Geodesic
About geophysical inverse problem from the point of view of strakhov's ideas
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 56-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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The approach of magnetotelluric sounding (MTS) inverse problems solving is considered in the aspect of V.N. Strakhov's ideas development and is based on solving of inverse geophysical problems without the corresponding forward problems solutions. For this aim it is sufficient to know mathematical operator which describes the corresponding field, including magnetotelluric impedance. The most important result of this approach is the possibility of inverse problems solving for anisotropic and bianisotropic models of the geological medium, while the usage of the method of solving inverse problems according to A.N. Tikhonov encounters difficulties in minimizing the residual functional due to an increase in the number of unknown electromagnetic parameters wanted to be determined, and leads to instability and ambiguity in the interpretation of MT-data. Riccati equations for magnetotelluric impedance and admittance (the most common linear electromagnetic properties of rocks and materials) for bianisotropic medium are obtained. Received results of numerical experiments confirm the possibility of applying V.N. Strakhov's ideas for MTS inverse problems solving. Further development of this approach is associated with the incorrect problems solving due to the presence of various kinds of experimental data noises.
Keywords: magnetotelluric sounding, inverse problem, one-dimensional horizontally homogeneous medium, conductance anisotropy, bianisotropic medium. 
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P. N. Aleksandrov; O. B. Zabinyakova. About geophysical inverse problem from the point of view of strakhov's ideas. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 56-69. http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a3/

[1] Berdichevskiy M. N., Dmitriev V. I., Modeli i metody magnitotelluriki [Models and methods of magnetotellurics], Nauchnyy mir, M., 2009, 680 pp.

[2] Zhdanov M. S., Teoriya obratnykh zadach i regulyarizatsii v geofizike [Geophysical Inverse Theory and Regularization Problems], Nauchnyy mir, M., 2007, 712 pp.

[3] Magnitotelluricheskie polya v trekhmernykh modelyakh geoelektriki [Magnetotelluric fields in three-dimensional models of geoelectrics], Nauchnyy mir, M., 1999, 204 pp.

[4] Strakhov V. N., “Printsipial'no novaya teoriya interpretatsii dannykh o potentsial'nykh polyakh (gravitatsionnykh i magnitnykh anomaliy) [Fundamentally new theory of interpretation of potential fields data (gravitational and magnetic anomalies)]”, Geofizicheskiy zhurnal, 25:1 (2003), 3–7 | MR

[5] Strakhov V.N., Stepanova I.E., Grichuk L.V., “O reshenii obratnykh zadach gravimetrii bez resheniya pryamykh [On solving inverse problems of gravimetry without solving of forward]”, Voprosy teorii i praktiki kompleksnoy geologicheskoy interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh poley, Tezisy dokladov Mezhdunarodnoy shkoly-seminara, 3-8 oktyabrya 2002, Apatity, 2002, 81–84

[6] Berdichevskiy M. N., Dmitriev V. I., Magnitotelluricheskoe zondirovanie gorizontal'no-odnorodnykh sred [Magnetotelluric Sounding of Horizontally Homogeneous Media], Nedra, M., 1992, 250 pp.

[7] Sidorov V. A., Impul'snaya induktivnaya elektrorazvedka [Pulse Inductive Electrical Exploration], Nedra, M., 1985, 192 pp.

[8] Aleksandrov P. N., “Metod szhimayushchikhsya oblastey v zadachakh geofiziki [The method of contracting areas in geophysics problems]”, Voprosy teorii i praktiki kompleksnoy geologicheskoy interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh poley, materialy mezhdunarodnoy shkoly-seminara, 15-24 noyabrya 2000, g. Ukhta, 2001, 6–12

[9] Aleksandrov P. N., “Pryamaya zadacha geoelektriki v odnomernykh bianizotropnykh sredakh [The forward geoelectrics problem in one-dimensional bianisotropic media]”, Fizika Zemli, 4 (2001), 51–61

[10] Aleksandrov P. N., “Effektivnye elektromagnitnye parametry kapillyarnoy sistemy elektroprovodnosti gornoy porody [Effective electromagnetic parameters of a capillary system of electrical conductivity of rock]”, Fizika Zemli, 2 (2000), 87–94

[11] Gantmakher F. R., Teoriya matrits. Izdanie vtoroe, dopolnennoe [Matrix theory. Second edition, supplemented], Nauka, M., 1966, 576 pp. | MR