Maximum-likelihood Estimation of Planetary Lithospheric Rigidity from Gravity and Topography

Abstract:

Gravity and surface topography remain among the best available tools with which to study the lithospheric structure of planetary bodies. Numerous techniques have been developed to quantify the relationship between these fields in both the spatial and spectral domains, to constrain geophysical parameters of interest. Simons and Olhede (2013) describe a new technique based on maximum-likelihood estimation of lithospheric parameters including flexural rigidity, subsurface-surface loading ratio, and the correlation of these loads. We report on the first applications of this technique to planetary bodies including Venus, Mars, and the Earth. We compare results using the maximum-likelihood technique to previous studies using admittance and coherence-based techniques. 

While various methods of evaluating the relationship of gravity and topography fields have distinct advantages, we demonstrate the specific benefits of the Simons and Olhede technique, which yields unbiased, minimum variance estimates of parameters, together with their covariance. Given the unavoidable problems of incompletely sensed gravity fields, spectral artifacts of data interpolation, downward continuation, and spatial localization, we prescribe a recipe for application of this method to real-world data sets. In the specific case of Venus, we discuss the results of global mapped inversion of an isotropic Matérn covariance model of its topography. We interpret and identify, via statistical testing, regions that require abandoning the null-hypothesis of isotropic Gaussianity, an assumption of the maximum-likelihood technique.