Principles of a Fast Probability-Based, Data-Adaptive Gravity Inversion Method for 3D Mass Density Modelling

The aim of this paper is to present a 3D Probability-based Earth Density Tomography Inversion (PEDTI) method derived from the principles of the Gravity Probability Tomography (GPT). The new method follows the rationale of a previous Probability-based Electrical Resistivity Inversion (PERTI) method, which has proved to be a fast and versatile user-friendly approach. Along with PERTI, PEDTI requires no external a priori information. In this paper, after recalling the GPT imaging method, the PEDTI theory is developed and concluded with a key inversion formula that allows a wide class of equivalent solutions to be computed. Two synthetic cases are discussed to show the resolution that can be achieved in the determination of density contrasts and to examine the nature of the gravity non-uniqueness problem. Regarding the first issue, it is shown that the estimate of the density by PEDTI can change by about two orders of magnitude and get closer to reality with a more focused solution on a specific source body. Regarding the second problem, it is shown that two levels of equivalence can be classified, i.e., weak and strong equivalence, for a finer selection among the solutions. This is obtained by defining two appropriate statistical indices based on the information power of both the input and output gravity datasets.