Pure and Applied Geophysics

, Volume 176, Issue 4, pp 1691–1700 | Cite as

Magnetotelluric Responses of a Horizontally Nonhomogeneous Model of the Earth with Anisotropic Conductivity Structures

  • Linjiang QinEmail author
  • Changfu Yang


A quasistatic analytical approach is applied to the magnetotelluric responses of an idealized two-dimensional (2-D) horizontally nonhomogeneous model consisting of any number of segments with electrical anisotropic conductivity underlain by a perfect conductor basement. For this model, the magnetic field vector is everywhere parallel to the vertical contacts and to the Earth’s surface. The solution to the magnetotelluric responses of the model are derived, and detailed expressions for the electric and magnetic fields for a specialized case are presented. The resulting quasianalytical solution is then given for use in validation of numerical algorithms.


Quasianalytical solution computational electromagnetics electrical anisotropy electromagnetic induction magnetotellurics 



Dr. J. T. Weaver is deeply acknowledged for making his computer code 2DANALB publicly available. The authors gratefully acknowledge Dr. Michael Commer (Editor), Dr. Colin Farquharson (reviewer), and another anonymous reviewer for their thorough reading of the manuscript and their insightful questions and constructive comments, which certainly improved the quality of this paper. Q.L. would like to thank the National Natural Science Foundation of China (grant no. 41776079) and the Scientific Research Fund of the Second Institute of Oceanography, SOA (grant no. JG1705) for funding. Y.C. greatly acknowledges the National Natural Science Foundation of China (grant nos. 40774035 and 41474054) for funding.


  1. Azeez, K. K. A., Unsworth, M. J., Patro, P. K., Harinarayana, T., & Sastry, R. S. (2013). Resistivity structure of the Central Indian Tectonic Zone (CITZ) from multiple magnetotelluric (MT) profiles and tectonic implications. Pure and Applied Geophysics, 170(12), 2231–2256. Scholar
  2. Cagniard, L. (1953). Basic theory of the MT methods of geophysical prospecting. Geophysics, 18(3), 605–635. Scholar
  3. Campbell, W. H. (1990). The magnetospheric disturbance ring current as a source for probing the deep earth electrical conductivity. Pure and Applied Geophysics, 134(4), 541–557. Scholar
  4. Čermák, V., & Laštovičková, M. (1987). Temperature profiles in the earth of importance to deep electrical conductivity models. Pure and Applied Geophysics, 125(2–3), 255–284. Scholar
  5. Chetayev, D. N. (1960). The determination of anisotropic coefficient and the angle of inclination of homogeneous anisotropic medium, by measuring the impedance of natural electromagnetic field. Bulletin of the Academy of Sciences of the USSR Geophysics Series English, Transl, 407–408.Google Scholar
  6. Eaton, D. W., Jones, A. G., & Ferguson, I. J. (2004). Lithospheric anisotropy structure inferred from collocated teleseismic and magnetotelluric observations: Great Slave Lake shear zone, northern Canada. Geophysical Research Letters, 31(19), L19614. Scholar
  7. Geyer, R. G. (1976). Magnetotelluric probing for buried geologic structures. IEEE Transactions on Geoscience Electronics, 14(4), 223–230. Scholar
  8. de Groot-Hedlin, C. (2006). Finite-difference modeling of magnetotelluric fields: Error estimates for uniform and nonuniform grids. Geophysics, 71(3), G97–G106. Scholar
  9. Ingham, M. R., & Reeves, R. (1993). Magnetotelluric soundings and structure of the Tokaanu Geothermal Field, New Zealand. Journal of Geomagnetism and Geoelectricity, 45, 729–740. Scholar
  10. Kao, D., & Rankin, D. (1980). Magnetotelluric response on inhomogeneous layered earth. Geophysics, 45(12), 1793–1802. Scholar
  11. Kong, J. A. (1972). Electromagnetic fields due to dipole antennas over stratified anisotropic media. Geophysics, 37(6), 985–996. Scholar
  12. Kováč, M., Plašienka, D., Soták, J., Vojtko, R., Oszczypko, N., Less, G., et al. (2016). Paleogene palaeogeography and basin evolution of the Western Carpathians, Northern Pannonian domain and adjoining areas. Global and Planetary Change, 140, 9–27. Scholar
  13. Leibecker, J., Gatzemeier, A., Honig, M., Kuras, O., & Soyer, W. (2002). Evidence of electrical anisotropic structures in the lower crust and the upper mantle beneath the Rhenish Shield. Earth and Planetary Science Letters, 202(2), 289–302. Scholar
  14. Li, Y. G. (2002). A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures. Geophysical Journal International, 148(3), 389–401. Scholar
  15. Loewenthal, D., & Landisman, M. (1973). Theory for magnetotelluric observations on the surface of a layered anisotropic half space. Geophysical Journal International, 35(1–3), 195–214. Scholar
  16. Mackie, R. L., Madden, T. R., & Wannamaker, P. E. (1993). Three-dimensional magnetotelluric modeling using difference equations-Theory and comparisons to integral equation solutions. Geophysics, 58(2), 215–226. Scholar
  17. Malcolm, I., & Colin, B. (2010). A magnetotelluric study of the Alpine Fault, New Zealand. Geophysical Journal of the Royal Astronomical Society, 135(2), 542–552. Google Scholar
  18. Mitsuhata, Y., & Uchida, T. (2004). 3D magnetotelluric modeling using the T-Ω Ω finite-element method. Geophysics, 69(1), 108–119. Scholar
  19. Mohan, K., Chaudhary, P., Kumar, G. P., Kothyari, G. C., Choudhary, V., Nagar, M., et al. (2018). Magnetotelluric investigations in Tuwa-Godhra Region, Gujarat (India). Pure and Applied Geophysics, 2018, 1–21. Scholar
  20. Negi, J. G., & Saraf, P. D. (1972). Effect of anisotropy of the earth on the impedance measurements. Pure and Applied Geophysics, 96(4), 37. Scholar
  21. Negi, J., & Saraf, P. (1989). Anisotropy in geoelectromagnetism. Amsterdam: Elsevier.Google Scholar
  22. O’Brien, D. P., & Morrison, H. F. (1967). Electromagnetic fields in an N-layered anisotropic half-space. Geophysics, XXXII(4), 668–677. Scholar
  23. Osella, A. M., & Martinelli, P. (1993). Magnetotelluric response of anisotropic 2-D structures. Geophysical Journal International, 115(3), 819–828. Scholar
  24. Pek, J., & Verner, T. (1997). Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media. Geophysical Journal International, 128, 505–521. Scholar
  25. Qin, L., & Yang, C. (2016). Analytic magnetotelluric responses to a two-segment model with axially anisotropic conductivity structures overlying a perfect conductor. Geophysical Journal International, 205(3), 1729–1739. Scholar
  26. Qin, L., Yang, C., & Chen, K. (2013). Quasi-analytic solution of 2-D magnetotelluric fields on an axially anisotropic infinite fault. Geophysical Journal International, 192(1), 67–74. Scholar
  27. Rankin, D. (1962). The magneto-telluric effect on a dike. Geophysics, 27(5), 666–676. Scholar
  28. Reddy, I. K., & Rankin, D. (1971). Magnetotelluric effect of dipping anisotropies. Geophysical Prospecting, 19(1), 84–97. Scholar
  29. Reddy, I. K., & Rankin, D. (1975). Magnetotelluric response of laterally inhomogeneous and anisotropic media. Geophysics, 40(6), 1035–1045. Scholar
  30. Robertson, R. C. (1986). The magnetotelluric field for a two-dimensional earth modeled by a nonuniform buried thin sheet. IEEE Transactions on Geoscience and Remote Sensing, GE-24(2), 204–211. Scholar
  31. Robertson, R. C. (1989). The E-parallel polarization response of a two-dimensional heterogeneous layer modeled by two thin sheets. IEEE Transactions on Geoscience and Remote Sensing, 27(4), 369–374. Scholar
  32. Simpson, F., & Bahr, K. (2005). Practical magnetotellurics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  33. Ślęzak, K., Jóźwiak, W., Nowożyński, K., & Brasse, H. (2016). 3-D inversion of MT data for imaging deformation fronts in NW Poland. Pure and Applied Geophysics, 173(7), 1–12. Scholar
  34. Tikhonov, A. N. (1950). The determination of the electrical properties of the deep layers of the earth’s crust. Doklady Akademii Nauk SSR, 73, 295–297. (in Russian).Google Scholar
  35. Ting, S. C., & Hohmann, G. W. (1981). Integral equation modeling of three-dimensional magnetotelluric response. Geophysics, 46(2), 182–197. Scholar
  36. Unsworth, M. (2005). New developments in conventional hydrocarbon exploration with electromagnetic methods. Canadian Society of Exploration Geophysicists Recorder, 30, 34–38.Google Scholar
  37. Upadhyay, S., & Niwas, S. (1971). Apparent resistivity over a three layer earth with anisotropic interstratum. Pure and Applied Geophysics, 87(1), 155–160. Scholar
  38. Wait, J. R., & Spies, K. P. (1974). Magneto-Telluric fields for a segmented overburden. Journal of Geomagnetism and Geoelectricity, 26(5), 449–458. Scholar
  39. Wannamaker, P. E., Jiracek, G. R., Stodt, J. A., Caldwell, T. G., Gonzalez, V. M., McKnight, J. D., et al. (2002). Fluid generation and pathways beneath an active compressional orogen, the New Zealand Southern Alps, inferred from magnetotelluric data. Journal of Geophysical Research-Solid Earth. Scholar
  40. Wannamaker, P. E., Stodt, J. A., & Rijo, L. (1987). A stable finite-element solution for two-dimensional magnetotelluric modeling. Geophysical Journal of the Royal Astronomical Society, 88(1), 277–296. Scholar
  41. Weaver, J. T. (1963). The electromagnetic field within a discontinuous conductor with reference to geomagnetic micropulsations near a coastline. Canadian Journal of Physics, 41(3), 484–495. Scholar
  42. Weaver, J. T. (1994). Mathematical methods for geo-electromagnetic induction. Taunton: Research Studies Press.Google Scholar
  43. Weaver, J. T., Lequang, B. V., & Fischer, G. (1985). A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction. 1. B-polarization calculations. Geophysical Journal of the Royal Astronomical Society, 82(2), 263–277. Scholar
  44. Weaver, J. T., Lequang, B. V., & Fischer, G. (1986). A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction-11. E-polarization calculations. Geophysical Journal of the Royal Astronomical Society, 87(3), 917–948. Scholar
  45. Yang, C. (1997). MT numerical simulation of symmetrically 2D anisotropic media based on the finite element method (in Chinese). Northwestern Seismological Journal, 19(2), 27–33.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Key Laboratory of Submarine GeosciencesState Oceanic AdministrationHangzhouChina
  2. 2.Second Institute of OceanographyState Oceanic AdministrationHangzhouChina
  3. 3.School of Earth SciencesZhejiang UniversityHangzhouChina

Personalised recommendations