The subsurface of Mars is impossible to measure directly, yet it has been the subject of many studies. An understanding of the subsurface of Mars would yield large amounts of information on the history of the planet. Two of the tools available to indirectly interact with the Martian subsurface, in particular the lithosphere, are the gravity and topography signals of the planet. These two datasets can be combined using a variety of geological theories in order to investigate the subsurface. In this study, an isostatic model (Airy-type) and two flexural isostatic models (an infinite plate model and a thin shell model) will be the methods of choice. A distinction is made between isotropic or global models, which use one set of physical parameters for the entire planet, and anisotropic or multi-region models which allow for regional variation in physical parameters. The goal of this study is to investigate the performance of the novel thin shell model as compared to the older infinite plate model.

To investigate this, the theory behind each model is explained, after which the models are validated using results from literature. Several regions of interest are defined, mostly among large geological formations or gravity anomalies. Two parameters are chiefly investigated: the average thickness of the lithosphere and the lithospheric elastic thickness, which is a measure of the strength of the lithosphere. Each model is run globally for a variety of these two parameters, and the best fitting parameters are identified. After this, the planet is split into different regions with their own physical parameters. The first study is a dichotomy study which splits the planet into a northern and southern hemisphere, aimed at characterizing the disparity between the Martian north and south. After this, each region is assigned its best fitting physical parameters and the regions are combined into a 'global' regional model. A best fitting multi-region model is obtained via manual observation of the results and adjustment of the inputs until a visual best fit is achieved.

The results are then discussed. A key takeaway is that better methods of judging the performance of models without human visual inspection of their results is necessary in order to realize the full potential of the flexural isostasy models presented in this study. The lack of suitable methods leads to a manifold of best fitting solutions for many of the problems modelled in this study, hindering firm conclusions about the subsurface of Mars. Having said this, global average lithospheric values of about 200 km combined with very low effective lithospheric elastic thickness values of 0 to 40 km are the best fits found in this study. Literature values are typically lower, but this can partially be explained by differences between the flexural isostasy models in this study and the models from literature. Regionally there are large variations, with some features (Hellas basin, Alba mons) being isostatically compensated, others being supported by locally strong lithospheres (much of the Tharsis region), and others resting on buried mass anomalies that cannot be explained with the models in this study (Isidis planitia, Argyre basin). In a dichotomy study, the best fitting values were found for a northern lithosphere zero to ten kilometers thinner than the southern lithosphere. In general, the thin shell model is more sensitive to nonzero lithospheric elastic thickness values, providing very strong lithospheres at low elastic thicknesses. This is due to its aggressive flexural response function's filtering of higher spherical harmonic degree signals. The thin shell models yields higher residuals in the global analyses, but lower residuals in the multi-region studies. At the same time, 80% of the error in all models can be attributed to spherical harmonic degrees between 1 and 10. These signals are likely not caused by flexural isostasy, and require models incorporating more physics (mantle plumes, mass anomalies, etc) to be explained.