Abstract
<jats:p>Gravity observations have proven highly effective in constraining the internal structure of terrestrial planets, from surface features to deep interiors. In the case of Mercury, several studies have used gravity data to infer properties of the crust–mantle interface, average crustal density, and crustal thickness. However, gravity data have so far been only marginally exploited to derive quantitative models of subsurface density variations.In this study, we present a 3D density model of selected sectors of Mercury obtained through inversion of gravity data derived from the HgM009 gravity field model (Genova et al., 2023). To this end, we developed a 3D inversion algorithm specifically designed for Mercury and operating in spherical coordinates. The inversion procedure is constrained through model-weighting functions, including radial depth weighting (Liang et al., 2014) and compactness constraints (Last and Kubik, 2001; Maiolino et al., 2024), which reduce source spreading and produce geologically plausible subsurface models.Specifically, the inversion minimizes the following objective function (Maiolino et al., 2024; Milano et al., 2026):(1)where d is the data vector, m is the model to be estimated, and A is the sensitivity matrix containing the gravity effect of element of the model domain. The parameter μ is the regularization weight, and ‖Am − d‖² represents the squared L₂-norm data misfit between the observed data d and the model-predicted response Am. The subsurface volume is discretized into tesseroids. Accordingly, the sensitivity matrix A was computed by adapting the forward modeling algorithm proposed by Uieda et al. (2016) to Mercury’s physical parameters. Compactness constraints are introduced through a compactness function, where ε is a small scalar added to avoid singularities and to iteratively minimize the source volume. The radial weighting term () further constrains the inversion by imposing depth-dependent weighting. Unlike Liang et al. (2014), however, the radial depth weighting adopted here is defined as a function of the structural index of the source (e.g., Cella et al., 2012).The inversion approach was first validated using synthetic gravity data generated from a tesseroid-based model consisting of a deep undulating interface, representing the crust–mantle boundary, together with smaller intrusive bodies (Figure 1a). The forward gravity response was computed assuming the average spatial resolution of gravity observations in Mercury’s northern hemisphere and the average satellite altitude above the surface (Figure 1b).Figure 1. Tesseroid-based synthetic model including an undulating crust–mantle interface and intrusive bodies (a), and corresponding forward gravity response (b).The inversion was performed iteratively in order to obtain compact source geometries while minimizing the misfit between simulated and predicted gravity data. The results demonstrate that the proposed inversion scheme successfully reconstructs the overall geometry and average density contrast of both deep and shallow sources (Figure 2a). Moreover, the modeled gravity field closely reproduces the simulated gravity anomalies (Figure 2b).Figure 2. Inverted source model obtained from the synthetic gravity dataset (a), and corresponding computed gravity field (b).The method was subsequently applied to real gravity observations in Mercury’s Victoria quadrangle. The dataset was derived from the isostatic gravity anomaly map presented by Buoninfante et al. (2024), since isostatic anomalies better isolate the contribution of intracrustal sources. The gravity field was generated with a spatial sampling of 1° at an altitude of 50 km above Mercury’s mean radius and constrained using degree-strength values.The subsurface domain was discretized into 4500 tesseroids (30 × 30 × 5), with lateral dimensions of 1° and a radial thickness of 7 km.The inversion of isostatic gravity anomalies provided insights into small-scale crustal structures within the Victoria quadrangle, although interpretations remain limited by the spatial resolution of the available data. The resulting model reveals a broad positive density anomaly associated with a putative impact basin centered at approximately [50°N, −59°E], corresponding to an area of thin crust (≤25 km; Broquet, 2025). This feature is interpreted as related to mantle upwelling and crustal intrusive bodies.Additional shallow positive density anomalies in the eastern sector are likely associated with intrusive structures near smaller impact craters. In contrast, negative density contrasts are concentrated between longitudes −65°E and −50°E and latitudes 59°N–64°N, corresponding to an area of crustal thickening (≥45 km; Broquet, 2025). This region is bounded by the Carnegie and Larrocha thrust systems, likely characterized by high dip angles (Galluzzi et al., 2019).Future work will focus on reconstructing Mercury’s global crustal density distribution using updated gravity models from the BepiColombo mission, which are expected to provide improved spatial resolution, particularly in the southern hemisphere. The inversion framework could also be applied to reconstruct the internal structure of Ganymede using future gravity models derived from ESA’s Jupiter Icy Moons Explorer mission.ReferencesBuoninfante, S., et al. (2023). Gravity evidence for a heterogeneous crust of Mercury. Scientific Reports, 13(1), 19854.Broquet, A. (2025). Data for On the crustal architecture of the terrestrial planets [Data set]. Zenodo.Cella, F., Fedi, M., (2012). Inversion of potential field data using the structural index as weighting function rate decay. Geophys. Prospect. 60, 313–336. https://doi.org/10.1111/j.1365-2478.2011.00974.xGalluzzi, V., et al. (2019). Structural analysis of the Victoria quadrangle fault systems on Mercury: Timing, geometries, kinematics, and relationship with the high‐Mg region. Journal of Geophysical Research: Planets, 124(10), 2543-2562.Genova A. et al. (2023). Regional variations of Mercury's crustal density and porosity from MESSENGER gravity data. 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