used. If a large value is used, for example 1.0, the
result is essentially that of the conventional smoothness-constrained leastsquares
inversion method. If a very small value is used, for example 0.001, the
result is close to the true robust constrained inversion method.
Figure 26. Example of inversion results using the smoothness-constrain and
robust inversion model constrains. (a) Apparent resistivity pseudosection
(Wenner array) for a synthetic test model with a faulted block (100 ohm.m) in
the bottom-left side and a small rectangular block (2 ohm.m) on the right side
with a surrounding medium of 10 ohm.m. The inversion models produced by
(b) the conventional least-squares smoothness-constrained method and (c) the
robust inversion method.
90
Appendix L : Non-conventional or general arrays
This feature is to cater for electrode arrangements that do not fall under the
usual array types or electrode arrangements, or unusual ways of carrying out
the surveys. There are probably an infinite number of possible electrode
configurations that are limited only by the imagination of the user, but in most
cases they are likely to be slight variations of the standard arrays. Figure 27
shows four possible non-standard configurations.
Figure 27. Some possible non-conventional arrays. (a) Non-symmetrical fourelectrode
Wenner-Schlumberger type of array. (b) Dipole-dipole array with
dipoles of unequal size. (c) A possible but probably non-viable electrode
configuration.
One possibility is a non-symmetrical variation of a symmetrical array, such as
the Wenner-Schlumberger or the dipole-dipole array (Figures 27a and 27b).
Such a configuration could arise from surveys with multi-channel resistivity
meters where measurements are made with several pairs of potential electrodes
for a common pair of current electrodes.
While the program gives the user greater latitude in the electrode arrangement,
some arrays that are technically possible but would have very low potential
signals should be avoided.
To accommodate the various possibilities, a data format which is similar to that
used for cross-borehole surveys (Appendix I) is used. The x-location as well as
the elevation of all the electrodes used in a measurement must be given. The
file MIXED.DAT is an example data file with such a format. This is actually a
synthetic data set with a mixture of measurements using the Wenner-
91
Schlumberger and dipole-dipole arrays. The initial part of this data file with
comments about the format is given below.
MIXED.DAT file Comments
Mixed array | Title
1.0 | Unit electrode spacing
11 | Array type (11 for general array)
0 | Sub-array type
Type of measurement (0=app. resistivity,1=resistance) | Header
0 | 0 here to indicate apparent resistivity values
407 | Number of data points
1 | Indicator for type of x-location
0 | No IP values, 1 if I.P present
4 0.00 0.00 3.00 0.00 1.00 0.00 2.00 0.00 10.158 | The format for each data point is
4 1.00 0.00 4.00 0.00 2.00 0.00 3.00 0.00 10.168 | Number of electrodes used in
4 2.00 0.00 5.00 0.00 3.00 0.00 4.00 0.00 10.184 | measurement, x- and z-location of
4 3.00 0.00 6.00 0.00 4.00 0.00 5.00 0.00 10.225 | C1 electrode, x- and z-location of
4 4.00 0.00 7.00 0.00 5.00 0.00 6.00 0.00 10.337 | C2 electrode, x- and z-location of
4 5.00 0.00 8.00 0.00 6.00 0.00 7.00 0.00 10.708 | P1 electrode, x- and z-location of
4 6.00 0.00 9.00 0.00 7.00 0.00 8.00 0.00 11.668 | P2 electrode, apparent resistivity
4 7.00 0.00 10.00 0.00 8.00 0.00 9.00 0.00 12.542 | or resistance value.
The sub-array type indicator is used when the electrode configuration follows
one of the conventional arrays, for example the Wenner-Schlumberger array.
As an example, the file MIXEDWS.DAT has the data for a WennerSchlumberger
array only but the information is arranged in a general array
format. In this case the sub-array number is 7. The file RATHCMIX.DAT has
the data for the Rathcrogan mound (described earlier in Figure 8) for the
Wenner array but in a general array format (thus it has sub-array number of 1).
For these data sets, the apparent resistivity vales can be displayed in the form
of a pseudosection. The file MIXED.DAT is a combined data set with a
mixture of measurements with the Wenner-Schlumberger and dipole-dipole
array. In this case, there is no consistent array type, so the sub-array number is
given as 0.
Concerning the indicator for the type of x-location, there are two possible
values. A value of 1 is used if the x-location values are the true horizontal
distances, while a value of 2 is used if it is the distance along the ground
surface. This is similar to the convention used for topography data (Section 7).
In the RATCMIX.DAT file, the topography information is included as the
elevation for each electrode in every data line. In some cases, it might be more
convenient to enter the topography information in a separate list, much like for
data in the normal format. One example with data in the general array format
but with the topography in a separate list after the apparent resistivity data lines
is given in the file ITALY_CAVE.DAT. Part of the file is shown below.
92
ITALY_CAVE file Comments
Italy cave survey | Title
1.00 | Unit electrode spacing
11 | Array type (11 for general array)
3 | Sub-array type (dipole-dipole)
Type of measurement (0=app. resistivity.1=resistance) | Header
0 | 0 here to indicate apparent resistivity values
584 | Number of data points
2 | Indicator for type of x-location (surface
| distance)
1 | Note presence of I.P. data
Chargeability | IP data in chargeability
mV/V | IP unit
0.16,0.5 | IP measurement parameters
4 2.00 0.00 0.00 0.00 4.00 0.00 6.00 0.00 126.16 0.23 | First 2 data lines
4 2.00 0.00 0.00 0.00 6.00 0.00 8.00 0.00 169.15 -2.80 | Note 0.0 for elevation
. | Other data lines
. |
4 88.00 0.00 86.00 0.00 92.00 0.00 94.00 0.00 44.73 1.71 | Last 2 data lines
4 90.00 0.00 88.00 0.00 92.00 0.00 94.00 0.00 42.93 1.37 |
Topography in separate list | Header to indicate the topography information
2 | is in a separate list after the data lines. Format
85 | for topography data is same as for data in
0,94.158 | normal format. First 2 topography points.
2,94.269 |
. | Other topography data points
. |
94,101.948 | Last 2 topography data points
95,102.062 |
1 | Indicates first electrode coincides with first
0 | topography point
0 | Ends with a few zero’s
0 |
Note the addition of a header line “Topography in separate list” that indicates
the topography information is in a separate list after the apparent resistivity
data lines. Note also in the data lines, the elevation for each electrode is given
as 0.00. The program will calculate the elevation for the electrodes from the
topography information.
The measurement can be given in terms of resistance or apparent resistivity. If
there is no topography, i.e. the z-locations are all equal to zero or the same, the
conventional formula can be used to calculate the apparent resistivity. The
geometric factor k is given by the following equation
k = 2 pi / (1/r1 - 1/r2 - 1/r3 + 1/r4)
93
where r1 is the distance between the C1 and P1 electrodes, r2 is the distance
between the C1 and P2 electrodes, r3 is the distance between the C2 and P1
electrodes and r4 is the distance between the C2 and P2 electrodes. In the case
when there is no topography, the distance between two electrodes is simply the
difference in the x-locations of the two electrodes.
In the case where topography is present, there is no widely accepted
convention. To be consistent with the format used earlier, two different
conventions are used depending on the type of x-location given in the data file.
If the x-locations are given as distances along the surface (i.e. not true
horizontal distances), the distance between two electrodes is calculated by
using the difference in the values of the x-locations only.
If the x-locations are true horizontal distances, the true distance between two
electrodes is used in the calculation of the geometric factor. For example, if the
C1 and P1 electrodes are located at (x1,z1) and (x2,z2) respectively, then
r1= sqrt (dx2
+ dz2
)
where dx = x1 - x2
dz = z1 - z2
In the case where the ground surface has a constant slope, both conventions
will give the same geometric factor.
Note that in the general array data format, the z-location is the elevation of the
electrode which is positive in the upwards direction. This unfortunately is
different from the format for the borehole data set where the z-values are
positive in the downwards direction.
Figure 28 shows an interesting arrangement where the electrodes are arranged
such that the true horizontal distances between adjacent electrodes are
constant. When the slope of the ground surface is not constant, this results in an
arrangement where the distance between adjacent electrodes as measured along
the ground surface is not constant but depends on the slope. In areas where the
slope is steeper, the distance between adjacent electrodes along the ground
surface is greater. To accommodate such an arrangement, the general array
format can be used. In this case, the indicator for the type of x-location must be
1 since the true horizontal distances are given in the data. Very often, the
survey is carried out with one of the conventional arrays, such as the WennerSchlumberger,
so the appropriate sub-array number should also be given.
94
Figure 28. Arrangement of the electrodes along a survey line such that the true
horizontal distance between adjacent electrodes is constant regardless of the
slope of the ground surface. Note that the distance between adjacent electrodes
along the ground surface is greater at the steeper part of the slope.
In some cases, the 2-D data set is generated from a series of collinear 1-D
sounding lines. In such a situation, the distance between adjacent electrodes is
not constant, whether as measured along the surface or in the true horizontal
direction. For such a case, the general array format (with a sub-array type of 0)
can be used.
For data sets with a sub-array type of 0, the data cannot be displayed in the
form of a pseudosection, nor can it edited with the "Exterminate bad data
points" option. To remove bad data points from the data set, you need to first
carry out an inversion of the entire data set. However, you need to use the
"Robust data constrain" (see Appendix K) to ensure that bad data points do not
have a large effect on the inversion results. Next, go to the "Display" window
and read in the file with the inversion results. Select the "RMS error statistics"
sub-option under the "Edit data" menu. This will display a histogram where the
data points are grouped according to the difference between the measured and
calculated apparent resistivity values. This allows you to remove the data
points where a large difference occurs, for example more than 100 percent.
After removing the more noisy data points, save the trimmed data set in a file
and carry out the inversion again with the trimmed data set.
The suboption "Generate model blocks" under the "Inversion" option on the
main menu allocates the arrangement of the blocks in the model using the
sensitivity values as a guide. Figure 29 shows the sensitivity values of the
MIXEDWS.DAT data set using the default extended model, and for the
"Generate model blocks" option. Note that this option increases the width of
the blocks near the sides in the deeper parts of the model section in order to
increase the sensitivity values of the blocks. This option can also be used for
95
normal data sets with the standard arrays. By default, the program uses a
heuristic algorithm partly based on the position of the data points to generate
the size and position of the model blocks. The "Generate model blocks" uses a
more quantitative approach based the sensitivity values of the model blocks.
However, in practice, the simpler and faster heuristic algorithm gives
reasonably good results for most data sets.
Figure 29. The arrangement of the model blocks used by the program for the
inversion of the MIXEDWS.DAT data set using (a) the default extended model
and (b) a model generated so that any single block the does not have a relative
sensitivity value that is too small.
96
Appendix M : Array types in RES2DINV
A list of the arrays supported by the RES2DINV program together with their
number codes are given below.
Array name Number code
Wenner (alpha) 1
Pole-pole 2
Inline dipole-dipole 3
Wenner (beta) 4
Wenner (gamma) 5
Pole-dipole 6
Wenner-Schlumberger 7
Equatorial dipole-dipole 8
Non-conventional/General array 11
Cross-borehole survey (apparent resistivity values) 12
Cross-borehole survey (resistance values) 13
Gradient array (only used as sub-array number with
data in the general array format) 15
Note that the Wenner array has three different variations (Figure 30). The
"normal" Wenner array is actually the Wenner alpha array.
Figure 30. Arrangement of the electrodes for the Wenner alpha, beta and
gamma arrays.
97
The Wenner beta array is a special case of the dipole-dipole array where the
"n" factor is always 1. The RES2DINV program will automatically convert a
Wenner beta array data file into a dipole-dipole array data set.
The Wenner gamma array is not frequently used but it has direct support in
RES2DINV. The file GAMMA.DAT is an example data file for this array. A
case history of a field survey in Africa using this array is given in section 18 of
this manual.
98
Appendix N – Saving results in SURFER format
This option allows the user to save the apparent resistivity pseudosections and
model sections in the XYZ format used by the SURFER graphics 2-D plotting
program. After reading in an INV file containing the in inversion results in the
'Display' window, it is recommended that you display the pseudosections at
least once before using the option to save the results in SURFER format. If the
inversion file contains topographical data, such as the example
RATCHRO.INV file provided with this software package, you will need to use
select option 'Include topography in model display' to display the model section
with the topography. After that, you can click 'Save data in SURFER format'
option under the File menu. For the RATCHRO.INV file, the following dialog
box will be displayed.
In this dialog box, you can select the iteration number for which you want to
save the inversion results. Also, you can choose to save the resistivity values
directly, or the logarithm of the resistivity values which might be more suitable
if the resistivity values have a large range. SURFER will plot the sections as a
rectangular section. In many cases, especially a model section with topography,
this might not be appropriate. To remove the sections outside of the model
section, SURFER provides two methods of blanking part of the displayed
contoured section. The default and normally better method is to use the Base
99
Map Overlay feature in SURFER. In the bottom half of the dialog box, all the
various possible data or model sections are displayed. For a particular inversion
file, not all the possible sections are available. For example, the
RATHCRO.INV file does not have IP data, so the circles to the right of the
dialog box are not checked. As an exercise, click the 'Model resistivity with
topography' option for the RATHCRO.INV file. After clicking the OK button,
the program will then save the various sections. For a particular section, the
program will save 5 different files that are used for different functions in
SURFER. As an example, follow the following steps to plot the resistivity
(logarithm) model section with topography for the RATHCRO.INV file. The
different files are provided in the RES2DINV software package.
1). Create contour file. Click 'Grid' on the top menu bar, and then 'Data' to read
in the RATCHRO_TOPRESLOG.DAT file. After reading in the data file,
SURFER will show the 'Scattered Data Interpolation' dialog box. In the 'Grid
Line Geometry' section, the number of lines that SURFER uses to interpolate
the data values into a rectangular grid is shown. For this data set, the default
values are probably 50 lines in the X direction and 6 lines in the Y direction. In
most cases, you should increase the default values by a factor of 4 to 10 times
to improve the accuracy of the interpolation. For this example, try changing the
number of lines in the X and Y directions to 250 and 30 respectively (i.e.
increase the default values by a factor of 5). The SURFER program will create
a corresponding RATCHRO_TOPRESLOG.GRD file. Next click 'Map' on the
top menu bar and then 'Contour'. In the 'Contour' option, read in the
RATCHRO_TOPRESLOG.GRD file. Next the 'Contour Map' dialog box will
be shown. In this dialog box, click the 'Fill Contours' option. Next click the
'Load' button, and then read in the RATCHRO_TOPRESLOG.LVL file to set
the contour values and colours. If you wish to display the colour scale and
smooth the contours, click the 'Color Scale' and 'Smooth Contours' options.
Next click OK.
2). Next you need to mask out sections of the contour display. In the 'Map'
menu, click 'Load Base Map'. Choose the RATCHRO_TOPRESLOG.BLN as
the base map file. In the 'GS Blanking Import Options', just click OK. Do not
use the 'Areas to Curves' option. Next press F2, and then click the 'Overlap
Maps' option in the 'Map' menu. This will combine the contour map and the
base blanking map into a single map. Select the overlay by clicking near one of
the corners of the rectangle containing the contour map, and then select the
'Edit Overlays' command from the 'Map' menu. In the 'Edit Components' dialog
box, click the 'Base' and then click 'Move to Front' button. Next hold down the
CTRL key on the keyboard and click the overlay until the base map is
selected (as shown by the status indicator 'Map:Base' near the bottom left
corner of the screen). Next click the 'Draw' menu, and then choose the 'Fill
Attributes' option. Select the blank or white colour as the colour for the fill
100
attributes. Next click the 'Line Attributes', and also select the white colour so
that the overlay lines are not visible in the display.
3). Click the 'Post' command in the 'Map' menu, and then read in the
RATCHRO_TOPRESLOG_POST.DAT file (which contains the location of
the electrodes) in the 'Open Data' dialog box. After reading in this file, the 'Post
Map' dialog box will be shown. In this dialog box, select the symbol shape and
size and other options you want to use, and then click OK. After that, press F2,
and then click the 'Overlay Maps' command in the 'Map' menu. Next click the
figure and then the 'Edit Overlays' command in the 'Map' menu. Click 'Post'
and the 'Move to Front' , and the electrodes will be drawn on top of the model
section.
After drawing the section in the SURFER window, you can use other options
within SURFER to improve the model section, such as changing the font,
labels, titles etc., before printing the results or exporting it to another format.
SURFER supports a large variety of formats, including bit-mapped graphics
formats such as PCX, BMP, GIF etc.; and well as vector-based formats such as
the AUTOCAD DXF format.
For model sections without topography, step (3) where the post data map is
read is probably not necessary. However, you might need to adjust the tick
marks on the vertical scale on the left side of the contour plot. The depths are
given as negative values so that SURFER will plot the figure in the correct
orientation with the ground surface on top. As an example, draw the model
section for the Sting Cave example using the CAVE_MODRESLOG.DAT,
CAVE_MODRESLOG.LVL and CAVE_MODRESLOG.BLN files provided.
After you have drawn the model section, it is likely that you will only see the
0.0 mark on the left vertical axis for the depth scale. Click the left axis with the
right mouse button and the 'Left Axis' dialog box will be shown. Next click the
'Scaling' button in the dialog box. In the 'Axis Scaling' dialog box, change the
'Major Interval' value to 10 and the 'First Major Tick' to -40. Click OK to save
the values, and the left axis model section should then show ticks at depth
intervals of 10.
There will be slight differences in the contour sections drawn by SURFER and
RES2DINV due to the differences in the interpolation methods used. SURFER
does not use the original data points, but an interpolated rectangular grid of
points to draw the contours. The differences will probably be more obvious in
areas with very rapid changes in the resistivity. One way to reduce the
differences is to increase the number of grid lines used by SURFER for the
interpolation grid.
101
Appendix O : Model refinement
The RES2DINV program by default uses a model where the width of the
interior model cells is the same as the unit electrode spacing (for example as in
Figure 2). This works well in most cases. In some situations, particularly where
there are large resistivity variations near the ground surface, better results can
be obtained by using narrower model cells. There are two possible ways to
reduce the width of the model cells.
The first is by using the “Use model refinement” option on the ‘Inversion”
menu. Clicking this option will show the following dialog box.
This allows you to choose model cells with widths of half the unit electrode
spacing. In almost all cases, this gives the optimum results. After selecting this
option, you must read in the data file. The program will then automatically
reduce the unit electrode spacing it uses by half of that given in the data file.
The second method is to modify the data file directly using a text editor. The
unit electrode spacing is given in the second line of the apparent resistivity data
file. For example, the first few lines of the PIPESCHL.DAT file are reproduced
below.
Underground pipe survey
1.00
7
173
1
0
102
1.50 1.00 1 641.1633
In the second data line, the unit electrode spacing is given as 1.0 metre that is
the actual spacing used in this survey. When the RES2DINV reads in this data
file, it will set the width of the model cells to 1.0 metre. The file
PIPESCHL_HALF.DAT has the same data except that the unit electrode
spacing is now defined as 0.5 metre. The upper part of this file is shown below.
Underground pipe survey - half actual electrode spacing
0.5
7
173
1
0
1.50 1.00 1 641.1633
When the RES2DINV program reads this file, it will set the model cells to a
0.5 metre width. Figure 31 shows the inversion models for this data set using
cells with widths of 1.0 and 0.5 metre. The model with the 0.5 metre cell width
is able to more accurately model the high resistivity anomalies near the surface
between the 3 and 12 metres marks above the low resistivity pipe, and thus has
a slightly lower apparent resistivity RMS error. The Wenner-Schlumberger
array was used for this survey.
In most cases with large resistivity variations near the surface, using a model
with a cell width of half the actual unit electrode spacing is sufficient. In some
cases, using a narrower cell width of one-third or one-quarter the unit might be
justified, particularly if the survey was carried out using a pole-dipole or
dipole-dipole array with very high ‘n’ factors. If the cell width is one-quarter
the true unit electrode spacing, or less, oscillations in the model resistivity
values in the first few layers can occur. Thus the use of a cell width of less than
one-quarter the true unit electrode spacing is not advisable.
It is recommended that you refer to section 4.7j of the free notes “Tutorial : 2D
and 3-D electrical imaging surveys” that can be downloaded from the
www.geoelectrical.com web site. This section has a discussion on the effect of
using high ‘n’ factors with the pole-dipole array on the sensitivity of the array
to near-surface anomalies.
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Figure 31. (a) The apparent resistivity pseudosection for the PIPESCHL.DAT
data set. The inversion models using (b) cells with a width of 1.0 metre that is
the same as the actual unit electrode, and (c) using narrower cells with a width
of 0.5 metre. The pipe is marked by the low resistivity anomaly below the 12
metres mark. Note the near-surface high resistivity anomalies between the 3
and 12 metres marks. The Wenner-Schlumberger array was used for this
survey.
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Appendix P : Combining 2-D files
The RES2DINV program has 2 options for combining 2-D data files. In one
option, intended for a series of parallel survey lines, you can combine a number
of 2-D data files into a single 3-D data file. This is the “Collate data into
RES3DINV format” option under the “File” menu. In the second option,
intended for several roll-along survey lines, you can combine them into a
single 2-D data file. This is the “Concatenate 2-D data files” option under the
“File” menu.
Collate data into RES3DINV format
Ideally, a 3-D survey should be carried out using a rectangular grid of
electrodes with measurements in different directions (Loke and Barker 1996b).
However, for various reasons, this is sometimes not possible. In some surveys
a number of parallel 2-D survey lines, with possibly some tie lines in a
perpendicular direction, are used. This option enables the user the user to
combine the 2-D lines with data in the RES2DINV format into a single data
file in the format used by the RES3DINV program. While the RES3DINV
program will carry a true 3-D inversion (in that the resistivity values are
allowed to vary in all 3 directions simultaneously during the inversion process),
whether the data set contains sufficient 3-D information so as to produce a
reasonably accurate 3-D model is a different matter. A discussion of the
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various factors that influence the amount of 3-D information in a data set is
given by Loke (2001).
A script file is used to combine the 2-D files. The file COLLATE_2D_3D.TXT
is an example script file. The contents of this file together with a description of
the format used is given below.
COLLATE_2D_3D.TXT file | Comments
Conversion of RES2DINV data files | Title
Number of files to collate | Header for no. of data files
3 | Number of data files
File 1 parameters | Header for first file
Name of data file in RES2DINV format| Header for name of file
d:\test\FILE2D_1.DAT | Full name plus path of file
X and Y location of first electrode along this line | Header
0.0,0.0 | Coordinates of the first electrode
Line direction (0=X,1=Y) | Header
0 | Number specifying line direction
Line sign (0=positive,1=negative) | Header
0 | Specify whether electrode
| coordinates increase or decrease
| along line
File 2 parameters | Same set of parameters
Name of data file in RES2DINV format | for second file
d:\test\FILE2D_2.DAT |
X and Y location of first electrode along this line |
0.0,-0.5 |
Line direction (0=X,1=Y) |
0 |
Line sign (0=positive,1=negative) |
0 |
…. | Same for third
…. | file
Name of Output file in RES3DINV format | Header
d:\test\FILE_3D.dat | Name of 3-D data file
End of file | Header for end of file
The format used allows for the possibility that the survey had lines in 2
perpendicular directions.
A 2-D survey line has only one horizontal direction, and the coordinate of an
electrode along the survey line is given as the distance along the line, starting
from the first electrode. To determine the coordinate of the electrode in the XY
plane for a 3-D survey, we need to determine the coordinate of the first
electrode in the 2-D survey line within the X-Y survey grid. This gives a
reference point for which the coordinates of the other electrodes along the same
survey line can be calculated.
106
Secondly, it is necessary to know the orientation of the line, i.e. whether is
along the X-direction or Y-direction in the X-Y grid. Note that diagonal lines
are not allowed.
In a 2-D survey line, it is always assumed that the coordinate of the electrode
always increases starting from the first electrode (i.e. from left to right in a
typical pseudosection). However, the direction of increasing coordinate value
along the 2-D survey line might not always be the same as the positive X or Y
direction in the 3-D survey X-Y grid. The ‘Line sign’ parameters allows for the
possibility that the direction of the 2-D survey line is opposite to the direction
of the positive X or Y axis in the X-Y grid.
While it is possible to combine a number of 2-D lines into a 3-D data set, it
might not always be worthwhile to do so. Firstly, it is recommended that there
should be at least 5 parallel lines. Furthermore, the separation between the lines
should not be more than twice the unit electrode spacing along the lines. For
further details, please refer to Chapter 8 of the free “Tutorial : 2-D and 3-D
electrical imaging surveys” by M.H.Loke. If you do not have a copy, it can be
downloaded from the www.geoelectrical.com web site.
Concatenate data into RES2DINV format
This option enables the user to combine roll-along data files measured along
the same line into a single data file. All of the electrodes used in the survey
lines line along a single straight line. The file CONCATENATE_2D.TXT an
example script file. The contents of this file together with a description of the
format used is given below.
CONCATENATE_2D.TXT file | Comments
Concatenation of several data files in RES2DINV| Title
Number of files to concatenate | Header
3 | Number of data files
File 1 parameters | Header
Name of data file in RES2DINV format | Header
c:\data\file1.DAT | Full name plus path of file
X location of first electrode along this line | Header
0.0 | Coordinate of the first electrode
Line sign (0=positive,1=negative) | Header
0 | Specify whether electrode
| coordinates increase or decrease
| along line
File 2 parameters | Similar information for 2nd and 3rd
Name of data file in RES2DINV format | files follow
c:\data\file2.DAT |
…….. |
…….. |
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Name of Output file in RES2DINV format | Header
c:\data\file_123.DAT | Name of file to store combined data
End of file |
In some resistivity meter multi-electrode systems, each new record starts with a
zero location for the first data electrodes. In order to combine different data
files, the x-locations of the data points in some of the files will have to shifted
so that all of them have a common origin. In the above script file format, this is
done by entering the coordinate of the first electrode for the survey line. In
most cases, the direction of the lines are the same, for example the x-locations
increases from the left to the right. However, an option is provided where the
survey lines were measured in different directions.
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Appendix Q : Bedrock edge detection
In this option, the program attempts to pick the bedrock interface from the
model section and saves the x and y coordinates in an ASCII file. This method
is most successful where the bedrock has a sharp interface with the overlying
soil. One typical situation is shown in Figure 32. This survey was conducted to
map the a diorite bedrock with an intention of extending an existing quarry
(Turnbull 1986). The overburden has resistivities of less than 100 ohm.m while
the diorite has a resistivity of up to several hundred ohm.m.
The bedrock edge detection function is available within the ‘Display’ window,
as shown below.
On clicking this menu option, the model section will first be drawn, and then
the following dialog box is shown. On clicking the ‘Edge detection’ dialog is
shown.
There are 3 main parameters that the user need to select. The first is to set
upper and lower limits for the location of the boundary. By default, the
program will set them from 0 m. (on the ground surface) until the maximum
depth extent of the inversion model. In most cases, the upper limit is
commonly changed, particularly where there are large resistivity anomalies
near the surface (for example boulders). In this particular example, the
minimum depth is set at 15 m. for the bedrock interface.
The second important parameter is a minimum value for the bedrock. In this
example, a value of 150 ohm.m was chosen that probably corresponds to
partially weathered diorite. The third parameter is the maximum change in the
bedrock depth between adjacent electrodes. This is to prevent spikes in the
bedrock profile.
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In most cases, the default values for the other parameters should work well. By
default, it is assumed that the bedrock has a higher resistivity than the
overburden. However, a provision is made for cases where the bedrock or a
subsurface layer of interest has a lower resistivity.
For most situations, the robust model inversion option should be used
(Appendix K). This normally produces a sharper bedrock boundary in the
inversion model. Also, a model where cells have widths of half the actual unit
electrode spacing (Appendix O) is recommended. For example the Stud Farm
survey was conducted with a unit electrode spacing of 25 m., but inversion
model below uses smaller cell widths.
110
Figure 32. Apparent resistivity pseudosection from the Stud Farm survey
together with the inversion model. The interpreted bedrock profile is also
shown. Note that the bedrock on the right end of the line is below the
maximum depth of investigation of the survey line.
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Appendix R : Time-lapse resistivity inversion
In studying the changes of the subsurface resistivity with time, twodimensional
resistivity imaging surveys are often repeated over the same line at
different times. Such studies include the flow of water through the vadose
zone, changes in the water table due to water extraction (Barker and Moore
1998), flow of chemical pollutants and leakage from dams.
For time-lapse experiments, the changes in the subsurface resistivity are
estimated by using changes in the apparent resistivity measurements. Thus
accurate results can only be obtained if the apparent resistivity values
themselves are sufficiently accurate. It is best to avoid using the dipole-dipole
and pole-dipole arrays in such experiments if larger spacings are used due to
the relatively low signal to noise ratios. It might be safer to use the Wenner
array or preferably the Wenner-Schlumberger array. Otherwise, strange results
might be obtained.
The file TIMELAPS.DAT is an example data file with 3 sets of apparent
resistivity data. The upper part of the file together with comments about the
data format is as follows.
TIMELAPS.DAT file Comments
Example time-lapse data | Title
1.00 | Unit electrode spacing
7 | Array type, Wenner-Schlumberger in this
| example
350 | Number of datum points
1 | Mid-point of x-location of array is given
0 | No I.P. data
Time sequence data | Header to indicate time-lapse data
Number of time sections | Header
3 | Number of time series
Time unit | Header
Hours | Unit used in time measurement
Second time section interval | Header
1.0 | Time difference for second time data set
Second time section interval | Header
2.0 | Time difference for third time data set
1.50 1.00 1.0 11.868 11.868 11.868 | The format for each datum point is as follows :
2.50 1.00 1.0 11.867 11.867 11.867 | x-location, "a" electrode spacing, "n" factor,
3.50 1.00 1.0 11.863 11.863 11.863 | apparent resistivity for first data set, apparent
4.50 1.00 1.0 11.859 11.860 11.860 | resistivity for second data set,
5.50 1.00 1.0 11.855 11.856 11.856 | apparent resistivity for third data set.
6.50 1.00 1.0 11.851 11.851 11.851 |
The data format is largely similar to the normal data set with only one set of
readings. For a time-lapse data file, the main difference is the extra section just
112
before the data block with the apparent resistivity values. Here the header
"Time sequence data" is used to indicate the presence of the extra data sets
corresponding to the later time measurements. The following part of this extra
section contains information on the number of time series measurements (3 in
this example). The maximum number of time series data sets allowed is 12 if
the computer has at least 256 MB RAM, and 6 if the memory available is less.
For each data point, the format for the initial part is identical to that used for
the normal data sets. The only addition is that after the apparent resistivity
value for the first data set, the corresponding apparent resistivity values for the
later time data sets are given.
This program allows the use of joint inversion techniques using different types
of cross model constrains. When you select the "Select time-lapse inversion
method" under the "Change settings" menu, the follow dialog box is shown.
In the first set of options in the dialog box, several possible constrains which
guides the inversion process for multi-time data sets provided. Frequently, the
data from time-lapse surveys conducted at different times are inverted
independently. This method corresponds to the 'No constrains" option in the
above dialog box. The changes in the subsurface resistivity values are then
113
determined by comparing the model resistivity values obtained from the
inversions of an initial data set and the later time data sets. In many cases, such
an approach has given satisfactory results. However, in theory since the
inversion of each data set is carried out independently, there is no guarantee
that the differences in the resistivity values are only due to actual changes in
the subsurface resistivity with time.
In this program, a joint inversion technique that uses the model from the initial
data set to constrain the inversion of the later time data sets is used to minimise
possible distortions (Loke 1999). The initial data set inversion model is used as
a reference model in the inversion of the later time-lapse data sets. In the
"Minimise changes" option, a simple damped least-squares constrain to
minimise the differences in the model resistivity values between the initial
model and the time-lapse model is used. The "Least-squares smoothness
constrain" option uses a least-squares smoothness constrain to ensure that the
differences in the model resistivity values vary in a smooth manner. Finally, in
the "Robust smoothness constrain" option, a robust (Claerbout and Muir 1973)
smoothness constrain which minimises the absolute changes in the model
resistivity values is used.
In the second set of options, the user can choose to carry out the inversion of
all the time data sets simultaneously or sequentially. In the simultaneous
inversion option, the inversion of the first or reference data set is followed by
the inversion of the later time data sets in each iteration. Note that even if the
"No constrains" options is chosen earlier, the model obtained at the final
iteration for the first data set is still used as the starting model for the later time
data sets.
In the sequential inversion option, the full inversion of the first data set is first
carried out for about 5 iterations (or the selected number of iterations). The
model for the first data set for the final iteration is then used as the reference
model for the inversion of the later time data sets. The inversion of the later
time data sets starts only after the completion of the inversion of the first data
set. This sequential inversion is useful when the model section has very large
resistivity contrasts.
By default, the model obtained for the first data set is used as the reference
model for all the later time data sets, i.e. the same reference model is used for
all the other data sets. In case where there is a large change in the resistivity of
the models from the first to the last data set, an option is provided where the
model for the preceding data set is used as the reference model. In this case, the
model for the first data set is used as the reference model for the second data
set, while the model for the second data set is used as the reference model for
the third data set, and similarly for the other data sets.
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The last option, the time-constrain weight, gives the relative importance given
to keeping the later time models as similar as possible to the reference model.
If a large weight is used, for example 10.0, the models for the later time data
sets will be kept very similar to the reference model. This effectively
minimises changes across the time models and reduces the possibility of noise
in the data sets causing spurious changes between the models. However, this is
at the expense of increasing the data misfit, i.e. the RMS difference between
the calculated and measured data. By default, a value of 3.0 is used for the
time-constrain weight. A value of 1.0 gives equal importance to minimising the
time changes in the model and minimising the RMS data error.
After carrying out the inversion of the time-lapse data set, please switch to the
“Display” window to read in the results in the inversion file. Several options
are provided to display the results from the time-lapse models. The options
designed specifically for time-lapse inversion models are given near the bottom
of the “Display sections” list in the “Display” window, as shown below.
The "Display percentage change in resistivity" option will display the change
in the model resistivity obtained from the inversion of a later time data set
compared with the reference model from the inversion of the first data set. The
"Display resistivity ratio" option will display the ratio of resistivities of the
later time model compared with the reference model.
After displaying the sections with the percentage change in the model
resistivity values, you can change the time-lapse data set selected by using the
'Home' and 'End' keys. By default the results for the last time-lapse data set will
115
be shown. You can show the results of an earlier data set by pressing the
'Home' key.
Just below the menu options to display the time-sections, there is a " Change
factor in Archie's Law" sub-option. Archie's Law which gives the relationship
between the resistivity of a porous rock and the fluid saturation factor is
applicable for certain types of rocks and sediments, particularly those that have
a low clay content. In the case, the electrical conduction is assumed to be
through the fluids filling the pores of the rock. Archie's Law is given by
where ρ is the rock resistivity, ρw is fluid resistivity, φ is the fraction of the
rock filled with the fluid, while a and m are two empirical parameters (Keller
and Frischknecht 1966). For most rocks, a is about 1 while m is about 2. Under
certain special conditions, the above equation can be used to determine the
change in the fluid saturation or fluid resistivity with time.
If initially the subsurface material is saturated with water, and the change in the
resistivity is caused by withdrawal of water (i.e. a reduction in the fraction per
unit volume of the rock which is filled with water), the desaturation factor
(Keller and Frischknecht 1966) can be calculated from the change in the
subsurface resistivity. To calculate the desaturation factor, the value of the m
parameter in Archie's Law is needed. By default it is set to 2.0 but this value
can be changed by the user.
On the other extreme, consider a case where the fluid saturation factor does not
change but the resistivity of the fluid changes (for example in tracer
experiments with a conductive salt below the water table). The ratio of the
resistivity of the fluid at the later time to the initial resistivity can be calculated
directly from the model resistivities.
It must be emphasised that the above two situations are ideal cases. The results
are only valid if Archie's Law holds for the subsurface medium. In many cases,
the relationship between the medium resistivity and water content is much
more complicated (Olivar et al. 1990).
As an example of a field experiment of time-lapse measurements, Figures 33
and 34 shows the results from the tests on the flow of water through the
unsaturated zone conducted in Birmingham (Barker and Moore, 1998). Forty
thousand litres of water was poured on the ground surface near the 24 metres
mark along the survey line (Figure 33) over a period of 10 hours. The initial
data set collected before the water irrigation began together with the
corresponding inversion model is shown in Figures 33a and 33b. The
m
wa −
= φρρ
116
subsurface consists of sand and gravel is highly inhomogeneous. As a
comparison, Figure 33c shows the inversion model for the data collected after
the irrigation of the ground surface was completed. The distribution of the
water is not very clear from a direct comparison of the inversion models alone.
Figure 33. (a) The apparent resistivity and (b) inversion model sections from
the survey conducted at the beginning of the Birmingham infiltration study.
This shows the results from the initial data set which forms the base model in
the joint inversion with the later time data sets. As a comparison, the model
obtained from the inversion of the data set collected after 10 hours of irrigation
is shown in (c).
The water distribution is more easily determined from a plot of the percentage
change in the subsurface resistivity in the inversion models for the data sets
taken at different times (Figure 34) when compared with the initial data set
model. The data set collected at 5 hours after the pumping began shows a
reduction in the resistivity (of up to over 50 percent) near the ground surface in
the vicinity of the24 metres mark. The near-surface low resistivity zone reaches
its maximum extent and maximum amplitude after about 10 hours when the
pumping was stopped (Figure 34b). Twelve hours after the pumping was
stopped, the low resistivity plume has spread downwards and slightly outwards
due to infiltration of the water through the unsaturated zone. There is a
117
decrease in the maximum percentage reduction in the resistivity values near the
surface due to migration of the water from the near surface zone. This effect of
the spreading of the plume becomes increasingly more pronounced after 24
hours, 36 hours and 52 hours (Figures 34d, 34d, 34f) due to further migration
of the water. Note that the bottom boundary of the zone with approximately 20
percent reduction in the resistivity values tends to flatten out at a depth of about
3 metres (Figure 28e) where the plume from the surface meets the water table.
Missing data :- If a measurement was missing from a time series, enter 0.0 as
the value of the apparent resistivity for that particular time series. The program
will assume that a zero value is an indication of a missing data point.
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Figure 34. Sections showing the change in the subsurface resistivity values
with time obtained from the inversion of the data sets collected during the
infiltration and recovery phases of the study.
119
Appendix S : Incorporating data noise estimates
Some types of resistivity surveying instruments record an estimate of the
random noise for each measurement. This is usually made by repeating the
same measurement several times. The data error estimate is then calculated
from the standard deviation in the readings. This actually gives a measure of
the repeatability in the readings, i.e. the random noise. Note that this data error
estimate does not included sources of systematic errors such as coupling
between the cables.
To include the data error estimate in a data file, the error values are entered
after the apparent resistivity value. The file MODEL35_N.DAT is an example
of a data file from a surface survey with the error values. Part of the file is
shown below with an explanation of the changes needed.
MODEL35_N.DAT Comments
Block Model | Title
1.00 | Unit electrode spacing
7 | Wenner-Schlumberger array
230 | Number of data points
1 | Type of x-location (center)
0 | No IP
Error estimate for data present | Header to indicate error values
| present
Type of error estimate (0=same unit as data) | Header for type of error
0 | 0 to indicate it is same unit as data
| value
1.500 1.000 1.000 10.0145 0.1434 | x-loc., ‘a’ value, ‘n’ value, apparent
2.500 1.000 1.000 9.9706 0.1882 | resistivity, data point error value
3.500 1.000 1.000 10.3357 0.1761 |
Note there are two new additions in the data format. Firstly, just before the
section of the file with the measured apparent resistivity data points, there are 3
extra lines. The first line ‘Error estimate for data present’ is a header to indicate
that the data file contains the data error estimates. The second new line is a
header to explain the use of the next line. The third line contains a flag to
indicate to the program the units used in the error estimate. At present, use a
value of ‘0’ to indicate that the error value has the same units as the data value.
For example, if the measurements are given as ohm.m, then the error values
must also be in ohm.m The measurements in most instruments are given as
resistance values (i.e. ohm), or voltage plus current values which can be
converted to resistance values. To calculate the apparent resistivity value, the
resistance value is multiplied by a geometric factor. The error value recorded
by the instrument is probably in the form of a resistance (ohm) value. Thus the
error estimate recorded by the instrument must also be multiplied by the same
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geometric factor before it is entered into the DAT file format used by this
program.
The use of the flag for the unit used by the error value makes it possible for
future versions of the program to allow the use of other units for the error
value, for example the data in ohm.m while the error in ohm. Another
possibility is the error given as a percentage value.
The least-squares equation in (2) is modified to the following equation
( ) kd
T
d
T
d
T
d
T
qFgWWJdFJWWJ µµ −=+
where dW is a diagonal weighting matrix that incorporates the effect of the
data errors. Data points with a smaller error are given a greater weight in the
inversion process.
In an ideal situation, the noise estimate should be measured (for example by
reciprocal measurements). However, in most field surveys such noise estimates
are not measured due to time constraints. In such a situation, the best option is
probably to use the ‘Robust data constraint’ option (Appendix K) so that the
effect of outliers in the data on the inversion model is minimized. With this
option, a linear weight is given to the difference between the measured and
calculated apparent resistivity values. This makes the inversion result less
sensitive to outliers compared to the normal least-squares constraint where the
square of the difference between the measured and calculated apparent
resistivity values is used.
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Appendix T : Incorporating boundaries of known layers
In some cases, the depth profile of a boundary between two layers with very
different resistivity values is known from other sources; such as borehole data
or seismic refraction surveys. Very frequently, there is a rapid and sharp
change across the boundary, such as between a clay and sand layer. If the depth
to the boundary is known, this information can be incorporated into the
inversion so that the resistivities of the layers can be more accurately
determined.
The file CLIFLAYER4.DAT is an example data file where the boundary
between a gravel and underlying clay layer is known from a seismic refraction
survey (Scott et al. 2000). Part of the file is shown below with an explanation
of the changes needed.
CLIFLAYER4.DAT Comments
Clifton | Title
2 | Unit electrode spacing
1 | Wenner array
392 | Number of data points
1 | Type of x-location (center)
0 | No IP
3 2 58.63305 | x-loc., ‘a’ value, apparent resistivity
5 2 56.77204 | Second data point
7 2 54.79331 | Third data point
. | Other data points
. |
48 32 18.1012 |
50 32 17.94035 | Last data point
0 | No topography
0 | No fixed regions
0 | No water layer
Sharp layers present | Header to indicate sharp boundaries present
Number of boundaries | Information header
2 | Number of boundaries, two in this case
Boundary 1 parameters | Header for first boundary
Boundary type | Header for type of boundary
Layer | Layer type
Group weight | Header for weight, for future use
1.0 | Enter 1.0 here, not used at present
Number of points on boundary | Header
16 | 16 points for this boundary
x and z coordinates of pts | Header
0.0 2.3 | x-location and depth of first point
18.0 2.3 | x-location and depth of second point
. | x-location and depth of other points
. | along the boundary
88.0 3.2 | x-location and depth of second last point
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92.0 3.2 | x-location and depth of last point
Boundary 2 parameters | Header for second boundary
Boundary type | Header for type of boundary
Layer | Layer type
Group Weight | Header for weight, for future use
1.0 | Enter 1.0 here, not used at present
Number of points on boundary | Header
3 | 3 points for this boundary
x and z coordinates of points | Header
0.0 6.7 | x-location and depth of first point
45 6.7 | x-location and depth of second point
92 6.7 | x-location and depth of last point
0 | end with a few zero’s
0 |
0 |
In the above example, there are two boundaries. If there is more boundaries,
the section with ‘Boundary 3 parameters’ until the x-location and depth of the
last point along the second boundary is repeated. The file
MODEL_BOUNDARY_GENERAL.DAT gives an example of a data file with
the general array format with only one boundary.
Figure 35 shows the inversion of the CLIFLAYER4.DAT data set using
different inversion options. The first model using the smooth inversion method
shows a gradational transition between the sand and underlying lower
resistivity clay layer (Figure 35b). The depth to the boundary is not well
determined. The use of the blocky or robust inversion method (Loke et al.
2003) gives a much sharper boundary (Figure 35c). The addition of the
boundary from the seismic refraction survey helps to further sharpen the
boundary (Figure 35d).
The greatest limitation of this option at present is that the depths to the layers
are fixed throughout the inversion. An option to allow the depths to be
automatically changed will probably be added in a future update.
123
Figure 35. Models for the Clifton survey from the different inversion methods
are shown together. Note the boundary between the high resistivity sand layer
and the underlying low resistivity clay layer is much better resolved in the
blocky and sharp boundary inversion methods.
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Appendix U : Special topography information for mineral exploration
surveys
The RES2DINV software was originally written for surveys by engineering
and environmental geophysicists. Thus the default settings in the program
follow the practices in this field. One important difference is that in
engineering/environmental surveys, the electrodes are laid out such that the
distance along the ground surface is constant by using a multicore cable with a
constant spacing between the takeouts. This saves time and the expense of
carrying out a detailed topographical survey before the resistivity survey. The
RES2DINV program assumes that the x-locations of the electrodes are given in
terms of distances along the ground surface.
However for mineral exploration surveys (with bigger budgets) it is common to
carry out a detailed topographical survey before the resistivity and IP survey,
and the electrodes are placed such that the true horizontal distance (rather than
the surface distance) between the electrodes is constant. In areas with steep
topography, it is possible for the vertical distance between two adjacent
electrodes to exceed the horizontal distance (but still less than the surface
distance). For surveys where the true horizontal distance is used for the xlocation
of the electrodes, the general array data format must be used (see
Appendix L). Furthermore, the indicator for the type of x-location in the data
file must be set to 1 (see the MIXED.DAT example in page 91, and also the
description for such a case in pages 93 and 94).
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Appendix V : Plotting methods for the gradient array.
There is currently no standard method to plot the apparent resistivity data from
surveys with gradient array. There are probably two types of surveys with the
gradient array. The first and traditional type survey use very few different C1C2
positions (usually only one with C1 and C2 located at the two ends of the
line), but many different P1-P2 positions. This was mainly used in mineral
exploration surveys.
The second and modern type, mainly used with multi-channel multi-electrode
resistivity meter systems, uses many different C1-C2 positions. To
accommodate both possibilities, two types of data plotting options are
available. As most surveys will likely to be carried out using the second type of
survey with multiple C1-C2 positions, this is described in more detail. The
papers by Dahlin and Zhou (2004, 2005) have some information about such
surveys.
Firstly, a brief description of the data format for data from gradient array
surveys. The general array data format (Appendix L) must be used with a subarray
number of 15. Below is the initial part of the example GRADIENT.DAT
file with comments about the format.
GRADIENT.DAT file Comments
Gradient array | Title
1.0 | Unit electrode spacing
11 | Array type (11 for general array)
15 | Sub-array type 15
Type of measurement (0=app. resistivity,1=resistance) | Header
0 | 0 here to indicate apparent resistivity values
1792 | Number of data points
1 | Indicator for type of x-location
0 | No IP values, 1 if I.P present
4 0.0,0.0 9.0,0.0 1.0,0.0 2.0,0.0 5.0588 | The format for each data point is
4 1.0,0.0 10.0,0.0 2.0,0.0 3.0,0.0 5.0724 | Number of electrodes used in
.
.
4 46.0,0.0 118.0,0.0 78.0,0.0 86.0,0.0 4.2571 | Last two data
4 48.0,0.0 120.0,0.0 80.0,0.0 88.0,0.0 4.2258 | points
0,0,0,0,0 | End with a few zeros
To select the type of plotting method to use, before reading the data file, click
'Change Settings' and then 'Data/Display Selection', and then 'Type of gradient
array plot' as shown in the following figure.
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On selecting the ‘Type of gradient array’ sub-option, the following dialog box
is shown.
The ‘Use exact pseudodepth’ choice is the default option. However, the
program will automatically change to the approximate pseudodepth method if
it finds the exact pseudodepth method is not suitable for the data file. This
occurs for surveys with the traditional type of gradient arrays where only a few
C1-C2 positions are used.
As an example, the plot of the GRADIENT.DAT file data set in the form of
profiles is shown below.
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Figure 36. Plot of GRADIENT.DAT data in the form of profiles.
Note the data set each pseudodepth is split into two profiles which are drawn in
different colours. This is because there are two possible configurations with the
same pseudodepth.
Figure 37. Two different configurations of the gradient array with the same
pseudodepth but with the potential electrodes at different ends of the array.
Gradient array configuration with (a) right parity and (b) left parity.
In the above example, the distance between the C1 and C2 electrodes are the
same. The offset of the P1-P2 dipole from the C1 electrode in (a) is the same as
the offset of the dipole from the C2 electrode in (b). However, the two
configurations are sensitive to different parts of the subsurface (Dahlin and
Zhou 2005). To provide a smooth plot for the profile, the data from the ‘right’
and ‘left’ configurations are plotted in different profiles.
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The inversion model of the GRADIENT.DAT data set that also shows the plot
of the data in apparent resistivity pseudosections is shown below.
Figure 38. The inversion result of the GRADIENT.DAT data with the apparent
resistivity and model sections.
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Special OhmMapper Note
Data collected by the OhmMapper system can be converted into the format
used by the RES2DINV program using the 'DataMap for OhmMapper'
program provided by Geometrics, Inc. This is a Windows 95/98/2000/NT
based program. After starting the program, please click the EXPORT option to
carry out the data conversion. For futher details, please refer to the
OhmMapper manual provided by Geometrics.
The figure below shows an example of a data set collected by the OhmMapper
system together with the inversion model produced by the RES2DINV
program. The survey was conducted over an area with weathered granite. The
data set is given in the file OHMMAPPER.DAT. The measurements were
made using the dipole-dipole array with a dipole length "a" spacing of 10
metres and with n values of 0.5 to 3.5 (Appendix A). The data set has 732 data
points while the inversion model consist of 1240 cells. The inversion of this
data set it took about 15 minutes on a 300 MHz Pentium II computer.
Figure 39 : (a) Apparent resistivity pseudosection measured with an
OhmMapper mobile resistivity surveying system. (b) Model section obtained
by RES2DINV program.
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DISCLAIMER
This software is provided "as is" without any express or implied warranties
including its suitability for a particular purpose. Neither the author nor the
subagent will assume responsibility for any damage or loss caused by the use
of this program. In the event of program bugs, every effort will be made to
correct the bugs and a replacement program will be provided for a nominal
charge to cover postage and handling. Faulty dongles or program disks will be
replaced free of charge within the first 6 months from the date of purchase to
registered users. Registered users are entitled to free updates and support
within the first year.
SUPPORT
Please contact your distributor if you have any questions concerning this
program. A frequent source of queries is when the results obtained are not what
you expect, or the program refuses to accept your data file. In such a case,
support will only be provided if a copy of the data file is sent together as an
attachment with your email, preferably compressed into a ZIP file. The most
common causes of problems are (a) the data in the DAT file is not given in the
correct RES2DINV format (b) excessive noise in the data set (particularly for
dipole-dipole surveys and/or IP data sets) (c) instrument malfunction or field
survey errors. It is only possible to trace the source of the problem if a copy of
the data file is provided.
Please note that support is only available for registered users of the full version
of the program. It is not possible to provide technical support for users of the
demo version of this software. For technical support, you can contact the
software provider by email at the following addresses. Please attach a copy of
your data file to your email.
geotomo@tm.net.my
support@geoelectrical.com
The following information will be required before technical support is
provided.
1). Your dongle ID number. This ID number is displayed near the bottom of
the initial information box when the RES2DINV program starts up if the
dongle is attached to the computer.
2). The name of your company or institution.
3). Approximate date your company/institution purchased the software.
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What’s New
Version 3.00 - Major upgrade to Windows 3.1 and 95. Maximum number of
electrodes increased to 500. Multi-tasking support for Windows 95. Support for
any Windows compatible graphics card and printer.
Version 3.01 - Improvements to finite-difference subroutine to calculate the
Jacobian matrix which is now about twice as fast as the earlier versions.
Version 3.10 - Support for underwater surveys. Direct incorporation of
topography into inversion model using a distorted finite-element grid.
Version 3.11 - The time taken by the finite-element subroutine to calculate the
Jacobian matrix is reduced. An option to use a finer mesh for the finitedifference
or finite-element forward modelling method is added.
Version 3.12 - Non-integer values for the “n” factor for the dipole-dipole, poledipole
and Wenner-Schlumberger arrays supported (please refer to Appendix
A). The maximum limits for the number of data levels and model layers
increased to 52 and 17 respectively.
Version 3.13 - The ratio of the largest electrode spacing to unit electrode
spacing for the Wenner and pole-pole array was increased from 32 to 64. The
maximum number of data levels is now 64. The maximum number of model
layers was also increased to 18.
Version 3.20 - Support for IP data added.
Version 3.21 - The maximum number of electrodes was increased to 650.
Improvements has been made to the disk-memory swapping subroutines so that
for a given amount of RAM the number of datum points the program can
handle is increased. For computer systems with more than one hard-disk drive,
the program will automatically select the drive with the most free disk space to
store the temporary disk swap files.
Version 3.22 - Slight improvements to the use of memory in the IP inversion
section. The size of the IP data set that can be handled for a given amount of
memory was increased. An option to optimise the damping factor
automatically during the inversion process was added. Support for the
“reverse” pole-dipole array added (see Appendix A). Support for a command
line batch mode included (see Appendix I). An option to plot the model section
in the form of rectangular blocks was also added.
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Version 3.30 - Support for cross-borehole surveys added. An option to allow
the number of model parameters to exceed the number of datum points was
also added.
Version 3.31 - An option for a used defined model added. In this model, the
user specifies the thickness of the first layer and the factor to increase the
thickness for each subsequent deeper layer. The program will also
automatically update the directory used for the input data files and the output
inversion files listed in the RES2DINV.INI file.
Version 3.32 - An option to extend the subdivision of the subsurface into
blocks to the edges of the survey line was added. Option to display the
uncertainty in the model resistivity values was also added. Version 3.33 - An
option to incorporate the effects of the remote electrodes used in surface
resistivity surveys with the pole-pole and pole-dipole arrays was added.
Version 3.34 - A few bug fixes. The user can now scale the depths of the model
layers so that the depth to the last layer can be much greater than the default
limit allowed by the program. When the program saves the model values in the
XYZ format, it will now also save the coordinates of the corners of the blocks
in the model. An option to use a very fine mesh in the vertical direction for
resistivity contrasts of greater than 250:1 was added, as well as an option for 6
nodes in the horizontal direction between adjacent electrodes.
Version 3.35 - The user can now set the maximum number of electrodes, from
150 to 1500, via the JACOBWIN.EXE program. Drawing of colour contour
sections is now significantly faster on most computers.
Version 3.36 - A robust least-squares inversion option was added. For very
noisy data with ‘outliers’, the resulting model will be less sensitive to such
datum points when the robust data inversion method is selected. For areas
where the subsurface geology has sharp interfaces, the robust model inversion
method will give better results.
Version 3.40 - Support for non-conventional arrays for resistivity surveys.
Version 3.41 – Two new methods for topographic modelling using a damped
distorted grid and the inverse Schwartz-Christoffel transformation added.
Version 3.42 - Support for remote electrodes for IP surveys.
Version 3.43 - Support for the Wenner Gamma array, and underwater surveys
with non-conventional arrays. Maximum number of electrodes increased to
2000. The program has also been optimised for data sets where the unit
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electrode spacing has been reduced by half of the actual value so as to get a
model where the width of the blocks is half the usual size. This helps in cases
where there are very large lateral resistivity variations near the surface.
Version 3.44 - Support for IP surveys with non-conventional arrays. This
feature is useful in some cases where data from a series of overlapping
collinear 1D sounding survey lines can be combined into a single 2-D data set
to obtain a 2-D model.
Version 3.45 - Option to save results in SURFER format added. Also support
for surveys with some electrodes underwater and some electrodes above the
water surface level added.
Version 3.46 - Minor additions for data in general array format. Option to use a
model with half the unit electrode spacing for data in general array format is
added (see the file RATCMIX2.DAT for an example). It is now possible to
carry out the inversion of data in the general array format with the demo
version, but the results will only be displayed temporarily on the screen during
the inversion. The damped distorted grid finite-element method is set as the
default method for topographic modelling.
Version 3.47 – An option to carry out the inversion of IP data sequentially was
added. Slight changes in the menu structure.
Version 3.48 – Support for up to 4 boreholes in cross-borehole option.
Version 3.49 – Incomplete Gauss-Newton inversion option added. Maximum
number of electrodes increased to 4000, and maximum number of data points
to 20000. Option to combine a number of 2-D data files in RES2DINV format
into a single 3-D data file in RES3DINV format added.
Version 3.50 – Bedrock edge detection and time-lapse options added.
Version 3.51 – Option to include data noise estimates included.
Version 3.52 – Option for surveys with floating electrodes added. Support for
topography in cross-borehole surveys included.
Version 3.53 – Sparse inversion option for very long survey lines (2000 to
16000 electrode positions) added. This method inverts the entire data set and
model at a single time to produce a continuous and seamless model. New
format for batch mode option script file which makes use of the files
containing the inversion parameters produced by the RES2DINV program.
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Version 3.54 – Option to include boundaries of layers from seismic or borehole
surveys added.
Version 3.55 – Plot of profiles and pseudosections for the gradient array.