Analytic Solution to the MT Responses of a Two-Segment Model with Axially Anisotropic Conductivity Structures Overlying a Perfect Insulator

doi:10.13278/j.cnki.jjuese.201604304

Abstract

Abstract:

The analytic solution of the magnetotelluric fields for an idealized 2-D model which is composed of two segments with diagonal anisotropy underlain by a perfect insulator basement is considered using a quasi-static analytic approach. The analytic magnetotelluric responses for a particular model are presented. The resulting analytic solution could be used to check the numerical solutions given by numerical algorithms before more complex situations are investigated.

Key words: anisotropy, magnetotellurics, analytic solution, two-dimensional

CLC Number:

P631.3

Qin Linjiang, Yang Changfu. Analytic Solution to the MT Responses of a Two-Segment Model with Axially Anisotropic Conductivity Structures Overlying a Perfect Insulator[J].Journal of Jilin University(Earth Science Edition), 2016, 46(4): 1260-1267.

References

[1] Shearer P, Orcutt J. Anisotropy in the Oceanic Lithosphere: Theory and Observations from the Ngendei Seismic Refraction Experiment in the South-West Pacific[J]. Geophysical Journal of the Royal Astronomical Society, 1985, 80(2): 493-526.

[2] Negi J, Saraf P. Anisotropy in Geoelectromagnetism[M]. Amsterdam: Elsevier, 1989.

[3] Kellett R, Mareschal M, Kurtz R. A Model of Lower Crustal Electrical Anisotropy for the Pontiac Subpro-vince of the Canadian Shield[J]. Geophysical Journal International, 1992, 111(1): 141-150.

[4] Klein J. Saturation Effects on Electrical Anisotropy[J]. Log Analyst, 1996, 37: 47-49.

[5] Eisel M, Haak V. Macro-Anisotropy of the Electrical Conductivity of the Crust: a Magnetotelluric Study of the German Continental Deep Drilling Site (KTB)[J]. Geophysical Journal International, 1999, 136(1): 109-122.

[6] Eaton D W, Jones A G, Ferguson I J. Lithospheric Anisotropy Structure Inferred from Collocated Teleseismic and Magnetotelluric Observations: Great Slave Lake Shear Zone, Northern Canada[J]. Geophysical Research Letters, 2004, 31(19): L19614.

[7] Wannamaker P E. Anisotropy Versus Heterogeneity in Continental Solid Earth Electromagnetic Studies: Fundamental Response Characteristics and Implications for Physicochemical State[J]. Surveys in Geophysics, 2005, 26(6): 733-765.

[8] Clavaud J B. Intrinsic Electrical Anisotropy of Shale: The Effect of Compaction[J]. Petrophysics, 2008, 49(3): 243-260.

[9] Ben F, Liu Y, Huang W, et al. MCSEM Response for Anisotropic Media in Shallow Water[J]. Journal of Jilin University (Earth Science Edition), 2016, 46(2): 594-602.

[10] Srnka L J, Lu X, Burtz O M. Method for Determining Earth Vertical Electrical Anisotropy in Marine Electromagnetic Surveys: U S, Patent 7 894 989[P]. 2011-02-22.

[11] Brown V, Hoversten M, Key K, et al. Resolution of reservoir Scale Electrical Anisotropy from Marine CSEM Data[J]. Geophysics, 2012, 77(2): E147-E158.

[12] Everett M E, Constable S. Electric Dipole Fields over an Anisotropic Seafloor: Theory and Application to the Structure of 40 Ma Pacific Ocean Lithosphere[J]. Geophysical Journal International, 1999, 136(1): 41-56.

[13] Rauen A, Lastovickova M. Investigation of Electrical Anisotropy in the Deep Borehole KTB[J]. Surveys in Geophysics, 1995, 16(1): 37-46.

[14] Kurtz R, Craven J, Niblett E, et al. The Conductivity of the Crust and Mantle Beneath the Kapuskasing Uplift: Electrical Anisotropy in the Upper Mantle[J]. Geophysical Journal International, 1993, 113(2): 483-498.

[15] Bahr K, Duba A. Is the Asthenosphere Electrically Anisotropic?[J]. Earth and Planetary Science Letters, 2000, 178(1): 87-95.

[16] Bahr K, Bantin M, Jantos C, et al. Electrical Anisotropy from Electromagnetic Array Data: Implications for the Conduction Mechanism and for Distortion at Long Periods[J]. Physics of the Earth and Planetary Interiors, 2000, 119(3): 237-257.

[17] Bahr K. Electrical Anisotropy and Conductivity Distribution Functions of Fractal Random Networks and of the Crust: The Scale Effect of Connectivity[J]. Geophysical Journal International, 1997, 130(3): 649-660.

[18] Cull J. Magnetotelluric Soundings over a Precambrian Contact in Australia[J]. Geophysical Journal International, 1985, 80(3): 661-675.

[19] Rasmussen T. Magnetotellurics in Southwestern Sweden: Evidence for Electrical Anisotropy in the Lower Crust?[J]. Journal of Geophysical Research: Solid Earth (1978-2012), 1988, 93(B7): 7897-7907.

[20] Tikhonov A N. The Determination of the Electrical Properties of the Deep Layers of the Earth'S Crust[J]. Dokl Acad Nauk SSR, 1950, 73: 295-297 (in Russian).

[21] Tikhonov A N. On Determining Electrical Characte-ristics of the Deep Layers of the Earth's Crust[M]// Vozoff K. Magnetotelluric Methods. Tulsa: Society of Exploration Geophysicists, 1986: 2-3.

[22] Cagniard L. Basic Theory of the MT Methods of Geophysical Propecting[J]. Geophysics, 1953, 18(3): 605-635.

[23] Reddy I K, Rankin D. Magnetotelluric Response of Laterally Inhomogeneous and Anisotropic Media[J]. Geophysics, 1975, 40(6): 1035-1045.

[24] Pek J, Verner T. Finite-Difference Modelling of Magnetotelluric Fields in Two-Dimensional Anisotropic Media[J]. Geophysical Journal International, 1997, 128: 505-521.

[25] Li Y. Numerische Modellierungen von Elektromagnetischen Feldern in 2-und 3-Dimensionalen Anisotropen Leitf higkeitsstrukturen der Erde Nach der Methode der Finiten Elemente[M]. Gttingen: Cuvillier, 2000.

[26] Li Y G. A finite-Element Algorithm for Electromagnetic Induction in Two-Dimensional Anisotropic Conductivity Structures[J]. Geophysical Journal International, 2002, 148(3): 389-401.

[27] Yang C. MT Numerical Simulation of Symmetrically 2D Anisotropic Media Based on the Finite Element Method(in Chinese)[J]. Northwestern Seismological Journal, 1997, 19(2): 27-33.

[28] Osella A M, Martinelli P. Magnetotelluric Response of Anisotropic 2-D Structures[J]. Geophysical Journal International, 1993, 115(3): 819-828.

[29] Saraf P, Negi J. On Multifrequency Magneto Telluric Sounding over the Himalayan Type Colliding Plate Boundaries[J]. Geophysical Journal of the Royal Astronomical Society, 1983, 74(3): 809-817.

[30] Weaver J T, Lequang B V, Fischer G. A Comparison of Analytic and Numerical Results for a Two-Dimensional Control Model in Electromagnetic Induction: 1: B-Polarization Calculations[J]. Geophysical Journal of the Royal Astronomical Society, 1985, 82(2): 263-277.

[31] Weaver J T, Lequang B V, Fischer G. A Comparison of Analytic and Numerical Results for a Two-Dimensional Control Model in Electromagnetic Induction: 1: E-Polarization Calculations[J]. Geophysical Journal of the Royal Astronomical Society, 1986, 87(3): 917-948.

[32] Weaver J T. Mathematical Methods for Geo-Electromagnetic Induction[M]. Taunton: Research Studies Press, 1994.

[33] Qin L,Yang C,Chen K.Quasi-Analytic Solution of 2-D Magnetotelluric Fields on an Axially Anisotropic Infinite Fault[J]. Geophysical Journal International, 2013, 192(1): 67-74.

[34] O'brien D P, Morrison H F. Electromagnetic Fields in an N-Layered Anisotropic Half-Space[J]. Geophysics, 1967, XXXII(4): 668-677.

[35] Loewenthal D, Landisman M. Theory for Magnetotelluric Observations on the Surface of a Layered Anisotropic Half Space[J]. Geophysical Journal International, 1973, 35(1/2/3): 195-214.

[36] Chetayev D N. The Determination of Anisotropic Coefficient and the Angle of Inclination of Homogeneous Anisotropic Medium, by Measuring the Impedance of Natural Electromagnetic Field[J]. Bull Acad Sci USSR, Geophysics ser, English Transl, 1960: 407-408.

[37] Reddy I K, Rankin D. Magnetotelluric Measurements in Central Alberta[J]. Geophysics, 1971, 36(4): 739-753.

[38] Kong J A. Electromagnetic Fields due to Dipole Antennas over Stratifield Anisotropic Media[J]. Geophysics, 1972, 37(6): 985-996.

[39] Qin L, Yang C. Analytic Magnetotelluric Responses to a Two-Segment Model with Axially Anisotropic Conductivity Structures Overlying a Perfect Conductor[J]. Geophysical Journal International, 2016, 205(3): 1729-1739.

[40] Rankin D. The Magneto-Telluric Effect on a dike[J]. Geophysics, 1962, 27(5): 666-676.

[41] D'erceville I, Kunetz G. The Effect of a Fault on the Earth's Natural Electromagnetic Field[J]. Geophy-sics, 1962, 27(5): 651-665.

[42] Wait J R, Spies K P. Magneto-Telluric Fields for a Segmented Overburden[J]. Journal of Geomagnetism and Geoelectricity, 1974, 26(5): 449-458.

[43] Simpson F, Bahr K. Practical Magnetotellurics[M]. Cambridge: Cambridge University Press, 2005.

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