doi: 10.18698/2309-3684-2018-1-4154
The problem of the electrophysical parameter recovery of layered media, which is the inverse problem of mathematical physics, is solved on the basis of the electromagnetic field measurement results. Various optimization methods for its solution are formulated. The mathematical model is proposed for a horizontally layered medium with specified parameters consistent with real values. The algorithm is developed for solving the direct problem allowing finding an analytical solution for various environmental parameter values. For solving inverse problems the complete enumeration and Hook - Jeeves methods as well as the developed modified method of complete enumeration are used. According to the results of solving the direct problem, the characteristic features of the medium are found for various values of the electrophysical parameters. When solving the inverse problem using various optimization methods, the features of each algorithm are described.
[1] Alpin L.M., Daev D.S., Karinsky A.D. Teoriya poley, primenyaemykh v razvedochnoy geofizike [The theory of the fields applied in exploratory geophysics]. Moscow, Nedra Publ., 1985, 407 p.
[2] Andreyeva E.V., Berdichevsky M.N., Golubtsova N.S., Koldaev D.S., Yakovlev A.G. Izvestiya Akademii nauk SSSR. Ser. Fizika Zemli — Izvestiya, Physics of the Solid Earth, 1991, no. 10, pp. 89–95.
[3] Auzin A.K. Elektrorazvedka. Spetskurs po induktivnym i radiovolnovym metodam rudnoy elektrorazvedki [Geoelectrical prospecting. Special course on inductive and radio wave methods of ore electrical prospecting]. Moscow, Nedra Publ., 1977, 134 p.
[4] Berdichevsky M.N. Elektricheskaya razvedka metodom magnetotelluricheskogo profilirovaniya [Geoelectrical prospecting by magneto-telluric profiling]. Moscow, Nedra Publ., 1968, 254 p.
[5] Berdichevsky M.N. Elektricheskaya razvedka metodom telluricheskikh tokov [Geoelectrical prospecting by telluric currents]. Moscow, Gostoptekhizdat Publ., 1960, 239 p.
[6] Berdichevsky M.N., Dmitriev V.I. Magnitotelluricheskoe zondirovanie gorizontalno-odnorodnykh sred [Magneto-telluric sounding of horizontally homogeneous media]. Moscow, Nedra Publ., 1992, 352 p.
[7] Zubarev K.M. Ivanova T.L. Politekhnicheskiy molodezhnyy zhurnal (Polytechnic youth magazine), 2016, no. 3. DOI: 10.18698/2541-8009-2016-3-26
[8] Dmitriyev V.I. Izvestiya Akademii nauk SSSR. Ser. Fizika Zemli — Izvestiya, Physics of the Solid Earth, 1970, no. 1, pp. 64–69.
[9] Zhdanov M.S. Electrorazvedka [Geoelectrical prospecting]. Moscow, Nedra Publ., 1986, 316 p.
[10] Zhdanov M.S., Varentsov I.M., Golubev N.G., Krylov V.A. Metody modelirovaniya elektromagnitnykh poley [Methods for electromagnetic field simulation]. Materialy mezhdunarodnogo proekta COMEMI [Materials of the International Project COMEMI]. Moscow, Nauka Publ., 1990, 198 p.
[11] Kraev A.P. Osnovy geoelektriki [Geoelectrics basics]. Leningrad, Nedra Publ., 1965, 587 p.
[12] Matveev B.K. Electrorazvedka [Geoelectrical prospecting]. Moscow, Nedra Publ., 1990, 368 p.
[13] Nikitin A.A. Teoreticheskie osnovy obrabotki geofizicheskoy informatsii [Principal theory of geophysical information processing]. Moscow, Nedra Publ., 1986, 342 p.
[14] Hmelevsky V.K. Osnovnoy kurs elektrorazvedki. V 3 chastyakh [Basic course of geoelectrical prospecting. In 3 parts]. Moscow, MGU Publ., 1970–1975, Part 1, 1970, 324 p.; part 2, 1971, 383 p.; part 3, 1975, 402 p.
[15] Sheynmann S.M. Sovremennye fizicheskie osnovy teorii elektrorazvedki [The modern principal physics of the geoelectrical prospecting theory]. Leningrad, Nedra Publ., 1969, 242 p.
[16] Yakubovsky Yu.V., Lyakhov L.L. Electrorazvedka [Geoelectrical prospecting]. Moscow, Nedra Publ., 1980, 365 p.
[17] Goltsman F.M. Izvestiya Akademii nauk SSSR. Ser. Fizika Zemli — Izvestiya, Physics of the Solid Earth, 1977, no. 12, pp. 75–86.
[18] Goltsman F.M. Statisticheskie modeli interpretatsii [Statistical interpretation models]. Moscow, Nauka Publ., 1971, 328 p.
[19] Gribov A.F., Zhidkov E.N., Krasnov I.K. Inzhenernyy zhurnal: Nauka i innovatsii — Engineering Journal: Science and Innovation, 2013, no. 9. DOI: 10.18698/2308-6033-2013-9-964
[20] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. V 4 tomakh. T. 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnoy sredy [Continuum mechanics. In 4 volumes. Vol. 2. Universal laws of continuum mechanics and lectrodynamics]. Moscow, BMSTU Publ., 2011, 560 p.
[21] Dimitrienko Yu.I., Krasnov I.K., Resh G.F., Akinkin D., Kuznetsov I. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences. Spec. issue no. 3“Mathematical modeling”, 2012, pp. 55–63.
[22] Dimitrienko Yu.I., Gubareva E.A., Markevich M.N., Sborshchikov S.V. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2016, no. 1, pp. 76–89.
[23] Apeltsin V.F. Mozzhorina T.Yu. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2014, no. 2 (2), pp. 3–27.
Краснов И.К., Зубарев К.М., Иванова Т.Л. Численное решение задачи восстановления электрофизических параметров по результатам зондирования переменным током. Математическое моделирование и численные методы, 2018, № 1, с. 41-54
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