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Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users

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Abstract

In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.

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References

  • Abubakar A, Habashy TM, Li M, Liu J (2009) Inversion algorithms for large-scale geophysical electromagnetic measurements. Inv Prob 25:1–30

    Article  Google Scholar 

  • Árnason K, Eysteinsson H, Hersir GP (2010) Joint 1D inversion of TEM and MT data and 3D inversion of MT data in the Hengill area, SW Iceland. Geothermics 39:13–34

    Article  Google Scholar 

  • Avdeev D (2005) Three-dimensional electromagnetic modeling and inversion from theory to application. Surv Geophys 26:767–799

    Article  Google Scholar 

  • Avdeev D, Avdeeva A (2009) 3D Magnetotelluric inversion using a limited-memory quasi-Newton optimization. Geophysics 74:F45–F57

    Article  Google Scholar 

  • Bahr K (1991) Geological noise in Magnetotelluric data: a classification of distortion types. Phys Earth Plan Int 66:24–38

    Article  Google Scholar 

  • Becken M, Ritter O, Burkhardt H (2008a) Mode separation of Magnetotelluric responses in three-dimensional environments. Geophys J Int 172:67–86

    Article  Google Scholar 

  • Becken M, Ritter O, Park SK, Bedrosian PA, Weckmann U, Weber M (2008b) A deep crustal fluid channel into the San Andreas Fault system near Parkfield, California. Geophys J Int 173:718–732

    Article  Google Scholar 

  • Boonchaisuk S, Vachiratienchai C, Siripunvaraporn W (2008) Two-dimensional direct current (DC) resistivity inversion: data space Occam’s approach. Phys Earth Plan Int 168:204–211

    Article  Google Scholar 

  • Borner RU (2010) Numerical modeling in geo-electromagnetics: advances and challenges. Surv Geophys 31:225–245

    Article  Google Scholar 

  • Broyden CG (1967) Quasi-Newton methods and their application to function minimization. Math Comput 21:368

    Article  Google Scholar 

  • Caldwell TG, Bibby H, Brown C (2004) The magnetotelluric phase tensor. Geophys J Int 158. doi:10.1111/j.1365-246X.2004.02281.x

  • Chave AD, Smith JT (1994) On electric and magnetic galvanic distortion tensor decompositions. J Geophys Res 99:4669–4682

    Google Scholar 

  • Chen X, Weckmann U (2010) From forward modeling of MT phases over 90° towards 2D anisotropic inversion, IAGA WG 1.2 on electromagnetic induction in the earth, 20th workshop abstract, Giza, Egypt, September 18–24

  • Commer M, Newman GA (2008) New advances in three-dimensional controlled-source electromagnetic inversion. Geophys J Int 172:513–535

    Article  Google Scholar 

  • Commer M, Newman GA (2009) Three-dimensional controlled-source electromagnetic and Magnetotelluric joint inversion. Geophys J Int. doi:10.1111/j.1365-246X.2009.04216.x

  • Constable CS, Parker RL, Constable CG (1987) Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 52:289–300

    Article  Google Scholar 

  • Cumming W, Mackie R (2010) Resistivity imaging of geothermal resources using 1D, 2D and 3D MT inversion and TDEM static shift correction illustrated by a Glass Mountain case history. In: Proceedings world geothermal congress 2010, Bali, Indonesia, 25–29 April

  • Degroot-Hedlin C, Constable S (1990) Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics 55(12):1613–1624

    Google Scholar 

  • Egbert G (2010) Efficient inversion of multi-frequency and multi-transmitter EM data, IAGA WG 1.2 on electromagnetic induction in the earth, 20th workshop abstract, Giza, Egypt, September 18–24

  • Farquharson CG, Craven JA (2008) Three-dimensional inversion of Magnetotelluric data for mineral exploration: an example from the McArthur River uranium deposit, Saskatchewan, Canada. J Appl Geophys 68:450–458

    Article  Google Scholar 

  • Farquharson CG, Oldenburg DW (1996) Approximate sensitivities for the electromagnetic inverse problem. Geophy J Int 126:235–252

    Article  Google Scholar 

  • Fletcher R, Powell MJD (1963) A rapidly convergent descent method for minimization. Comput J 6:163–168

    Google Scholar 

  • Fletcher R, Reeves CM (1964) Function minimization by conjugate gradients. Comput J 7:149–154

    Article  Google Scholar 

  • Goldak D, Kosteniuk P (2010) 3D inversion of transient magnetotelluric data: an example from Pasfield Lake, Saskatchewan, EGM 2010 International Workshop, 11–14 April, 2010. Capri, Italy

    Google Scholar 

  • Gribenko A, Zhdanov M (2007) Rigorous 3D inversion of marine CSEM data based on the integral equation method. Geophysics 72:WA73–WA84

    Google Scholar 

  • Gribenko A, Green M, Cuma M, Zhdanov MS (2010) Efficient 3D inversion of MT data using integral equations method and the receiver footprint approach: application to the large-scale inversion of the EarthScope MT data: expanded Abstracts of the SEG meeting, Denver, Colorado, pp 644–649

  • Groom RW, Bailey R (1989) Decomposition of Magnetotelluric impedance tensors in the presence of local three-dimensional galvanic distortion. J Geophys Res 94:1913–1925

    Article  Google Scholar 

  • Gunther T, Rucker C, Spitzer K (2006) Three-dimensional modeling and inversion of dc resistivity data incorporating topography–II. Inv Geophys J Int 166:506–517

    Article  Google Scholar 

  • Haber E (2005) Quasi-Newton methods for large scale electromagnetic inverse problem. Inverse Problem 21:305–317

    Article  Google Scholar 

  • Haber E, Asher U, Oldenburg D (2000) On optimization techniques for solving nonlinear inverse problems. Inv Prob 16:1263–1280

    Google Scholar 

  • Haber E, Ascher U, Oldenburg D (2004) Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach. Geophysics 69:1216–1228 (n5)

    Google Scholar 

  • Haber E, Oldenburg DW, Shekhtman R (2007) Inversion of time domain three-dimensional electromagnetic data. Geophys J Int 171:550–564

    Article  Google Scholar 

  • Han N, Nam MJ, Kim HJ, Lee TJ, Song Y, Suh JH (2008) Efficient three-dimensional inversion of Magnetotelluric data using approximate sensitivities. Geophys J Inter 175:477–485

    Article  Google Scholar 

  • Han N, Nam MJ, Kim HJ, Song Y, Suh JH (2009) A comparison of accuracy and computation time of three-dimensional Magnetotelluric modeling algorithms. J Geophys Eng 6:136. doi:10.1088/1742-2132/6/2/005

    Article  Google Scholar 

  • Hautot S, Tarits P (2009) A new coarse-to-fine 3-D Magnetotelluric inversion method—application to field data for hydrocarbon exploration, Society of Petroleum Engineers—71st European association of geoscientists and engineers conference and exhibition, 1, pp 663–667

  • Heise W, Caldwell TG, Bibby HM, Bannister SC (2008) Three-dimensional modelling of magnetotelluric data from the Rotokawa geothermal field, Taupo Volcanic Zone, New Zealand. Geophys J Inter 173:740–750

    Article  Google Scholar 

  • Heise W, Caldwell TG, Bibby HM, Bennie SL (2010) Three-dimensional electrical resistivity image of magma beneath an active continental rift, Taupo Volcanic Zone, New Zealand. Geophys Res Lett 37(10):art. No. L10301

  • Hill GJ, Caldwell TG, Heise W, Chertkoff DG, Bibby HM, Burgess MK, Cull JP, Cas RAF (2009) Distribution of melt beneath Mount St Helens and Mount Adams inferred from magnetotelluric data. Nat Geosci 2:785–789. doi:10.1038/NGE0661

    Article  Google Scholar 

  • Hohmann GW (1975) Three dimensional induced polarization and EM modeling. Geophysics 40:309–324

    Article  Google Scholar 

  • Ichihara H, Mogi T (2009) A realistic 3-D resistivity model explaining anomalous large magnetotelluric phases: the L-shaped conductor model. Geophys J Int 179:14–17

    Article  Google Scholar 

  • Ichihara H, Mogi T, Uyeshima M, Sakanaka S (2010) Three dimensional conductor models explaining out of quadrant magnetotelluric phases, IAGA WG 1.2 on Electromagnetic Induction in the earth, 20th workshop abstract, Giza, Egypt, September 18–24

  • Ingham MR, Bibby HM, Heise W, Jones KA, Cairns P, Dravitzki S, Bennie SL, Caldwell TG, Ogawa Y (2009) A Magnetotelluric study of Mount Ruapehu volcano, New Zealand. Geophys J Inter 179:887–904

    Google Scholar 

  • Jones KA, Ingham MR, Bibby HM (2008) The hydrothermal vent system of Mount Ruapehu, New Zealand–a high frequency MT survey of the summit plateau. J Volcanol Geotherm Res 176:591–600

    Article  Google Scholar 

  • Kelbert A, Egbert GD, Schultz A (2008) Non-linear conjugate gradient inversion for global EM induction: resolution studies. Geophys J Int 173:365–381

    Article  Google Scholar 

  • Ledo J (2006) 2-D versus 3-D Magnetotelluric data interpretation. Surv Geophys 27:111–148

    Article  Google Scholar 

  • Li M, Abubakar A, Habashy TM (2009) Regularized Gauss–Newton method using compressed Jacobian matrix for controlled source electromagnetic data inversion: expanded abstracts of the SEG meeting, Houston, Texas, pp 704–708

  • Lilley FEM, Weaver JT (2010) Phases greater than 90° in MT data: analysis using dimensionality tools. J Appl Geophys 70:9–16

    Article  Google Scholar 

  • Lin C, Tan H, Tong T (2008) Three-dimensional conjugate gradient inversion of Magnetotelluric sounding data. Appl Geophys 5:314–321

    Article  Google Scholar 

  • Lin C, Tan H, Tong T (2009) Parallel rapid relaxation inversion of 3D Magnetotelluric data. Appl Geophys 6:77–83

    Article  Google Scholar 

  • Mackie RL, Madden TR (1993) Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys J Int 115:215–229

    Article  Google Scholar 

  • Mackie R, Watts MD (2007) Joint 3D inversion of marine CSEM and MT data, SEG, San Antonio 2007 annual meeting, pp 574–578

  • Mackie RL, Smith JT, Madden TR (1994) Three-dimensional electromagnetic modeling using finite difference equations: the Magnetotelluric example. Radio Sci 29:923–935

    Article  Google Scholar 

  • Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Indust Appl Math 11:431–441

    Article  Google Scholar 

  • Marti A, Queralt P, Ledo J (2009) WALDIM: A code for the dimensionality analysis of Magnetotelluric data using the rotational invariants of the Magnetotelluric tensor. Comput Geosci 35:2295–2303

    Article  Google Scholar 

  • McNeice G, Jones AG (2001) Multisite, multifrequency tensor decomposition of Magnetotelluric data. Geophysics 66:158–173

    Article  Google Scholar 

  • Newman GA, Alumbaugh DL (1997) Three-dimensional massively parallel electromagnetic inversion—I. Theory Geophys J Int 128:345–354

    Article  Google Scholar 

  • Newman GA, Alumbaugh DL (2000) Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys J Int 140:410–424

    Article  Google Scholar 

  • Newman GA, Boggs PT (2004) Solution accelerators for large-scale three-dimensional electromagnetic inverse problems. Inv Prob 20:S151–S170

    Article  Google Scholar 

  • Newman GA, Hoversten GM (2000) Solution strategies for two- and three-dimensional electromagnetic inverse problems. Inv Prob 16:1357–1375

    Google Scholar 

  • Newman GA, Recher S, Tezkan B, Neubauer FM (2003) Case History 3D inversion of a scalar radio Magnetotelluric field data set. Geophysics 68:791–802

    Article  Google Scholar 

  • Newman GA, Gasperikova E, Hoversten GM, Wannamaker PE (2008) Three-dimensional magnetotelluric characterization of the Coso geothermal field. Geothermics. doi:10.1016/j.geothermics.2008.02.006

  • Ogawa Y (2002) On two-dimensional modeling of magnetotelluric field data. Surv Geophys 23:251–272

    Article  Google Scholar 

  • Parker RL (1994) Geophysical inverse theory. Princeton University Press, Princeton

  • Patro PK, Egbert GD (2008) Regional conductivity structure of Cascadia: preliminary results from 3D inversion of USArray transportable array Magnetotelluric data. Geophys Res Lett 35:art. no. L20311

  • Polyak E, Ribiere G (1969) Note sur la convergence des methods conjugees. Rev Fr Inr Rech Oper 16:35–43

    Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in FORTRAN: the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge

  • Rodi WL (1976) A technique for improving the accuracy of finite element solutions for Magnetotelluric data. Geophys J Roy Astr Soc 44:483–506

    Google Scholar 

  • Rodi W, Mackie RL (2001) Nonlinear conjugate gradients algorithm for 2‐D magnetotelluric inversion. Geophysics 66:174–187

    Google Scholar 

  • Rung-Arunwan T, Siripunvaraporn W (2010) An efficient modified hierarchical domain decomposition for two-dimensional Magnetotelluric forward modeling. Geophys J Int 183:634–644

    Google Scholar 

  • Sasaki Y (2001) Full 3D inversion of electromagnetic data on PC. J Appl Geophys 46:45–54

    Article  Google Scholar 

  • Sasaki Y (2004) Three-dimensional inversion of static-shifted Magnetotelluric data. Earth Planets Space 56:239–248

    Google Scholar 

  • Sasaki Y, Meju MA (2006) Three-dimensional joint inversion for Magnetotelluric resistivity and static shift distributions in complex media. J Geophys Res B Solid Earth 111:art. no. B05101

  • Schultz A, Weiss C, Urquhart S (2010) Progress toward massively parallel frequency domain 3D EM forward/inverse solutions through domain decomposition on general purpose graphics processors, IAGA WG 1.2 on electromagnetic induction in the earth, 20th workshop abstract, Giza, Egypt, September 18–24

  • Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24:647–656

    Google Scholar 

  • Simpson F, Bahr K (2005) Practical magnetotellurics. Cambridge.

  • Siripunvaraporn W, Egbert G (2000) An effcient data-subspace inversion method for 2D magnetotelluric data. Geophysics 65(3):791–803

    Article  Google Scholar 

  • Siripunvaraporn W, Egbert G (2007) Data space conjugate gradient inversion for 2-D Magnetotelluric data. Geophys J Int 170:986–994

    Article  Google Scholar 

  • Siripunvaraporn W, Egbert G (2009) WSINV3DMT: vertical magnetic field transfer function inversion and parallel implementation. Phys Earth Planet Int 173:317–329

    Article  Google Scholar 

  • Siripunvaraporn W, Sarakorn W (2011) An efficient data space conjugate gradient Occam’s method for three-dimensional Magnetotelluric inversion. Geophys J Int. doi:10.1111/j.1365-246x.2011.05079.x

  • Siripunvaraporn W, Egbert G, Lenbury Y (2002) Numerical accuracy of magnetotelluric modeling: a comparison of finite difference approximations. Earth Planets Space 54(6):721–725

    Google Scholar 

  • Siripunvaraporn W, Uyeshima M, Egbert G (2004) Three-dimensional inversion for Network-Magnetotelluric data. Earth Planets Space 56:893–902

    Google Scholar 

  • Siripunvaraporn W, Egbert G, Lenbury Y, Uyeshima M (2005a) Three-dimensional Magnetotelluric inversion: data-space method. Phys Earth Plan Int 150:3–14

    Article  Google Scholar 

  • Siripunvaraporn W, Egbert G, Uyeshima M (2005b) Interpretation of two-dimensional Magnetotelluric profile data with three-dimensional inversion: synthetic examples. Geophys J Int 160:804–814

    Article  Google Scholar 

  • Smith JT (1996) Conservative modeling of 3-D electromagnetic fields, Part II: biconjugate gradient solution and an accelerator. Geophysics 61:1319–1324

    Article  Google Scholar 

  • Smith JT, Booker JR (1991) Rapid inversion of two- and three-dimensional magnetotelluric data. J Geophys Res 96:3905–3922

    Article  Google Scholar 

  • Spichak V (1999) Three-dimensional inversion of MT fields using Bayesian statistics. In: Oristaglio M, Spies B (eds) Three-dimensional electromagnetics. SEG, Tulsa, USA, pp 406–417

  • Spichak V, Popova I (2000) Artificial neural network inversion of Magnetotelluric data in terms of three-dimensional earth macroparameters. Geophys J Int 142:15–26

    Article  Google Scholar 

  • Spichak VV, Borisova VP, Fainberg EB, Khalezov AA, Goidina AG (2007) Electromagnetic 3D tomography of the Elbrus volcanic center according to Magnetotelluric and satellite data. J Volcanol Seismol 1:53–66

    Article  Google Scholar 

  • Streich R (2009) 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: direct solution and optimization for high accuracy. Geophysics 74(5):F95–F105

    Article  Google Scholar 

  • Swift CM (1967) A magnetotelluric investigation of electrical conductivity anomaly in the southwestern United States. PhD thesis, MIT, Cambridge, MA

  • Szarka L, Novak A, Szalai S, Adam A (2006) Imaging experiences in Magnetotellurics and in geoelectrics, 17th international geophys congress & exhibition, November 14–17

  • Toh H, Honma S (2008) Mantle upwelling revealed by genetic algorithm inversion of the magnetovariational anomaly around Kyushu Island, Japan. J Geophys Res 113:B10103. doi:10.1029/2006JB004891

    Article  Google Scholar 

  • Tuncer V, Unsworth MJ, Siripunvaraporn W, Craven JA (2006) Exploration for unconformity-type uranium deposits with audiomagnetotelluric data: a case study from the McArthur River mine, Saskatchewan, Canada. Geophysics 71:B201–B209

    Article  Google Scholar 

  • Türkoǧlu E, Unsworth M, Pana D (2009) Deep electrical structure of northern Alberta (Canada): implications for diamond exploration. Can J Earth Sci 46:139–154

    Article  Google Scholar 

  • Unsworth M, Bedrosian P, Eisel M, Egbert G, Siripunvaraporn W (2000) Along strike variations in the electrical structure of the San Andreas Fault at Parkfield, California. Geophys Res Lett 27:3021–3024

    Article  Google Scholar 

  • Uyeshima M (2007) EM monitoring of crustal processes including the use of the Network-MT observations. Surv Geophys 28:199–237

    Article  Google Scholar 

  • Vachiratienchai C, Boonchaisuk S, Siripunvaraporn W (2010) A hybrid finite difference-finite element method to incorporate topography for 2D direct current (DC) resistivity modeling. Phys Earth Plan Int 183(3–4), 426–434

    Google Scholar 

  • Virginie M, Wanamaker P (2010) Parallelizing a 3D finite difference MT inversion algorithm on a multicore PC using OpenMP. Comput Geosci 36:1384–1387

    Article  Google Scholar 

  • Vozoff K (1972) The magnetotelluric method in the exploration of sedimentary basins. Geophysics 37:98–141

    Article  Google Scholar 

  • Wannamaker PE (1991) Advances in three dimensional magnetotelluric modeling using integral equations. Geophysics 56:1716–1728

    Article  Google Scholar 

  • Weaver JT, Agarwal AK, Lilley FEM (2000) Characterization of the Magnetotelluric impedance tensor. Geophys J Inter 129:133–142

    Google Scholar 

  • Weidelt P (1975) EM induction in three dimensional structures. Geophysics 41:85–109

    Google Scholar 

  • Xiao Q, Cai X, Xu X, Liang G, Zhang B (2010) Application of the 3D Magnetotelluric inversion code in a geologically complex area. Geophys Prospect. doi:10.1111/j.1365-2478.2010.00896.x

  • Zhanxiang H, Hu Z, Luo W (2010) Mapping reservoirs based on resistivity and induced polarization derived from continuous 3D Magnetotelluric profiling: case study from Qaidam basin, China. Geophysics 75:B25–B33

    Article  Google Scholar 

  • Zhdanov MS (2002) Geophysical inverse theory and regularization problems. Elsevier, Amsterdam, p 609

  • Zhdanov MS (2009) Geophysical electromagnetic theory and methods. Elsevier, Amsterdam, p 848

  • Zhdanov MS, Fang S, Hursan G (2000) Electromagnetic inversion using quasi-linear approximation. Geophysics 65:1501–1513

    Article  Google Scholar 

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Acknowledgments

This research has been supported by the Thai Center of Excellence in Physics (ThEP) and by the Thailand Research Fund (TRF: RMU5380018).

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Siripunvaraporn, W. Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users. Surv Geophys 33, 5–27 (2012). https://doi.org/10.1007/s10712-011-9122-6

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