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

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.

27 pages

References in corpus (4)

• Dirichlet integral point-source harmonic interpolation over ${\mathbb{R}}^3$ spherical interiors: DIDACKS II
• Dirichlet integral dual-access collocation-kernel space analytic interpolation for unit disks: DIDACKS I
• Closed-form Dirichlet integral harmonic interpolation-fits for real n-dimensional and complex half-space: DIDACKS III
• Comments on the Reliability of Lawson and Hanson's Linear Distance Programming Algorithm: Subroutine LDP