A Regionalized Maximum-Likelihood Estimation of the Spatial Structure of Venusian Topography

Abstract

Venus has undergone a markedly different evolution than Earth. Its tectonics do not resemble Earth’s plate-tectonic system, and many surface features—such as tesserae and coronae—lack terrestrial equivalents. To understand Venus’ tectonics is to understand its lithosphere. Lithospheric parameters such as the flexural rigidity and effective elastic thickness can be estimated from the correlation between topography and gravity anomalies. Analyses of this type have been done, but they have been limited by by the available methods for spectral estimation and inversion. Simons & Olhede (2013) developed a more robust, maximum-likelihood approach to modeling these data fields to estimate the lihthospheric flexural rigidity. As part of their model, the input, driving, or "initial" topography is assumed to follow an isotropic, Matérn process. In this study, I evaluate this assumption. To do so, I created a geologically coherent, regionalized map of Venus so the topography could be modeled over the entire planet for regions of particular interest. Three Matérn parameters were estimated for every region though an iterative maximum-likelihood procedure until the parameters that best described the power spectral density of the topography in its Matérn form. The statistical distribution of the residuals from this procedure were analyzed to evaluate the quality of the best-fitting parameter set. For 77 Venusian regions, parameters for 73 regions were successfully estimated, and for 64 of those regions the fit was considered acceptable for future analysis. Anisotropy, which represents a departure of the assumed isotropic Matérn model, was observed for about 35 regions, but in most cases it did not greatly impact the goodness of fit. Thus, the assumptions made by Simons & Olhede (2013) in regards to how topography can be modeled were largely upheld. However, in the future this modeling of topography can improved upon, particularly in the application of tapers to the Venusian regions to better constrain the data of interest for each region. Ultimately, lithospheric parameters for these regions will be estimated via the joint statistical structure of both topography and gravity anomaly. The data sets used were spherical-harmonic models of topography and gravity anomaly based on measurements by the Magellan spacecraft (Konopliv et al., 1999; Rappaport et al., 1999). They remain the highest-resolution data sets, though with the affirmation of this new modeling and analysis method, future missions that would return topography and gravity data with better accuracy over smaller footprints, such as are now available for Earth, Moon, and Mars, would be useful.