Hamiltonian Monte Carlo Probabilistic Joint Inversion of 2D (2.75D) Gravity and Magnetic Data

Two-dimensional modeling of gravity and magnetic anomalies in terms of polygonal bodies is a popular approach to infer possible configurations of geological structures in the subsurface. Alternatively to the traditional trial-and-error manual fit of measured data, here we illustrate a probabilistic strategy to solve the inverse problem. First we derive a set of formulae for solving a 2.75-dimensional forward model, where the polygonal bodies have a given finite lateral extent, and then we devise a Hamiltonian Monte Carlo algorithm to jointly invert gravity and magnetic data for the geometry and properties of the polygonal bodies. This probabilistic approach fully addresses the nonlinearity of the forward model and provides uncertainty estimation. The result of the inversion is a collection of models which represent the posterior distribution, analysis of which provides estimates of sought properties and may reveal different scenarios.