Geophysical research: article

Gravity inverse problem solution with variable rate of gradient descent
L.S. Chepigo
I.V. Lygin
A.A. Bulychev
Lomonosov Moscow State University
Journal: Geophysical research
Tome: 23
Number: 1
Year: 2022
Pages: 5-19
UDK: 550.831
DOI: 10.21455/gr2022.1-1
Full text
Keywords: gravity exploration, inverse problem, gradient descent method, density modeling
Аnnotation: The article describes an approach to the automated solution of a linear inverse problem of gravity, which implements the construction of lateral and vertical gradient density models with the possibility to select the preferred depth of sources. The inverse problem is solved using the gradient descent method with variable rate. It is shown that if the gradient descent rate is increasing with depth, then deep cells are “included” in the process of selecting the density model. In particular, the rate of gradient descent can increase with depth as a power function. In general, the gradient descent rate depends on both depth and horizontal coordinates, and it can be specified functionally or explicitly. In the presence of a prior information, the gradient descent rate can be expressed in a more complex way, depending on the depth and on the horizontal coordinates. In this case, the maximum values of the gradient descent rate should be assigned to the cells in which, according to a prior data, density inhomogeneities are located or expected. These can be depth-velocity models, widely used in seismic exploration, so it opens the way for integration. The article shows the application of the approach on a test model consisting of two infinite horizontal rods located at different depths. The performance of the algorithm with different values of the power function is assessed by comparing the selected depths of the centers of mass with the true depths. It is shown that the optimal results of solving the inverse problem for the selected type of model are achieved using the gradient descent rate proportional to the square of the depth. The developed algorithm forms the basis of the author's software package GravInv [Chepigo, 2019].
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