A Generalized Method for the three-dimensional characterization of the internal structure of planetary bodies based on Markov Chain Monte Carlo (MCMC) techniques

This study presents a novel Bayesian framework for the three-dimensional characterization of the internal structure of planetary bodies, accounting for their irregular layering. The interior model inversion is formulated within a Markov Chain Monte Carlo (MCMC) approach and relies on three-dimensional model equations linking the physical properties of the internal layers to the spherical harmonic coefficients of the gravity field. The method produces statistically consistent posterior distributions of parameters that define the internal structure of each accepted model that match the target distributions of the observed gravity coefficients and complementary geophysical constraints (e.g., Love number k₂, librations).

Each interior model consists of concentric uniform ellipsoidal layers defined by size, density, and rheological properties. Crustal thickness variations are represented as deviations from a reference ellipsoid, providing a computationally efficient alternative to fully voxel-based representations while retaining sensitivity to lateral heterogeneities. Gravity coefficients are computed as the sum of a hydrostatic contribution, determined by the ellipsoidal shape of each layer, and a non-hydrostatic contribution derived from degree-dependent admittance.

The framework yields global grids of the crustal thickness together with the corresponding gravity spectra and associated residuals. These outputs provide constraints that cannot be captured by 1-D (spherical) or 2-D (ellipsoidal) interior models commonly adopted in the literature. The proposed approach is particularly suited to small bodies of the Solar System, including icy moons and dwarf planets, for which shape irregularities exert a first-order control on internal structure and geological evolution.