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.

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The long‐wavelength negative gravity anomaly over Hudson Bay coincides with the area depressed by the Laurentide Ice Sheet during the Last Glacial Maximum, suggesting that it is, at least partly, caused by glacial isostatic adjustment (GIA). Additional contributions to the static gravity field stem from surface dynamic topography, core‐mantle boundary (CMB) topography, and density anomalies in the subsurface. Previous estimates of the contribution of GIA to the gravity anomaly range from 25% to more than 80%. However, these estimates did not include uncertainties in all components that contribute to the gravity field. In this study, we develop a forward model for the gravity anomaly based on density models and dynamic models, investigating uncertainty in all components. We derive lithospheric densities from equilibrium constraints but extend the concept of lithospheric isostasy to a force balance that includes the dynamic models. The largest uncertainty in the predicted gravity anomaly is due to the lower mantle viscosity, uncertainties in the ice history, the crustal model, the lithosphere‐asthenosphere boundary, and the conversion from seismic velocities to density have a smaller effect. A preference for lower mantle viscosities >1022 Pa s is found, in which case at least 60% of the observed long‐wavelength gravity anomaly can be attributed to GIA. This lower bound on the lower mantle viscosity has implications for inferences based on models for mantle convection and GIA.@en