Geophysical research: article

A.S. Dolgal L.A. Khristenko
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
Full text
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 22 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 0.50.5 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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