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Forward and inverse problems of magnetotellurics

Authors: Zubarev K.M., Ivanova T.L.
Published in issue: #3(3)/2016
DOI: 10.18698/2541-8009-2016-3-26


Category: Mathematics | Chapter: Computational Mathematics

Keywords: electrical prospecting, magnetotellurics, apparent resistivity, Tikhonov - Cagniard model, horizontally stratified medium, resistivity, forward problem, inverse problem
Published: 02.12.2016

The article proposes a mathematical model for a horizontally stratified medium. We consider forward and inverse problems of magnetotellurics for preset multilayered medium parameters. We solved the magnetotellurics problem for a three-layer medium with various parameters. We supply results of solving the forward and inverse problems that allowed us to detect the specifics of each method and compare the algorithms implemented. The software package developed can be used for solving problems based on various medium models.


References

[1] Zhdanov M.S. Elektrorazvedka [Electric prospecting]. Moscow, Nedra Publ., 1986. 316 p. (in Russ.).

[2] Zhdanov M.S., Varentsov I.M., Golubev N.G., Krylov V.A. Metody modelirovaniya elektromagnitnykh poley. Materialy mezhd. proekta COMEMI [Methods for magnetic field simulation. Proc. of "COMEMI" Int. Project]. Moscow, Nauka Publ., 1990. 199 p. (in Russ.).

[3] Matveev B.K. Elektrorazvedka [Electric prospecting]. Moscow, Nedra Publ., 1990. 232 p. (in Russ.).

[4] Berdichevskiy M.N. Elektricheskaya razvedka metodom magnitotelluricheskogo profilirovaniya [Electric prospecting by magnetotelluric profiling method]. Moscow, Nedra Publ., 1968. 254 p. (in Russ.).

[5] Berdichevskiy M.N. Elektricheskaya razvedka metodom telluricheskikh tokov [Electric prospecting by electric current method]. Moscow, Gostoptekhizdat Publ., 1960. 239 p. (in Russ.).

[6] Berdichevskiy M.N., Dmitriev V.I. Magnitotelluricheskoe zondirovanie gorizontal’no-odnorodnykh sred [Magnetotelluric sounding of lateral-homogeneous medium]. Moscow, Dialog-MGU Publ., 1997. 352 p. (in Russ.).

[7] Vladimirov V.S. Uravneniya matematicheskoy fiziki [Mathematical physics equations]. Moscow, Nauka Publ., 1988. 512 p. (in Russ.).

[8] Gol’tsman F.M. Topical issues of information statistic interpretation theory for geophysical exploration. Izvestiya AN SSSR. Fizika Zemli, 1977, no. 12, pp. 75-86 (in Russ.).

[9] Gol’tsman F.M. Statisticheskie metody interpretatsii [Statistical interpretation methods]. Moscow, Nauka Publ., 1971. 328 p. (in Russ.).

[10] Dmitriev V.I. Direct and inverse problems of magnetotelluric layered earth sounding. Izvestiya AN SSSR. Fizika Zemli, 1970, no. 1, pp. 64-69 (in Russ.).

[11] Al’pin L.M., Daev D.S., Karinskiy A.D. Teoriya poley, primenyaemykh v razvedochnoy geofizike [Field theory used in exploratory geophysics]. Moscow, Nedra Publ., 1985. 407 p. (in Russ.).

[12] Andreeva E.V. Controlled transformation of magnetotelluric sounding curves. Izvestiya AN SSSR. Fizika zemli, 1991, no. 10, pp. 89-95 (in Russ.).

[13] Kraev A.P. Osnovy geoelektriki [Fundamentals of geoelectrical engineering]. Leningrad, Nedra Publ., 1965. 588 p. (in Russ.).

[14] Auzin A.K. Elektrorazvedka (spetskurs po induktivnym i radiovolnovym metodam rudnoy elektrorazvedki) [Electric prospecting (specialized course on inductive and radio-frequency methods of mine electric prospecting)]. Moscow, Nedra Publ., 1977. 134 p. (in Russ.).

[15] Nikitin A. A. Teoreticheskie osnovy obrabotki geofizicheskoy informatsii [Theoretical foundations of geophysical data processing]. Moscow, Nedra Publ., 1986. 342 p. (in Russ.).

[16] Khmelevskiy V.K. Osnovnoy kurs elektrorazvedki [Electric prospecting basic course]. Moscow, MSU Publ., 1970. 245 р. (in Russ.).

[17] Sheynmann S.M. Sovremennye fizicheskie osnovy teorii elektrorazvedki [Modern physical principles of electric prospecting theory]. Leningrad, Nedra Publ., 1969. 242 p. (in Russ.).

[18] Yakubovskiy Yu.V., Lyakhov L.L. Elektrorazvedka [Electric prospecting]. Moscow, Nedra Publ., 1980. 365 p. (in Russ.).

[19] Gribov A.F., Zhidkov E.N., Krasnov I.K. A numerical solution of inverse problem of head transfer. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2013, no. 9 (in Russ.). DOI: 10.18698/2308-6033-2013-9-964

[20] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. T. 2: Universal’nye zakony mekhaniki i elektrodinamiki sploshnoy sredy [Continuum mechanics. Vol. 2. Universal continuum mechanics and electrodynamics laws]. Moscow, Bauman MSTU Publ., 2011. 560 p. (in Russ.).

[21] Dimitrienko Yu.I., Krasnov I.K., Resh G.F., Akinkin D., Kuznetsov I. Development of computing technology for solving the geometrically inverse problems of thermal diagnostics of three-layer welded constructions. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2012. no. 2 (in Russ.). DOI: 10.18698/2308-6033-2012-2-37

[22] Dimitrienko Yu.I., Gubareva E.A., Markevich M.N., Sborshchikov S.V. Mathematical modelling of dielectric properties of nanostructural composites using asymptotic homogenizing method. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki [Herald of the Bauman Moscow State Technical University. Ser. Natural Sciences], 2016, no. 1, pp. 76-89 (in Russ.). DOI: 10.18698/1812-3368-2016-1-76-89

[23] Apel’tsin V.F., Mozzhorina T.Yu. Properties of one-dimensional photonic crystal as a reflective or wave guiding structure when excited by H-polarization. Matematicheskoe mod-elirovanie i chislennye metody, 2014, no. 2 (2), pp. 3-27 (in Russ.). DOI: 10.18698/2309-36842014-2-327