SynthGen: A Gravitational Simulator For Planetary Interior Modelling

Determining the internal structure of planetary bodies from gravitational observations is a key challenge in planetary geophysics. Gravity inversion techniques make it possible to estimate mass distribution by combining information on a body's shape, gravitational field, and rotational dynamics. However, gravity data alone present a well-known ambiguity between mass magnitude and depth, making the interpretation of internal layering a complex inverse problem.

 

We present SynthGen, a code developed to simulate the gravitational response of planetary bodies based on parametric interior models. It exploits the spherical harmonics framework described in Wieczorek [1], through the computation of gravitational harmonic coefficients [C_nm, S_nm] which characterise the global gravitational field, thanks to the SHTools [6] routines. SynthGen takes as input a simplified multi-layer interior model, assuming them homogenous. Model parameters consist of the number of internal layers, their mean thickness and density, and eventually, the topography of internal interfaces. On the latter, several ways are implemented: sphere, polar/equatorial flattened ellipsoid, randomly generated topography, downwarded Bouguer anomaly (see Wieczorek & Phillips [2], avoiding isostacy assumptions) and finally an input user grid. Given these inputs, SynthGen computes the corresponding gravitational potential, Free-Air anomalies, and Bouguer anomaly fields for the modelled body, generating full-resolution global maps.

SynthGen outputs can be used in two ways: if it is used to simulate a known body, so a gravity model is already available, the synthetic results can be compared to the real measurements, assessing the validity of the evaluated interior model and measuring its performance through different metrics. In this case, SynthGen performed an automated parameter-space exploration (controlled by the user). By randomly sampling model parameters within physically plausible bounds that it is user-configurable (constrained by the satisfaction of the conservation of total mass and moment of inertia, together with external shape constraints), it iteratively evaluates a wide range of configurations. The optimal internal structure is determined by identifying the parameter set that minimises discrepancies between simulated and observed gravitational data. This is performed through a suite of statistical metrics (e.g. RMSE, MAE, R², SSIM, NCC, PSNR, etc.), finally combined into one. We tested this procedure on Mercury, using a publicly available MESSENGER-derived gravitational model (namely HgM009, from Genova et al, 2015 [3]), exploring a simple 3-layers structure and one with an internal core differentiation (4-layers). SynthGen retrieves a best-fit crust-mantle boundary at approximately 34.5 +/- 10.7 [km] depth and the core parameters at ~7267.2 +/- 47.5 [kg/m³] and core bulk radius at 1984.1 +/- 14.4 [km], in agreement with recent geophysical studies [4,5,6]. These results validate the method’s robustness and reliability.

In addition to this procedure, SynthGen can be used predictively in case of an “unmeasured” body. It enables forward modelling of gravitational signals expected from future targets such as Ganymede [5], which will be studied in detail by ESA’s upcoming JUICE mission. It can thus serve as a valuable tool for testing theoretical interior structures and simulating their measurable gravitational signatures.

By combining analytical modelling, numerical efficiency, and flexibility across planetary scenarios, SynthGen offers a useful platform for planetary interior investigations from the gravitational point of view. It can handle various planetary shapes, datasets, and scientific objectives, and it is user configurable, together with already implemented configuration files for Mercury, Venus, Earth and Moon, together with a model of Ganymede.

 

Acknowledgements:
E.S.M. and G.M. acknowledge support from the Italian Space Agency (project 2023-6-HH.0). This research has been conducted within the framework 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”, JGR: 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, 2023.
[4] S. Buoninfante et al., “Gravity evidence for a heterogeneous crust of Mercury”, Scientific Reports, vol. 13, 19854, 2023. https://doi.org/10.1038/s41598-023-46081-4

[5] A. Rivoldini, T. Van Hoolst, “The interior structure of Mercury constrained by the low-degree gravity field and the rotation of Mercury”, Earth and Planetary Science Letters, 2013, https://doi.org/10.1016/j.epsl.2013.07.021.

[6] Margot, Jean-Luc, et al. "Mercury's internal structure." arXiv preprint arXiv:1806.02024 (2018).

[7] D. M. Fabrizio et al., ‘Observability of Ganymede’s gravity anomalies related to surface features by the 3GM experiment onboard ESA’s JUpiter ICy moons Explorer (JUICE) mission’, Icarus, 2021.

[8] Mark A. Wieczorek and Matthias Meschede (2018). “SHTools — Tools for working with spherical harmonics”, Geochemistry, Geophysics, Geosystems, 19, 2574-2592, doi:10.1029/2018GC007529.