Magnetic Anisotropy of Rocks Martin Chadima AGICO Inc., Brno, Czech Republic (chadima@agico.cz) Institute of Geology of the Czech Academy of Sciences, Prague, Czech Republic  Tarling, D.H. & Hrouda, F. 1993. The Magnetic Anisotropy of Rock. Chapman & Hall, 217 pp.  Lanza, R. & Meloni, A. 2006. The Earth’s Magnetism: An Introduction for Geologist. Springer, 278 pp. (Chapter 5).  Hrouda, F. 2007. Magnetic Susceptibility, Anisotropy. Encyclopedia of Geomagnetism and Paleomagnetism. Springer. 546-560.  Sagnotti, L. 2009. Magnetic anisotropy. Encyclopedia of Solid Earth Geophysics. Springer. 717-729.  Tauxe, L. 2013. Lectures in paleomagnetism. http://magician.ucsd.edu/Essentials_2/WebBook2ch13.html#x15-15500013.  Hrouda, F., 1982. Magnetic anisotropy of rocks and its application in geology and geophysics. Geophysical Surveys, 5, 37–82.  Borradaile, G. J. & Henry, B. 1997. Tectonic applications of magnetic susceptibility and its anisotropy. Earth Science Reviews, 42, 49–93.  Jackson,M.J. & Tauxe, L. 1991. Anisotropy of magnetic susceptibility and remanence: developments in the characterization of tectonic, sedimentary, and igneous fabric. Reviews of Geophysics, 29, 371–376.  Rochette, P., Jackson, M. J. & Aubourg, C. 1992. Rock magnetism and the interpretation of anisotropy of magnetic susceptibility. Reviews of Geophysics, 30, 209–226. Magnetic Anisotropy of Rocks Literature Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing Magnetic Anisotropy of Rocks Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 1. Definition and application in geology  Magnetic anisotropy is a directional variability of a certain magnetic property, usually Anisotropy of Magnetic Susceptibility (AMS)  Tool to study rock texture (Petrofabric)  Compared to the other methods of fabric analysis (U-stage, X-ray texture goniometry, neutron texture goniometry, EBSD), AMS is fast, cheap, high-resolution, non-destructive.  It can be applied to many samples covering whole outcrops, drill cores, or geological units.  Application in structural geology and tectonics, volcanology, sedimentology, and paleomagnetism. Definition 1. Definition and application in geology H M k = M / H M = Mi + Mr Mi = k  H Magnetic susceptibility Remanent magnetizationInduced magnetization 1. Definition and application in geology  Magnetic susceptibility is the ability to acquire induced magnetization, i.e. ability to get magnetized k = Mi / H Diamagnetism k < 0 Paramagnetism Ferromagnetism (s.l.) M M M k > 0 k >> 0 Induced magnetization antiparallel to the external field Induced magnetization parallel to the external field Complex relationship between external field and induced magnetization: hysteresis curve Magnetic susceptibility relatively low and negative Magnetic susceptibility relatively low and positive Magnetic susceptibiliy relatively high No remanence No remanence Remanent magnetization quartz calcite aragonite pyroxene hornblende olivine micas iron magnetite hematite pyrrhotite 1. Definition and application in geology M = k  H  Magnetic susceptibility is the ability to acquire induced magnetization, i.e. ability to get magnetized Contribution of selected minerals to whole rock susceptibility k = M / H 1. Definition and application in geology Magnetically isotropic material M1 = k H1 M2 = k H2 M3 = k H3 Magnetization of anisotropic materials M1 = k11 H1 + k12 H2 + k13 H3 M2 = k21 H1 + k22 H2 + k23 H3 M3 = k31 H1 + k32 H2 + k33 H3 Matrix notation M1 = k11 k12 k13 H1 M2 = k21 k22 k23 H2 M3 = k31 k32 k33 H3 Anisotropy magnetic susceptibility (AMS) Vector of magnetization Susceptibility tensor Vector of field intensity 1. Definition and application in geology Anisotropic magnetizing ellipsoidal grain  If one magnetizes an ellipsoidal grain of magnetite and the magnetizing field is parallel to ellipsoid axes, the magnetization is parallel to the field.  Otherwise, the magnetization deflects from the field.  The relationship between field and magnetization is described by the susceptibility tensor. M = k  H 1. Definition and application in geology M1 = k11 k12 k13 H1 M2 = k21 k22 k23 H2 M3 = k31 k32 k33 H3 Ellipsoid as geometrical visualization of tensor 1. Definition and application in geology Rock fabric defined from magnetic anisotropy Magnetic fabric Shape parameter Degree of anisotropy X Y k1  k2  k3 km = (k1 + k2 + k3) / 3 P = k1 / k3 T = (2h2 - h1 - h3) / (h1 - h3) where h1 = ln k1, h2 = ln k2, h3 = ln k3 +1 > T > 0 oblate (planar) fabric -1 < T < 0 prolate (linear) fabric Mean susceptibility Principal susceptibilities 1. Definition and application in geology Shapes of anisotropy ellipsoids Rotational prolate Triaxial prolate Triaxial oblate Neutral Rotational oblate 1. Definition and application in geology k1  k2  k3 km = (k1 + k2 + k3) / 3 P = k1 / k3 L = k1 / k2 F = k2 / k3 T = (2h2 - h1 - h3) / (h1 - h3) where h1 = ln k1, h2 = ln k2, h3 = ln k3 +1 > T > 0 -1 < T < 0 Pj = Pa a = (1+T2 / 3) Quantitative parametrs of anisotropy principal susceptibilities mean susceptibility degree of anisotropy degree of magnetic lineation degree of magnetic foliation shape parameter oblate (planar) ellipsoid prolate (linear) ellipsoid corrected degree of anisotropy 1. Definition and application in geology 1. Definition and application in geology Flinn diagram (L-F plot) 1. Definition and application in geology Jelinek diagram (Pj-T plot) N 90 180 270 Geographic coordinate system Equal-area projection N=35 Max Int Min D 50 55 60 65 70 75 80 85 90 95 100 105 Km [E-03 SI] 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 P 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 P -1.0 -0.5 0.0 0.5 1.0 T Lambert projection, Lower hemisphere Degree of anisotropy vs. Mean susceptibility P-T plot (Jelinek plot) 1. Definition and application in geology Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 2. Magnetic anisotropy of minerals Shape anisotropy Magnetite Magnetocrystalline anisotropy All other minerals BiotiteBiotite 2. Magnetic anisotropy of minerals Hematite k1 = k2 >> k3 P > 100 Pyrrhotite k1 = k2 >> k3 P > 300 Magnetocrystalline anisotropy 2. Magnetic anisotropy of minerals Magnetocrystalline anisotropy 2. Magnetic anisotropy of minerals Biotite k1 = k2 > k3 P = 1.2-1.6 Muscovite k1 = k2 > k3 P = 1.3-1.4 Chlorite k1 = k2 > k3 P = 1.2-1.8 2. Magnetic anisotropy of minerals Magnetocrystalline anisotropy Mineral Susceptibility [10-6] Degree of anisotropy Shape of anisotropy Anisotropy type Magnetite 3000000 1.1 to 3.0 Variable Shape Hematite 1300 to 7000 >100 ~1.00 Magnetocrystalline Pyrrhotite 100 to 10000 ~1.00 Magnetocrystalline Actinolite 490 1.2 to 1.2 -0.40 to 0.40 Magnetocrystalline Hornblende 746 to 1368 1.665 -0.51 Magnetocrystalline Glaucophane 787 1.205 0.10 Magnetocrystalline Chlorite 70 to 1550 1.2 to 1.7 ~1.00 Magnetocrystalline Biotite 998 to 1290 1.2 to 1.6 ~1.00 Magnetocrystalline Phlogopite 1178 1.3 0.95 Magnetocrystalline Muscovite 122 to 165 1.4 0.44 Magnetocrystalline Quartz -13.4 to -15.4 1.01 1.00 Magnetocrystalline Calcite -13.8 1.11 1.00 Magnetocrystalline Aragonite -15.0 1.15 0.80 Magnetocrystalline Magnetic properties of selected minerals 2. Magnetic anisotropy of minerals Contribution of selected minerals to whole rock susceptibility 2. Magnetic anisotropy of minerals Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 3. Magnetic fabric vs. texture of rocks Rock anisotropy degree as a function of preferred orientation of its minerals 3. Magnetic fabric vs. texture of rocks 3. Magnetic fabric vs. texture of rocks Magnetic fabrics of higher order oblate fabric prolate fabric 3. Magnetic fabric vs. texture of rocks Comparison of magnetic fabric and neutron texture goniometry 3. Magnetic fabric vs. texture of rocks Shale, Rhenohercynian Belt, Czech Republic Isolines of chlorite c-axes AMS principal directions  1.00 1.20 1.40  1.60 N Eigenvectors of Orientation tensor Comparison of magnetic fabric and neutron texture goniometry Neutron texture goniometer TEX2 GKSS Forschungszentrum Geesthacht GmbH, Germany 3. Magnetic fabric vs. texture of rocks 3. Magnetic fabric vs. texture of rocks Comparison of magnetic fabric and neutron texture goniometry 3. Magnetic fabric vs. texture of rocks (courtesy F. Cifelli) Neogene basin, Southern Italy Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Magnetic susceptibility usually carried by paramagnetic minerals 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks P < 1.05 P < 1.30 K < 30010-6 K < 50010-6 Sedimentary rocks Anchimetamorphosed sediments •Anisotropy degree < 5% •Oblate fabric •Relatively low magnetic susceptibility 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks •calm sedimentation •slow current •fast (turbulent) current 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (after Tauxe 2013) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Pencil structure (southern Pyrenees, Spain) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Accretionary wedge 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Tertiary accretionary wedge, southern Pyrenees 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (Parés & van der Pluijm 1999) Tertiary accretionary wedge, southern Pyrenees 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (Parés & van der Pluijm 1999) Tertiary accretionary wedge, southern Pyrenees 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Paleozoic accretionary wedge Rhenohercynian Belt, Czech Republic 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (Chadima et al. 2006) Paleozoic accretionary wedge Rhenohercynian Belt, Czech Republic Anisotropy degree (P) Shape parameter (T) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks •Extentional setting •Neogene basin, southern Italy Extentional tectonic setting (courtesy F. Cifelli) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks paleosol silty paleosol paleosol loess loess loess 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks N 90 180 270 N=85 K1 K2 K3 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Cross-section of unconsolidated sediment from Baltic Sea Ref03_20150 90 180 270 Geographic Coordinate System Equal-Area Projection N = 88 Max Int Min -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 T 0 10 20 30 40 50 60 Counts 0 50 100 150 200 250 300 Kmean [E-06 SI] 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P -1.0 -0.5 0.0 0.5 1.0 T 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Ref03_20160 90 180 270 Geographic Coordinate System Equal-Area Projection N = 88 Max Int Min -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 T 0 10 20 30 40 50 60 70 80 90 Counts 0 50 100 150 200 250 300 Kmean [E-06 SI] 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P -1.0 -0.5 0.0 0.5 1.0 T 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Ref03_20170 90 180 270 Geographic Coordinate System Equal-Area Projection N = 88 Max Int Min -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 T 0 10 20 30 40 50 60 70 80 90 Counts 0 50 100 150 200 250 300 Kmean [E-06 SI] 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P -1.0 -0.5 0.0 0.5 1.0 T 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Ref03_2015(black) + 2016(blue) + 2017(red)0 90 180 270 Geographic Coordinate System Equal-Area Projection N = 264 Max Int Min -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 T 0 50 100 150 200 250 Counts 0 50 100 150 200 250 300 Kmean [E-06 SI] 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P -1.0 -0.5 0.0 0.5 1.0 T 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Ref03_2015 minus Ref03_20160 90 180 270 Geographic Coordinate System Equal-Area Projection N = 65 Max Int Min -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 T 0 2 4 6 8 10 12 14 16 Counts 0 50 100 150 200 250 300 Kmean [E-06 SI] 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P -1.0 -0.5 0.0 0.5 1.0 T 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (Hajná et al. 2010) (Hajná et al. 2010) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks (Hajná et al. 2010) 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 5. Magnetic fabric of igneous rocks 1. Volcanic rocks 2. Dikes 3. Plutonic rocks 5. Magnetic fabric of igneous rocks Magnetic susceptibility dominantly carried by magnetite 5. Magnetic fabric of igneous rocks P < 1.03 K < 50 0000 10-6 Very high magnetic susceptibility Relatively low anisotropy degree Igneous rocks 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Volcanic rocks A’a 5. Magnetic fabric of igneous rocks Pahoehoe Lava flows 5. Magnetic fabric of igneous rocks Lipari Island, Tyrrhenian Sea, Italy 5. Magnetic fabric of igneous rocks Lipari Island, Tyrrhenian Sea 5. Magnetic fabric of igneous rocks Chaîne des Puys, Massif Central, France (Loock et al. 2008) 5. Magnetic fabric of igneous rocks Section across lava flow (Gurioli et al. 2005) 5. Magnetic fabric of igneous rocks Pyroclastic flow, Pompeii, Italy 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks (Gurioli et al. 2005) 5. Magnetic fabric of igneous rocks Pyroclastic flow, Pompeii, Italy 5. Magnetic fabric of igneous rocks Dikes Estimate of flow direction 5. Magnetic fabric of igneous rocks Dikes 5. Magnetic fabric of igneous rocks •magnetic lineation is not always parallel to flow direction •preferably use imbrication of magnetic foliation 5. Magnetic fabric of igneous rocks Wilson, J. T. 1963. A possible origin of the Hawaiian Islands. Canadian Journal of Physics, 41, 863-670. 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Island of Oahu 5. Magnetic fabric of igneous rocks Geology of Oahu 5. Magnetic fabric of igneous rocks SENW Keneohe Bay Kawainui Swamp Waimanalo Bay 1 2 3 Koolau (Knight & Walker 1988) 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Plutonic rocks weakly magnetic (paramagnetic) granitoides S type (“Sedimentary”) carrier of magnetization mainly biotite (hornblende) Plutonic rocks strongly magnetic (ferromagnetic) granitoides I type (Igneous) carrier of magnetization mainly magnetite •bimodal distribution of magnetic susceptibility (granitoids of former USSR) 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Brno Massif 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Foliations and lineations in plutons originate by magma flow Magnetic foliation = magma flow plane Magnetic lineation = magma flow line Regional-scale investigation of magnetic fabric helps to decipher magma flow within whole pluton FLOW LINES FLOW PLANES VELOCITY GRADIENT FLOW DIRECTION RIGID WALL 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Monte Capanne granodiorite pluton (Elba Island, northern Tyrrhenian Sea, Italy) (Bouillin et al. 1993) Magnetic anisotropy in pluton scale Magnetic lineationMagnetic foliation 5. Magnetic fabric of igneous rocks 5. Magnetic fabric of igneous rocks Agenda 1. Definition and application in geology 2. Magnetic anisotropy of minerals 3. Magnetic fabric vs. texture of rocks 4. Magnetic fabric of sedimentary, deformed, and metamorphosed rocks 5. Magnetic fabric of igneous rocks 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing Oriented samples V = 11.15 ccm V = 8 ccm 6. Sampling, measurement and data processing Field Drilling Oriented Cores Petrol powered portable drilling machine 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing (Tauxe. 2005) Block specimens 6. Sampling, measurement and data processing R = T r, K = T k T', •r, R vectors in sample or geographical coordinate systems •k, K tensors in sample or geographical coordinate systems •T transformation matrix (T’ transposed matrix of T) Sample to geographical coordinate system transformation 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing KLY-1 (1967) KLY-2 KLY-3 & 4 Kappabridge (and PC) evolution 6. Sampling, measurement and data processing MFK1 Three operating frequencies and respective field ranges (peak values): •F1 (976 Hz): 2 - 700 A/m •F2 (3904 Hz): 2 - 350 A/m •F3 (15616 Hz): 2 - 200 A/m • Accuracy within one range:±0.1 % • Accuracy of absolute calibration: ±3.0 % 6. Sampling, measurement and data processing MFK1-FA X  15 directional measurements  Duration: ca. 9 min 15 position design 6. Sampling, measurement and data processing Three plane rotation  64 readings during each rotation  Multiple rotations  Duration: ca. 3-4 min 6. Sampling, measurement and data processing X  320 readings during full rotation  Repeated two times  640 directional measurements  Duration: ca. 1.5 min 3D Rotator 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing Safyr - Data acquisition software 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing Anisoft - Data processing software 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing 6. Sampling, measurement and data processing Mean tensor (Jelinek 1978, Hext 1963)  Mean directions  Confidence ellipses 6. Sampling, measurement and data processing 0 90 180 270 Geographic Coordinate System Equal-Area Projection N = 35 Max Int Min Bootstrap (Constable & Tauxe 1990) 6. Sampling, measurement and data processing •projection of mean susceptibilities •magnetic lineation of mean tensor •isolines of shape parameter (T) Data presentation in regional scale 6. Sampling, measurement and data processing  Tarling, D.H. & Hrouda, F. 1993. The Magnetic Anisotropy of Rock. Chapman & Hall, 217 pp.  Lanza, R. & Meloni, A. 2006. The Earth’s Magnetism: An Introduction for Geologist. Springer, 278 pp. (Chapter 5).  Hrouda, F. 2007. Magnetic Susceptibility, Anisotropy. Encyclopedia of Geomagnetism and Paleomagnetism. Springer. 546-560.  Sagnotti, L. 2009. Magnetic anisotropy. Encyclopedia of Solid Earth Geophysics. Springer. 717-729.  Tauxe, L. 2013. Lectures in paleomagnetism. http://magician.ucsd.edu/Essentials_2/WebBook2ch13.html#x15-15500013.  Hrouda, F., 1982. Magnetic anisotropy of rocks and its application in geology and geophysics. Geophysical Surveys, 5, 37–82.  Borradaile, G. J. & Henry, B. 1997. Tectonic applications of magnetic susceptibility and its anisotropy. Earth Science Reviews, 42, 49–93.  Jackson,M.J. & Tauxe, L. 1991. Anisotropy of magnetic susceptibility and remanence: developments in the characterization of tectonic, sedimentary, and igneous fabric. Reviews of Geophysics, 29, 371–376.  Rochette, P., Jackson, M. J. & Aubourg, C. 1992. Rock magnetism and the interpretation of anisotropy of magnetic susceptibility. Reviews of Geophysics, 30, 209–226. Magnetic anisotropy of rocks Literature Magnetic Anisotropy of Rocks Thanks for your Attention! www.agico.com agico@agico.cz chadima@agico.cz Telephone +420 511 116 303 FAX +420 541 634 328 Postal Address Ječná 29a, CZ-621 00 Brno, Czech Republic Electronic Mail agico@agico.cz ICO 60731354 VAT No. (DIC) CZ60731354 Contact Us