Vestnik Kamchatskoy regional'noy assotsiatsii «Uchebno-nauchnyy tsentr». Seriya: Nauki o Zemle
Institute of Volcanology and Seismology FEB RAS
Solving the inverse problem in direct current profiling methods in a linear formulation
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Keywords

electrical profiling
anisotropic media
inverse problem
volume integral equations

Section

Results of the Scientific Researches

Abstract

Profiling methods are used to study the physical properties of the geological environment in the horizontal direction, as a rule, of large geological objects in length or area, when the measuring installation moves along a given trajectory (profile) by means of a carrier. A feature of the profiling method is the fixation of the distance, mainly between sources and receivers, when moving the entire installation along the profile. The determination of the physical properties of a geological object is based on solving the inverse coefficient problem of mathematical physics. The paper proposes a new approach to solving inverse coefficient problems based on data measured by profiling installations in the direct current electrical exploration method, and based on linear volumetric integral equations. Examples of numerical implementation of the solution of the inverse profiling problem in three-dimensional inhomogeneous anisotropic models of the geological environment are considered.

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References

лександров П.Н., Кризский В.Н. Решение линейной коэффициентной обратной задачи геофизики на основе интегральных уравнений // Физика Земли. 2022. Т. 68. № 2. С. 136–143. https://doi.org/10.31857/S0002333722020016 [Alexandrov P.N., Krizsky V.N. Solution of a Linear Coefficient Inverse Problem of Geophysics Based on Integral Equations // Izvestiya, Physics of the Solid Earth. 2022. V. 58. № 2. P. 274–280. https://doi.org/10.1134/S106935132202001X].

Басниев К.С., Кочина И.Н., Максимов В.М. Подземная гидродинамика. М.: Недра, 1993. 416 с. [Basniev K.S., Kochina I.N., Maksimov V.M. Podzemnaya gidrodinamika. Moscow: Nedra, 1993. 416 p. (in Russian)].

Вержбицкий В.М. Основы численных методов. М.: Высшая школа, 2002. 840 с. [Verzhbickij V.M. Osnovy chislennyh metodov. Moscow: Vysshaya shkola, 2002. 840 p. (in Russian)].

Геофизика: учебник / Под ред. В.К. Хмелевского. 3-е изд. М.: КДУ, 2012. 320 с. [Geofizika: uchebnik / Pod red. V.K. Hmelevskogo. 3-e izd. Moscow: KDU, 2012. 320 p. (in Russian)].

Карманов В.Г. Математическое программирование. М.: Наука, 1986. 288 с. [Karmanov V.G. Matematicheskoe programmirovanie. Moscow: Nauka, 1986. 288 p. (in Russian)].

Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. М.: Наука, 1984. 832 с. [Korn G., Korn T. Spravochnik po matematike dlya nauchnyh rabotnikov i inzhenerov. Moscow: Nauka, 1984. 832 p. (in Russian)].

Кризский В.Н., Александров П.Н. Об определении удельной электропроводности локального включения кусочно-постоянной среды // Физика Земли. 2023. № 6. С. 259–268. https://doi.org/110.31857/S0002333723060108 [Krizskii V.N., Alexandrov P.N. On Determination of the Electrical Conductivity of a Local Inclusiuo of a Piecewise-Constant Isotropic Medium // Izvestiya, Physics of the Solid Earth. 2023. V 59. №6. P. 1056−1065. https://doi.org/110.1134/S1069351323060101].

Морс Ф.М., Фешбах Г. Методы теоретической физики. Т. 2. М.: Иностранная литература, 1960. 974 с. [Mors F.M., Feshbakh G. Metody teoreticheskoj fiziki. T. 2. Moscow: Inostrannaya literatura, 1960. 974 p.(in Russian)].

Тихонов А.Н., Арсенин В.Я. Методы решения некорректных задач. М.: Наука, 1986. 288 с. [Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnyh zadach. Moscow: Nauka, 1986. 288 p. (in Russian)].

Электроразведка: Справочник геофизика / Под ред. А. Г. Тархова. М.: Недра, 1980. 518 с. [Elektrorazvedka: Spravochnik geofizika / Pod red. A.G. Tarhova. Moscow: Nedra, 1980. 518 p. (in Russian)].

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