A closed-form energy-minimization basis for gravity field source estimation: DIDACKS IV

TL;DR

This paper introduces a new closed-form method based on energy minimization principles for estimating Earth's interior density, aiming for unique, physically meaningful solutions to inverse gravity problems.

Contribution

It develops a novel closed-form energy-minimization framework for gravity source estimation, improving solution uniqueness and addressing ill-posedness in inverse problems.

Findings

Provides a theoretical foundation for stable density estimation

Suggests practical tools for inverse-source Laplacian problems

Enhances solution uniqueness through energy minimization

Abstract

By building on the field energy minimization underpinnings of DIDACKS theory and by making certain natural assumptions about the general nature of the energy/density configuration of the Earth's interior it is shown that the problem of estimating the Earth's interior density, either globally or locally, can be naturally reframed as a energy minimization one. The basic idea is that a static stable density configuration is a minimum energy configuration, which tends to be unique (when all other things are equal); hence, a field energy minimization approach can be counted on to generally lead to a physically motivated unique solution. Techniques touched on should provide practical implementation tools, or at least some helpful hints, for handling many of the well-known ill-posedness issues associated with mass density estimation and other related inverse-source Laplacian problems.