Fluid extraction from sandstone reservoirs leads to reservoir compaction, potentially inducing surface subsidence and seismicity, as observed in the Groningen Gas Field, Netherlands. Such compaction is partly elastic, but can additionally be caused by instantaneous plastic and rate/time-dependent processes, such as subcritical crack growth, meaning that compaction may continue even if production is stopped. Despite the need to evaluate the impact of post-abandonment reservoir behavior (>10–100 years), few mechanism-based, rate/time-dependent compaction laws exist. Compaction due to grain breakage, either via critical or subcritical crack growth, is driven by tensile stresses acting on surface and volume flaws. We performed high-resolution 3D linear elastic finite element method simulations on simplified grain assemblies to investigate the effect of stress–strain boundary conditions, porosity and mineralogical variations on grain-scale stress fields. Our simulations showed tensile stress concentrations at grain contact edges and on pore walls, which increased in magnitude with increasing aggregate porosity and local porosity variation. The fraction of surface area with tensile stresses sufficient to extend flaws with a size up to 30μm showed a clear correlation with compactive yield envelopes for the Groningen reservoir sandstone. This suggests that compactive failure is related to the probability of pre-existing surface flaws, falling in a pore surface region where the Griffith criterion is satisfied. A preliminary, time-independent failure probability model, using the observed tensile stress distribution, qualitatively predicts a non-linear increase in grain cracking during deviatoric loading, and suggests a new route to predict sandstone compaction through brittle grain failure.

NASA’s InSight mission has brought new information about the Martian lithosphere (Banerdt et al. 2020), which warrants a re-analysis of the support of the crustal and sub-crustal masses. Furthermore, the discovery of a possible mantle plume underneath the region south of Elysium Mons (Broquet et al. 2023), gives evidence for recent magmatic activity underneath the crust of Mars causing dynamic support to volcanic structures.

Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: laterally varying density structures and a crust-mantle interface density. The differences between the four codes were all below 1.5% of the modelled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (<0.3 %). To examine the usability of the forward modelling codes for realistic geological structures, we use the global lithosphere model WINTERC-G that was constrained, among other data, by satellite gravity field data computed using a spectral forward modelling approach. This spectral code was benchmarked against the GSH, and it was confirmed that both approaches produce a similar gravity solution with negligible differences between them. In the comparison of the different WINTERC-G-based gravity solutions, again GSH and TESS performed best. Only short-wavelength noise is present between the spectral and tesseroid forward modelling approaches, likely related to the different way in which the spherical harmonic analysis of the varying boundaries of the mass layer is performed. The spherical harmonic basis functions produce small differences compared to the tesseroid elements, especially at sharp interfaces, which introduces mostly short-wavelength differences. Nevertheless, both approaches (GSH and TESS) result in accurate solutions of the potential field with reasonable computational resources. Differences below 0.5% are obtained, resulting in residuals of 0.076 mGal standard deviation at 250 km height. The biggest issue for TRI is the characteristic pattern in the residuals that is related to the grid layout. Increasing the resolution and filtering allow for the removal of most of this erroneous pattern, but at the expense of higher computational loads with respect to the other codes. The other spatial forward modelling scheme, HEX, has more difficulty in reproducing similar gravity field solutions compared to GSH and TESS. These particular approaches need to go to higher resolutions, resulting in enormous computation efforts. The hexahedron-based code performs less than optimal in the forward modelling of the gravity signature, especially with a laterally varying density interface. Care must be taken with any forward modelling software as the approximation of the geometry of the WINTERC-G model may deteriorate the gravity field solution.