Geodesic
The inverse problem of interpretation of gravitational and magnetic anomalies of hydrocarbon deposits
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 46-57.

Voir la notice de l'article provenant de la source Math-Net.Ru

Under consideration is the inverse problem of determining the source of gravitational or magnetic anomalies of hydrocarbon deposits as well as some algorithm for solving the problem. We suggest a procedure for determining the source domain. The inverse problem of finding the source density distribution is solved by the Monte Carlo method in the framework of statistical regularization. We present the results of a model experiment and estimate the errors in terms of the discrepancy when using the precise data and those with errors.
Keywords: inverse problem of interpretation, inverse boundary value problem, source inverse problem, Monte Carlo method, statistical regularization. 
@article{SJIM_2020_23_1_a4,
     author = {Yu. V. Glasko},
     title = {The inverse problem of interpretation of gravitational and magnetic anomalies of hydrocarbon deposits},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a4/}
}
TY  - JOUR
AU  - Yu. V. Glasko
TI  - The inverse problem of interpretation of gravitational and magnetic anomalies of hydrocarbon deposits
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2020
SP  - 46
EP  - 57
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a4/
LA  - ru
ID  - SJIM_2020_23_1_a4
ER  - 
%0 Journal Article
%A Yu. V. Glasko
%T The inverse problem of interpretation of gravitational and magnetic anomalies of hydrocarbon deposits
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2020
%P 46-57
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a4/
%G ru
%F SJIM_2020_23_1_a4
Yu. V. Glasko. The inverse problem of interpretation of gravitational and magnetic anomalies of hydrocarbon deposits. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 46-57. http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a4/

[1] M. M. Lavrent'ev, V. G. Romanov, S. P. Shishatskii, Ill-Posed Problems of Mathematical Physics and Analysis, Amer. Math. Soc., Providence, 1986 | MR | MR | Zbl

[2] H. Poincaré, Selected Works, v. 3, Nauka, M., 1974 (in Russian)

[3] S. K. Godunov, Mathematical Physics Equations, Nauka, M., 1979 (in Russian)

[4] V. N. Strakhov, “To the theory of plane problems of gravimetry and magnetometry: the “analytical world” generated by the Poincaré sweeping”, Izv. Akad. Nauk SSSR. Ser. Fiz. Zemli, 1978, no. 2, 47–73 (in Russian)

[5] S. K. Godunov, V. S. Ryaben'kii, Theory of Difference Schemes: An Introduction to the Underlying Theory, North-Holland, Amsterdam, 1987 | MR | MR

[6] D. P. Zidarov, To Solution of Some Inverse Problems of Potential Fields and Their Application to Geophysics Problems, Publ. Bolgarsk. Akad. Nauk, Sofiya, 1980 (in Russian)

[7] S. I. Kabanikhin, Y. S. Gasimov, D. B. Nurseitov, M. A. Shishlenin, B. B. Sholpanbaev, S. E. Kasenov, “Regularization of the continuation problem for elliptic equations”, J. Inverse Ill-Posed Probl., 21:6 (2013), 871–884 | MR | Zbl

[8] A. A. Samarskii, Theory of Difference Schemes, Nauka, M., 1989 (in Russian)

[9] A. N. Tikhonov, V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems, Nauka, M., 1979 (in Russian)

[10] V. M. Megerya, V. I. Starostenko, V. G. Filatov, S. V. Zinovkin et al, Density Determination of Rocks and Geological Objects in Oil and Gas Exploration, Publ. Ross. Gos. Geolog. Univ., M., 2011 (in Russian)

[11] Gravitational Prospecting. Handbook of Geophysicist, Nedra, M., 1981 (in Russian)

[12] M. M. Lavrent'ev, V. I. Starostenko, V. G. Filatov, Yu. V. Glasko et al, Application of Regularization in Gravitational-Magnetic Prospecting for Hydrocarbon Deposits, Publ. Ross. Gos. Geolog. Univ., M., 2010 (in Russian)

[13] V. M. Megerya, V. G. Filatov, V. I. Starostenko, I. N. Korchagin, A. M. Lobanov, Yu. V. Glasko, M. Yu. Volotskov, S. A. Skachkov, “Opportunities and prospects for nonseismic methods to search for hydrocarbon accumulations and the geosoliton concept of their formation”, Geofiz. Zh., 34:3 (2012), 4–21 (in Russian)

[14] A. G. Yagola, I. E. Stepanova, V. N. Titarenko, Inverse Problems and Methods for Solution of Them. Applications in Geophysics, BINOM, M., 2014 (in Russian)

[15] A. A. Nikitin, A. V. Petrov, V. M. Megerya, V. I. Starostenko et al., Optimal Filtration and Introcontinuation of Geofields with Account for Secondary Magnetic Mineral Formation in Oil-and-Gas Prospecting, NT Press, M., 2011 (in Russian)

[16] Yu. V. Glasko, “2D and 3D Algorithms of Introcontinuation”, Numer. Meth. Program, 17 (2016), 291–298

[17] A. G. Sveshnikov, V. V. Bogolyubov, V. V. Kravtsov, Lecture Notes in Mathematical Physics, Publ. Moskov. Gos. Univ., M.; Nauka, 2004 (in Russian) | MR

[18] Yu. V. Glasko, “The Problem of Concentration of Masses”, Izv. Physics of the Solid Earth, 51:2 (2015), 191–196 | DOI | DOI

[19] I. M. Sobol', Monte Carlo Method, Nauka, M., 1985 (in Russian) | MR

[20] E. S. Kochetkov, S. O. Smerchinskaya, V. V. Sokolov, Probability Theory and Mathematical Statistics, Forum, M.; Infa-M, 2014 (in Russian)

[21] Yu. V. Glasko, “Interpretation Algorithms for Hydrocarbon Deposits”, Practical and Theoretical Aspects of Geological Interpretation of Gravitational, Magnetic, and Electric Fields, Springer Proceedings in Earth and Environmental Sciences, 1, Springer-Verl., Switzerland, 2019, 113–125 | DOI

[22] Yu. P. Pyt'ev, I. A. Shishmarev, Course of Probability Theory and Mathematical Statistics for Physicists, Publ. Moskov. Gos. Univ., M., 1983 (in Russian)

[23] O. M. Alifanov, Identification of Heat Exchange Processes of Aircrafts, Mashinostroenie, M., 1979 (in Russian)

[24] V. N. Vapnik, Recovery of Dependences from Empirical Data, Nauka, M., 1979 (in Russian) | MR

[25] V. M. Megerya, V. I. Starostenko, V. G. Filatov, A. N. Lobanov et al, Unstructured Hydrocarbon Deposits and Their Manifestations in Gravitational Fields, Publ. Ross. Gos. Geolog. Univ., M., 2011 (in Russian)

[26] A. A. Samarskii, P. N. Vabishchevich, Numerical Methods for Solution of Convection-Diffusion Problems, Editorial URSS, M., 1999 (in Russian)

[27] A. G. Yagola, K. Yu. Dorofeev, “Sourcewise representation and a posteriori error estimates for ill-posed problems”, Fields Institute Communications, Operator Theory and Its Applications, 25, Amer. Math. Soc., Providence, 2000, 543–550 | MR | Zbl