Use of spheroidal models in gravitational tomography

TL;DR

This paper presents a method for solving gravitational tomography problems by modeling deposit bodies as spheroids and stabilizing the inverse problem through Tikhonov regularization, with numerical examples demonstrating its effectiveness.

Contribution

It introduces a spheroidal modeling approach for inverse gravimetry, transforming formulas for stability and modifying initial estimation algorithms.

Findings

Stable and unique solutions for inverse gravimetry problems.

Effective modeling of deposits as spheroids improves interpretability.

Numerical examples validate the method's accuracy.

Abstract

The direct gravimetry problem is solved using the subdivision of each body of a deposit into a set of vertical adjoining bars, and in the inverse problem each body of a deposit is modeled by a uniform ellipsoid of revolution (spheroid). Well-known formulas for z-component of gravitational intensity of a spheroid are transformed to a convenient form. Parameters of a spheroid are determined by minimizing the Tikhonov smoothing functional using constraints on the parameters. This 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 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 the intravision of the Earth's crust and mantle.