GRAVHEDRAL: a novel gravity inversion method to unravel planets interior

Suitable modelling capabilities paired with planetary-scale datasets provide fundamental information to unravel planets interior and evolution. Despite the key role and tremendous effort of decades of scientific missions in advancing the understanding of planets subsurface, knowledge about their crustal structures and processes shaping them is still limited. This is mainly due to a sparse record of return samples or meteorites, in addition to the scarcity of surface geophysical measurements. Planets crust is however a recorder of ancient geological events leading to nonhomogeneous 3D density distributions, expressed in the form of gravity anomalies. While on Earth combined geophysical data can inform on subsurface properties, for other planets such datasets are sparser, and orbiter-based gravity data is one of few or even the only global-scale source of information related to their interior. Developing an innovative modelling methodology suitable to exploit such orbiter-based data can help infer the 3D density distribution in planets crusts, providing key insights to reconstruct their geological history. Here we present GRAVHEDRAL, a fully non-linear 3D inversion methodology of gravity anomaly data suitable for both local- and planetary-scale studies and capable of addressing limitations of existing modelling strategies. Such limitations are related to the challenge of i) characterizing complex 3D density distributions, which are expected in actual geological scenarios, and ii) mitigating the non-uniqueness of the solution. Using GRAVHEDRAL, planets interiors (e.g., crust, mantle, etc.) are parameterized in terms of polyhedra with density contrasts expressed as high-order polynomial functions, whose gravity responses can be computed thanks to recently derived analytical formulae. The inversion scheme relies on the Hamiltonian Monte Carlo (HMC) method, a probabilistic approach that is currently gaining momentum in the geophysical community. Compared to other probabilistic approaches, the HMC strategy allows the model space to be explored more efficiently thanks to the gradient calculation of the posterior probability density of the model parameters (i.e., polyhedra node positions and/or density contrasts). Statistical analysis and uncertainty estimation on the model parameters can be performed from the collection of posterior models, enabling the appraisal of different probable geological scenarios to address the non-uniqueness of the solution. GRAVHEDRAL aims to provide the space science community with a flexible tool to help image the still poorly known 3D crustal density distribution of other celestial bodies of our solar system, allowing researchers to test the occurrence of Earth-like geological structures on other terrestrial planets and thus to decipher the reasons behind their different geological evolution.