Mars Gravity Inversion

Abstract

In 2018 the InSight mission was launched with the main objective of providing accurate 3D models of Mars’s interior. This was done by placing a seismometer on the surface of Mars to measure seismic activity. In 2021 three studies were published, one dedicated to the Martian core, one to the Martian mantle, and the last one focused on the Martian crust. Based on this seismic data, Khan et al. [2021] obtained a lithospheric thickness between the 400 and 600 km. The average Martian crust was found to lie between 24 to 72 kilometers. A restrictive range of crustal densities between 2700 to 3100 kg/m3 was used. The mantle extended up to 1560 km below the surface of Mars. The core is molten and has a radius of 1830 km. Before seismic data was available, the method to learn more about the interior of a planet was to study the topography and gravity data. This is still, on Mars, the only way to get a global picture of the subsurface. Only one seismometer is currently available on Mars, making it difficult to currently obtain full planet 3D maps from seismology alone.

The objective of this research is to study the lateral density variations within the Martian lithosphere. The lithosphere is the planet’s outermost shell, defined by its rigid mechanical properties. It is thought that the lithosphere of Mars consists of the crust and the outer part of the mantle. In previous research, the density of the Martian crust is most often taken as uniform. However, density variations exist at a small scale and potentially even at the largest Martian scale [Beuthe et al., 2012]. The thesis project aims to study these density variations within the Martian crust and upper mantle.

To study the lateral density variations in the crust and mantle, the MRO120D gravity data and MOLA topography data are used as input. The crust-mantle boundary is created based on thin shell isostasy [Qin, 2021]. A lower boundary of the lithosphere is chosen to be equal to 500 km. A mantle plume underneath Tharsis is added, based on the findings from van der Tang [2021]. This plume reached from a depth of 800 km up to a depth of 900 km and was centered around [110◦W 3◦N] and had a density variation of 400 kg/m3 with respect to the surrounding mantle. An inversion was performed from which the density of both the crust and the mantle was obtained. In this calculation, two assumptions are made. First of all, it is assumed that the mass of each column is equal. The second assumption is that the obtained gravity for the column can be split into 2 point mass sources, one corresponding to the mass of the crust, located in the center of mass of the crust, and one corresponding to the mass of the mantle, located in the center of mass of the mantle.

A reference planet with Te = 400 km, C = 105 km, ρc,ref = 2700 kg/m3, and ρm,ref = 3800 kg/m3, resulted in the smallest density differences within the crust, as well as the smallest gravitational tensor residual. When these input parameters were used for the inversion, a final density difference of approximately 1000 kg/m3 between the crust and mantle was obtained after the inversion. A mean crustal density of approximately 2750 kg/m3 and a mean mantle density of approximately 3750 kg/m3 were found. The density variations in the crust varied from -424 up to 618 kg/m3 around the mean crustal density and -228 and 133 kg/m3 around the mean mantle density. The optimal elastic thickness obtained through the inversion lies between the 450±50 km and the uniform crustal thickness between 100 ± 10 km.

For the large impact craters, high crustal densities were found compared to the mean crustal density of Mars. Densities for Hellas and Utopia lay between the 3200 and 3345 kg/m3, and for Isidis Basin, a slightly smaller impact crater, a crustal density of around 2870 kg/m3 was found. These large crustal densities, together with the large elastic thickness and density difference between the crust and mantle, resulted in the conclusion that the large impact craters may be compensated using a different isostasy method. For this study, the crust-mantle boundary was obtained by applying the flexural response function to the crust-mantle boundary obtained using Airy isostasy. A boundary based on Pratt isostasy, instead of the thin shell isostasy boundary used currently, might be a better fit for the larger impact craters. The volcanoes outside the Tharsis region were found to be well compensated using the thin shell method, and small densities were found compared to the volcanoes in the Tharsis region, as well as what has been found in previous literature. The smaller densities for these stand-alone volcanoes might have to do with the compensation of these volcanoes due to the curvature of the planet, which is taken into account with the thin shell isostasy model. The literature analyzed in this study used different isostasy methods. By studying the possibility of different isostasy methods for different regions on Mars, the current model could be improved further.

This study showed that it is possible to use gravity inversion to gain insights into the lithosphere of a planet. With these density differences, the Martian power spectrum could be fitted up to spherical harmonic degree 40. But, due to the resolution of the current gravity model, it was only possible to calculate the Martian density difference at a larger scale. To also be able to study the density differences at a smaller scale, higher resolution gravity data needs to become available.