Planetary Interior Modeling Using Synthetic Gravity Simulator

Gravity inversion techniques enable the characterisation of the internal mass distribution of planetary bodies by combining data from their shape, gravity, and rotation. However, the inherent ambiguity in scalar gravity signals, specifically, between mass and depth, poses a significant challenge for inferring internal structure. In this work, we introduce a novel approach leveraging the spherical harmonics framework described in [1], in particular, the gravitational harmonics coefficients [C_nm, S_nm]. Starting with a simplified interior structure (assuming homogeneous layers), interior model parameters are the number of layers, average layer thickness, average layer density, and the topography of layer interfaces (if present). Regarding the latter, in cases where Bouguer anomalies are available, the mantle-crust interface topography can be inferred using a filtering approach, as proposed in [2]. Notably, this method does not rely on assumptions of isostatic compensation but requires careful selection of the filtering parameters. From these parameters. the spherical harmonics coefficients for each layer and the global ones are computed (see [1]). From these coefficients, key quantities such as gravitational potential, Free-Air anomalies, and Bouguer anomaly maps are evaluated and then compared to space measurements, measuring the model performance by different metrics (e.g. RMSE, structural similarity index, Pearson correlation coefficient). By varying model parameters randomly within physically constrained ranges (e.g. by mass conservation, moment of inertia and observed shape), this process is repeated iteratively. The parameter combination minimizing the performance metrics between modelled and observed data represents the best-fit internal structure. This approach is robust and flexible at the same time, being able to accommodate diverse celestial bodies with a wide variety of planetary shapes, internal configurations, and gravitational data sets and to objectively identify the optimal parameter configuration. This method is benchmarked on Mercury [3], resulting in a mantle-crust interface at ~28 km depth and a mantle density of 3210 [kg/m³], consistent with existing literature (see [4]). Furthermore, this procedure can be used to compute the expected gravity signal from unknown bodies targeted by the upcoming missions and instruments (e.g. Ganymede for JUICE), test different theoric interior models, and obtain their gravitational response.

Acknowledgements: ESM and GM acknowledge support from the Italian Space Agency (2022-16-HH.1-2024). This paper and related research have been conducted during and with the support of the Italian national inter-university PhD programme in Space Science and Technology.

References: [1] M. A. Wieczorek, ‘Gravity and Topography of the Terrestrial Planets’, in Treatise on Geophysics, Elsevier, 2015, pp. 153–193. doi: 10.1016/B978-0-444-53802-4.00169-X.[2] M. A. Wieczorek and R. J. Phillips, ‘Potential anomalies on a sphere: Applications to the thickness of the lunar crust’, Journal of Geophysical Research: Planets, vol. 103, no. E1, pp. 1715–1724, 1998, doi: 10.1029/97JE03136.[3] A. Genova et al., Regional variations of Mercury’s crustal density and porosity from MESSENGER gravity data, Icarus, vol. 391, p. 115332, Feb. 2023.[4] S. Buoninfante, M. Milano, B. Negri et al. ‘Gravity evidence for a heterogeneous crust of Mercury’. Sci Rep 13, 19854 (2023), https://doi.org/10.1038/s41598-023-46081-4