Department of Geological Sciences, Faculty of Sciences
Masaryk University/Brno & Czech Geological Society
September 12-14, 2011
Short Course on Geological HazardsShort Course on Geological Hazards
Lecture 2Lecture 2 (Mon PM):(Mon PM):
Four Earthquake Topics Relevant to SHAFour Earthquake Topics Relevant to SHA
•• Tectonic EnvironmentTectonic Environment (Age, Stress Regime)(Age, Stress Regime)
•• KeyKey EquEqu. Parameters. Parameters (Mo,(Mo, Mw, stress drop, slip)Mw, stress drop, slip)
•• SeismicitySeismicity ParametersParameters (n[Mw],(n[Mw], MmaxMmax,, McharMchar))
•• Ground MotionsGround Motions (in Time and Spectral Domains)(in Time and Spectral Domains)
Klaus H. JacobKlaus H. Jacob
Lamont-Doherty Earth Observatory
of Columbia University, NY
jacob@ldeo.columbia.edu
Before Addressing Seismic Hazards Assessment (SHA)
itself, we first look at some basic Seismology Facts:
i.e. Basic Issues of:
•• The Tectonic EnvironmentThe Tectonic Environment (Age of Crust and Activity, Stress, ...)(Age of Crust and Activity, Stress, ...)
•• Individual EarthquakesIndividual Earthquakes (Moment, Magnitude, Stress Drop, ......)(Moment, Magnitude, Stress Drop, ......)
•• SeismicitySeismicity RatesRates (Gutenberg-Richter Power Law)(Gutenberg-Richter Power Law)
•• Ground MotionsGround Motions (as f(d,Mw), in Time and Spectral Domains, etc.)(as f(d,Mw), in Time and Spectral Domains, etc.)
that are Relevant to Seismic Hazard Assessment (SHA)
Basic Observations on:
•• The Seismo-Tectonic EnvironmentThe Seismo-Tectonic Environment
•• Individual Earthquakes,Individual Earthquakes,
==============================
•• Seismicity Rates, andSeismicity Rates, and
•• Ground MotionsGround Motions
Relevant to Seismic Hazard Assessment (SHA):
The principal stresses are ordered by magnitude:The principal stresses are ordered by magnitude: σσ11 >> σσ22 >> σσ33
σσ11 σσ22
σσ33
σσ11
σσ22
σσ33
σσ11
σσ22
σσ33
σσ11
σσ22
σσ33
σσ33
σσ11
σσ22
σσ33
σσ11
Distributed Rifting vs. Single Localized Rift Valley: both strongly attenuate propagation of seismic waves: “Low Q”
Active
M > 8
Old
Low Q / Very High Q / Medium Q /
High Attenuation Very Low attenuation Medium Attenuation
Questions?
2a
Basic Observations on:
•• The Tectonic EnvironmentThe Tectonic Environment
•• How to Quantify an Individual EarthquakeHow to Quantify an Individual Earthquake
(SHA-relevant parameters only)(SHA-relevant parameters only)
==============================
•• Seismicity Rates andSeismicity Rates and
•• Ground MotionsGround Motions
Relevant to Seismic Hazard Assessment (SHA):
Basic Earthquake Quantities and Relations for Quantifying Seismicity Rates:
EarthquakeEarthquake MomentMoment:: Mo = µAu µ is the elastic shear modulus of rock near the fault
A is the area of the earthquake rupture
u is average displacement across ruptured fault
Mo = (16/7) r3 Δσ with r fault radius and Δσ static stress drop ~const.
Moment MagnitudeMoment Magnitude:: Mw = 2/3 log10 Mo - 10.7
---------
Static Stress Drop:Static Stress Drop: ΔσΔσ == MMoo (7/16) / r(7/16) / r33
= (7/16)= (7/16) µµ (u/r)(u/r)
8.58.5 MMoo ((ffoo//ββ))33 ≈≈ constconst
Corner Frequency:Corner Frequency: ffoo = 0.37= 0.37 ββ / r =/ r =
~~ ββ / (/ (MMoo//ΔσΔσ))1/31/3 ~~ MMoo
-1/3-1/3
Moment Rate:Moment Rate: Mo= µAs
with s long-term slip rate
ΔσΔσ
Return PeriodReturn Period vsvs. Fault Slip. Fault Slip Rate and MagnitudeRate and Magnitude
Most Current PSHAs use Saturation-Free
MomentMoment Magnitude Mw
sec
m
m
SSSS
DSDS
Rupture Process / Duration of Rupture / Slip Distribution / Rise Times / Stress Asperities - Barriers / Directivity:
AllAll affect the Spectral Content of Radiated Seismic Wavesaffect the Spectral Content of Radiated Seismic Waves
Corner Frequency fo determined by Source
fmax determined largely by Crust:
Wave Scattering, Q etc.
ffoo = 0.37= 0.37 ββ / r (Corner Frequency)/ r (Corner Frequency)
slowlyslowly decreasesdecreases with Moment :with Moment :
ffoo ~~ ββ / (/ (MMoo//ΔσΔσ))1/31/3
and since stress dropand since stress drop ΔσΔσ ≈≈ const,const,
=>=> 1/T1/Too = f= foo ~~ MMoo
-1/3-1/3
or:or: TToo ~~ MMoo
1/31/3
Measurement of Distances to the Source:Measurement of Distances to the Source:
Details are important for Ground Motion Prediction EquationsDetails are important for Ground Motion Prediction Equations
(GMPE)(GMPE) and , therefore, PSHAand , therefore, PSHA !!!!
Depth is important for Ground Motion Prediction EquationsDepth is important for Ground Motion Prediction Equations
and , therefore, to PSHA, especially in Stable Continental Regions (SCR),and , therefore, to PSHA, especially in Stable Continental Regions (SCR),
wherewhere hypocenter depths tend to be very shallowhypocenter depths tend to be very shallow!!!!
Ground Motion Prediction EquationsGround Motion Prediction Equations (GMPEs, here for PGA) as a function of Distance for discrete Magnitudes(GMPEs, here for PGA) as a function of Distance for discrete Magnitudes
and for different authors/datasets for the Central and Eastern US,and for different authors/datasets for the Central and Eastern US, i.e.i.e. Stable Continental Regions (SCR).Stable Continental Regions (SCR).
Note the degree ofNote the degree of ““epistemicepistemic”” uncertainty between the different authorsuncertainty between the different authors’’ GMPEs.GMPEs.
Ground Motions can be represented either in Acceleration, Velocity or Displacement Space.Ground Motions can be represented either in Acceleration, Velocity or Displacement Space.
Although they contain the same information, they have differentAlthough they contain the same information, they have different Engineering Applications: Forces,Engineering Applications: Forces, vsvs. Strains. Strains vsvs. Displacements. Displacements
ET= Total Energy Radiated;
EEdd = Energy in “direct” Wave Package;
Ec = Scattered Energy transferred into the “coda” of the waves;
Qs = “Scattering-Q”
NOTE:NOTE: (1/Qs) is the energy scattered per wave length of propagation path;
High Qs => Low Scattering; Low Qs => High Scattering;
EEdd
Attenuation / Scattering:Attenuation / Scattering:
Questions?
2b
Basic Observations on:
•• The Tectonic EnvironmentThe Tectonic Environment
•• Individual Earthquakes,Individual Earthquakes,
•• Seismicity RatesSeismicity Rates (and Maps)(and Maps)
•• Ground MotionsGround Motions
Relevant to Seismic Hazard Assessment (SHA):
Probability PP, Exposure Time tt, Avg. Recurrence Period TT, and Annual
Avg. Frequency of Occurrence λλ=1/T=1/T, for a Poisson ProcessPoisson Process of
Randomly Occurring (causally independent) Events (Eqs., ....):
P = 1- e-t/T = 1 - e-λt with T = 1/λ or λ = 1/T
1-P = e-t/T ; ==> ln (1-P) = ln e-t/T = -t/T
λ = - [ln (1-P)] / t = average rate
T = - t / ln (1-P) = average Rec. Period
_____________________________
P% t(y) T (y)
_____________________________
10% 50y 475y
2% 50y 2475y
_____________________________
~~62%62% t = Tt = T
_____________________________
Note: For t << Tt << T ==> PP ≈≈ 1/T1/T = λ
TT
tt
4 5 6 7 8
N=1
10
100
1000
10 000
Log N = A - bM
N= 10(A - bM) = No/10bM
Log CumulativeLog Cumulative Number NN of Earthquakes with Magnitude ≥M per 100 yr
in the Contiguous US, vs. Magnitude MM.
Example: A=8 (No=108), and b=+1 (Slope is -1);
“Power Law”
Magnitude M
Basic Relations for Quantifying Seismicity Rates:
Gutenberg-RichterGutenberg-Richter (Power)(Power) LawLaw
of Cumulative Earthquake Frequency N vs. (Moment) Magnitude Mw:
log10 N = A - b Mw valid for a given area F(km2) and time period T (years)
N = 10 A - b Mw
Normalized Form:Normalized Form: log10 n = a - b Mw n = number of earthquakes per year per km2
n = 10 a- b Mw = no 10- b Mw = no/10b Mw
no = 10a is the number of earthquakes per year per km2 with magnitude M≥0
Using the Natural Logarithm lnNatural Logarithm lnee instead ofinstead of loglog1010, the exponential G-R frequency of
occurrence vs. Magnitude equation takes on the form:
ln n = no - β M n = number of earthquakes per year
n (M) = no e-βM with no=10a number of earthquakes per unit time for M≥0;
and β = b ln10 ≈ 2.3b; when minimum magnitude Mmin is used, then
n(M) = no min e-β(M-Mmin) for Mmin ≤ M ≤ ∞∞ and no min number of earthquakes
per unit time for M≥Mmin;
For Details on equations forFor Details on equations for truncated exponential functions with Mtruncated exponential functions with M≥≥MmaxMmax, as often, as often
used in PSHA, see McGuire (2004) pp. 38-43 and graph shown on subsequent slide.used in PSHA, see McGuire (2004) pp. 38-43 and graph shown on subsequent slide.
Use of truncatedtruncated G-R relation by specifying an upper bound magnitude mu
Using Different Felt Intensity Scales:Using Different Felt Intensity Scales:
MMI ModifiedMMI Modified MercalliMercalli Intensity,Intensity,
EMS (EuropeanEMS (European MacroseismicMacroseismic Scale)Scale)
andand
TranslatingTranslating them into Magnitudes:them into Magnitudes:
e.g.:e.g.:
mmll = 1.3 + 0.6 Ie= 1.3 + 0.6 Ie
WithWith IeIe = epicentral Intensity in MMI= epicentral Intensity in MMI
after Gutenberg & Richter, 1942after Gutenberg & Richter, 1942
Other Authors UseOther Authors Use Felt Area FFelt Area F
for a given MMIfor a given MMI
and relate it to magnitude (M,and relate it to magnitude (M, mmbb, m, mll, M, Mss, etc.), etc.)
Different Relations must be used for active regions vs. SCR when translating Felt Areas of historic earthquakes into Magnitudes,
Questions?
2c
Basic Observations on:
•• The Tectonic EnvironmentThe Tectonic Environment
•• Individual Earthquakes,Individual Earthquakes,
•• Seismicity RatesSeismicity Rates
•• Ground Motion RelationsGround Motion Relations
Relevant to Seismic Hazard Assessment (SHA):
Different GMPE must be used for active regions vs. SCR
ENA / CEUS = SCR
ground motions contain
more high frequencies
In WNA / tectonically active regions
high frequencies are suppressed !
The ENA / CEUS = SCR ground
motions
contain
more high frequencies
especially at large distances R
TrTr ≈≈ 500 yr500 yr
TrTr ≈≈ 10 000 yr10 000 yr
Uniform Hazards Spectra UHS
For two annual probabilities
10% and 0.5% in 50 years.
For a UHS, the likelihood is the same
for all spectral amplitudes Sa(f)
irregardless of frequency f.
The lower the annual probability,
the more the spectral
ground motion levels from ENA, or
Stable Continental Regions (SCR)
in general, start to exceed the WNA
(or active region -) spectral
Ground Motion levels,
at high frequencies f≥10Hz.
Note high scatter of data,Note high scatter of data,
represented in the GMPE byrepresented in the GMPE by εε
Ground Motions can be represented either in Acceleration, Velocity or Displacement Domain.Ground Motions can be represented either in Acceleration, Velocity or Displacement Domain.
Although they contain the same information, they have differentAlthough they contain the same information, they have different Engineering Applications: Forces,Engineering Applications: Forces, vsvs. Strains. Strains vsvs. Displacements. Displacements
=2π/Tο
Pick the largest response excursion xlargest response excursion xmaxmax of the damped single degree of freedom
oscillator (SDFO) with a given natural period To = 2π/(√ k/m), and damping
β=b/2m, and plot xxmaxmax at period To; then repeat for many To ==> This yields a
Displacement Response Spectrum SSdd((TToo).). Obtain “Pseudo” Velocity- and
Acceleration-Spectra SSvv and SSaa by multiplying Sd(To) by ω and ω2
, respectively.
Sd(To)
k b
ü(t)ü(t)
β=b/2m
What is a SDOF Damped Elastic Response Spectrum? And how to construct it:What is a SDOF Damped Elastic Response Spectrum? And how to construct it:
Peak Levels PGA, PGV, PGD on SeismogramsPeak Levels PGA, PGV, PGD on Seismograms
for Acceleration, Velocity and Displacementfor Acceleration, Velocity and Displacement
are lowerare lower than the Response Spectralthan the Response Spectral
valuesvalues SSaa , SSvv and SSDD , but at high frequencies, but at high frequencies ff
(short Periods T)(short Periods T) SSaa approaches PGAapproaches PGA
asymptotically.asymptotically.
SSaa
Site Response ….. is the local modification of ground motions due to near- & subsurface
soil and rock conditions. Microzonation Example: Ground Shaking
Amplification Map of the L.A. Basin and vicinity (Field et. al., 2000)
Site Response / Microzonation
To = 4HTo = 4Hss // ββss
ΑΑ ≈≈ Rock Imp. / Soil Imp.Rock Imp. / Soil Imp.
== ρρrrββrr // ρρssββss
This concludesThis concludes
Basic Observations on:
•• The Tectonic EnvironmentThe Tectonic Environment
•• Individual Earthquakes,Individual Earthquakes,
•• Seismicity Rates andSeismicity Rates and
•• Ground MotionsGround Motions
Relevant to Seismic Hazard Assessment (SHA):
Questions?
2d