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IMPROVEMENT OF COMPUTER TECHNOLOGY FOR SEPARATING GRAVITY ANOMALIES USING EQUIVALENT SOURCES
Mining Institute, Ural Branch of the Russian Academy of Sciences
Journal: Geophysical research
Tome: 24
Number: 1
Year: 2023
Pages: 31-43
UDK: 550.831.016
DOI: 10.21455/gr2023.1-2
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Dolgal
L.A A.S. IMPROVEMENT OF COMPUTER TECHNOLOGY FOR SEPARATING GRAVITY ANOMALIES USING EQUIVALENT SOURCES
// . 2023. Т. 24. № 1. С. 31-43. DOI: 10.21455/gr2023.1-2
@article{Dolgal
L.AIMPROVEMENT2023,
author = "Dolgal
L.A, A. S.",
title = "IMPROVEMENT OF COMPUTER TECHNOLOGY FOR SEPARATING GRAVITY ANOMALIES USING EQUIVALENT SOURCES
",
journal = "Geophysical research",
year = 2023,
volume = "24",
number = "1",
pages = "31-43",
doi = "10.21455/gr2023.1-2 ",
language = "English"
}
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Keywords: gravity exploration, transformation, approximation, equivalent source, matrix, vector, system of linear algebraic equations, Choletsky method, steepest gradient descent, accuracy.
Аnnotation: An efficient algorithm for separating gravity anomalies by the method of sourcewise approximation using two levels of placement of equivalent sources (point masses) corresponding to the regional and local components of the initial field has been developed. This entails the decomposition of the problem into two independent computational cycles. Determination of the masses of “deep” sources in the first cycle is carried out by solving the normal system of linear algebraic equations (SLAE) by the Choletsky method. Calculation of the masses of “near-surface” sources in the second cycle is performed by solving the band SLAE by the steepest gradient de-scent method.
The algorithm is implemented in the Delphi language in the APP_NG program, the results of which are given in the article. For a synthetic model consisting of three rectangular prisms with different effective densi-ties, estimates of the accuracy and speed of calculations are obtained. The construction of an analytical model of the gravitational field, presented as a 169×109 matrix, takes 5 s with an approximation accuracy of 0.003 mGl. The two-level approximation design reduces edge distortions by a factor of approximately 4,5 for the re-sults of recalculating the gravitational field into the upper half-space at a height of 5 km compared to placing equivalent sources at one fixed depth. In this case, the computational speed increases by almost 40 times.
The results of the joint use in the process of transformation of the results of medium- and large-scale gravitmetric surveys carried out in the northwestern part of the Siberian Platform are presented. The gravita-tional field specified at the network nodes of 22 km over an area of 380 thousand km2 is used to construct a regional background corresponding to sources located at the depth of 25 km. The local (difference) component of the field is calculated at network nodes of 0.50.5 km within the area of large-scale studies of 14 thousand km2 and is approximated by point masses located at the depth of 0.5 km. Calculation of transformants for this area is carried out by solving the direct problem of gravity exploration from “deep” and “near-surface” equiva-lent sources. In the future, the algorithm can be modified in relation to the spherical model of the Earth.
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Tafeev G.P., Sokolov K.P., Geologicheskaya interpretatsiya magnitnykh anomalii (Geological interpretation of magnetic anomalies), Leningrad, Nedra, Leningr. otd-nie, 1981, 327 p. [In Russian].
Veselkova N.V., Pugin A.V., The problem of accounting for third-party sources in the practice of transforming geopotential fields, Geofizika (Geophysics), 2010, no. 1, pp. 69-73. [In Russian].
Vychislitel'naya matematika i tekhnika v razvedochnoi geofizike: spravochnik geofizika (Computational Math-ematics and Engineering in Exploration Geophysics: Geophysics Handbook), Moscow, Nedra, 1990, 498 p. [In Russian].
Bakhvalov N.S., Zhidkov N.P., Kobel'kov G.M., Chislennye metody (Numerical Methods), Moscow, BINOM, Labratoriya znanii, 2008, 636 p. [In Russian].
Balk P.I., Dolgal A.S., Pugin A.V., Effective algorithms for sourcewise approximation of geopotential fields, Izvestiya. Physics of the Solid Earth, 2016, vol. 52, no. 6, pp. 896-911.
Blokh Yu.I., Interpretatsiya gravitatsionnykh i magnitnykh anomalii (Interpretation of gravitational and mag-netic anomalies), 2009, 232 p. [In Russian]. http://sigma3d.com/index.php/publications/books
Dolgal' A.S., Practical Aspects of Applying Approximation of Geopotential Fields by Source Functions, in In-zhenernaya i rudnaya geofizika 2020: 16-ya nauchno-prakticheskaya konferentsiya sovmestno s semi-narom “Inzhenernaya i rudnaya geologiya 2020”, Perm', 14–18 sentyabrya 2020 g. (Engineering and ore geophysics 2020: 16th scientific and practical conference jointly with the seminar “Engineering and ore geology 2020”, Perm, September 14–18, 2020), Perm', ООО “EAGE GEOMODEL”, 2020, pp. 1-10. [In Russian]. DOI: 10.3997/2214-4609.202051058
Dolgal' A.S., Kostitsyn V.I., Novikova P.N., Voroshilov V.A., Improving the Method of Analytical Approxima-tion of Magnetic Data, Geofizika (Geophysics), 2020, no. 5, pp. 31-38. [In Russian].
Dolgal A.S., Pugin A.B., Novikova P.N., History of the Method for Sourcewise Approximations of Geopoten-tial Fields, Izvestiya. Physics of the Solid Earth, 2022, vol. 58, no. 2, pp. 149-171.
Chepigo L.S., Lygin I.V., Bulychev A.A., Gravity inverse problem solution with variable rate of gradient de-scent, Geofizicheskie issledovaniya (Geophysical research), 2022, vol. 23, no. 1, pp. 5-19. [In Russian]. DOI: 10.21455/ gr2022.1-1
Gordin V.M., Tikhotskii S.A., Sourcelike Approximations of Gravitational and Magnetic Fields: Background, in Sbornik materialov 1-i vserossiiskoi konferentsii “Geofizika i matematika” (Collection of materials of the 1st All-Russian Conference “Geophysics and Mathematics”), Moscow, OIFZ RAN, 1999, pp. 55-57. [In Russian].
Gravirazvedka: Spravochnik geofizika (Gravity exploration: Handbook of geophysics), Moscow, Nedra, 1990, 607 p. [In Russian].
Kerimov I.A., Stepanova I.E., Raevskii D.N., Combined Approximation Methods for Solving Gravity and Mag-netic Problems, Geologiya i geofizika Yuga Rossii (Geology and geophysics of the South of Russia), 2018, vol. 8, no. 3, pp. 37-50. [In Russian]. DOI: 10.23671/VNC.2018.3.16544
Pugin A.V., Sourcewise Approximation of Geopotential Fields. From Theory to Practice, Geofizicheskie issle-dovaniya (Geophysical research), 2018, vol. 19, no. 4, pp. 16-30. [In Russian]. DOI: 10.21455/gr2018.4-2
Starostenko V.I., Ustoichivye chislennye metody v zadachakh gravimetrii (Stable Numerical Methods in Prob-lems of Gravimetry), Kiev, Nauk. Dumka, 1978, 227 p. [In Russian].
Stepanova I.E., Modified S-Approximation Method for the Solution of Inverse Problems in Geophysics and Geomophology, Geofizicheskie issledovaniya (Geophysical research), 2017, vol. 18, no. 1, pp. 63-84. [In Russian]. DOI: 10.21455/gr2017.1-5
Stepanova I.E., Raevskiy D.N., Shchepetilov A.V., On the interpretation of large gravimagnetic data by the modified method of S-approximations, Izvestiya. Physics of the Solid Earth, 2017, vol. 53, no. 1, pp. 116-129. DOI: 10.1134/S1069351316060112
Strakhov V.N., Kerimov I.A., Stepanova I.E., Razrabotka teorii i komp'yuternoi tekhnologii postroeniya lineinykh analiticheskikh approksimatsii gravitatsionnykh i magnitnykh polei (Development of the theo-ry and computer technology for constructing linear analytical approximations of gravitational and mag-netic fields), Moscow, IFZ RAN, 2009, 254 p. [In Russian].
Tafeev G.P., Sokolov K.P., Geologicheskaya interpretatsiya magnitnykh anomalii (Geological interpretation of magnetic anomalies), Leningrad, Nedra, Leningr. otd-nie, 1981, 327 p. [In Russian].
Veselkova N.V., Pugin A.V., The problem of accounting for third-party sources in the practice of transforming geopotential fields, Geofizika (Geophysics), 2010, no. 1, pp. 69-73. [In Russian].
Vychislitel'naya matematika i tekhnika v razvedochnoi geofizike: spravochnik geofizika (Computational Math-ematics and Engineering in Exploration Geophysics: Geophysics Handbook), Moscow, Nedra, 1990, 498 p. [In Russian].
