Spheroidal models of ore deposits in the framework of gravity tomography

Sizikov V.S., Karmanovskiy N.S., Rushchenko N.G., Belozubov A.V. Spheroidal models of ore deposits in the framework of gravity tomography. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2026, vol. 26, no. 2, pp. 385–392 (in Russian). doi: 10.17586/2226-1494-2026-26-2-385-392

This paper presents a solution to the gravimetry problem of determining ore deposits in the Earth’s mantle and crust by processing the gravitational field measured at the Earth’s surface. The proposed method addresses this formally technical problem by creating a mathematical model capable of computer simulation. Existing gravimetry approaches to locating deposits require the use of technical means, particularly drilling rigs. The proposed method makes it possible to estimate the occurrence of deposits by computer processing of the measured gravitational field on the Earth’s surface. The essence of solving the forward gravimetry problem consists of calculating the model (or measured) gravitational field at the Earth’s surface by dividing each deposit body into a set of vertical rods. When solving the inverse problem of determining the deposit, each body is modeled by a homogeneous spheroid. Known calculation relationships for the gravitational field of a spheroid are transformed into a form convenient for computer implementation using nonlinear programming. The spheroid parameters are determined using the Tikhonov smoothing functional minimization method with parameter constraints. This makes the inverse ill-posed (unstable) problem unambiguous and stable. The proposed method is illustrated by a numerical model example with a two- and five-body deposit. The inverse gravimetry problem is treated as gravity tomography, or “inner vision” of the Earth’s mantle and crust, allowing for deposit visualization without drilling into the Earth’s interior. The described algorithm enables mathematical and computational methods to determine the possible presence of a deposit and estimate its parameters (type, size, depth, density, etc.) with minimal technical and financial investment. Gravity tomography results can serve as an initial approximation when selecting well locations and depths. Existing gravimetric approaches require the use of technical means (drilling rigs, etc.) to locate deposits in the Earth. The presented method, however, allows for the estimation of deposit locations through mathematical and computer processing of the measured gravitational field on the Earth’s surface without the use of expensive technical means. Gravity tomography results can serve as an initial approximation when searching for deposits using technical means during well drilling.

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