Bars and spheroids in gravimetry problem

TL;DR

This paper introduces a method for solving the inverse gravimetry problem by modeling deposit bodies as spheroids and applying Tikhonov regularization to achieve stable, unique solutions, with practical numerical examples.

Contribution

It develops a novel approach to inverse gravimetry using spheroid models and Tikhonov regularization, improving stability and uniqueness of solutions.

Findings

Stable solutions for inverse gravimetry achieved using spheroid models.

Modified Bulakh algorithm for initial estimates enhances accuracy.

Numerical examples demonstrate effectiveness in modeling multiple deposits.

Abstract

The direct gravimetry problem is solved by dividing each deposit body into a set of vertical adjoining bars, whereas in the inverse problem, each deposit body is modelled by a homogeneous ellipsoid of revolution (spheroid). Well-known formulae for the z-component of gravitational intensity for a spheroid are transformed to a convenient form. Parameters of a spheroid are determined by minimizing the Tikhonov smoothing functional with constraints on the parameters, which makes the ill-posed inverse problem by unique and stable. The Bulakh algorithm for initial estimating the depth and mass of a deposit is modified. The proposed technique is illustrated by numerical model examples of deposits in the form of two and five bodies. The inverse gravimetry problem is interpreted as a gravitational tomography problem or, in other words, as "introscopy" of Earth's crust and mantle.