Principal Component Analysis of Terrestrial and Venusian Topography

Abstract:

We use Principal Component Analysis (PCA) as an objective tool in analyzing, comparing, and contrasting topographic profiles of different/similar features from different locations and planets.

To do so, we take average profiles of a set of features and form a cross-correlation matrix, which is then diagonalized to determine its principal components. These components, not merely numbers, represent actual profile shapes that give a quantitative basis for comparing different sets of features. For example, PCA for terrestrial hotspots shows the main component as a generic dome shape. Secondary components show a more sinusoidal shape, related to the lithospheric loading response, and thus give information about the nature of the lithosphere setting of the various hotspots.

We examine a range of terrestrial spreading centers: fast, slow, ultra-slow, incipient, and extinct, and compare these to several chasmata on Venus (including Devana, Ganis, Juno, Parga, and Kuanja). For upwelling regions, we consider the oceanic Hawaii, Reunion, and Iceland hotspots and Yellowstone, a prototypical continental hotspot. Venus has approximately one dozen broad topographic and geoid highs called regiones. Our analysis includes Atla, Beta, and W. Eistla regiones. Atla and Beta are widely thought to be the most likely to be currently or recently active.

Analysis of terrestrial rifts suggests shows increasing uniformity of shape among rifts with increasing spreading rates. Venus' correlations of uniformity rank considerably lower than the terrestrial ones. Extrapolating the correlation/spreading rate suggests that Venus’ chasmata, if analogous to terrestrial spreading centers, most resemble the ultra-slow spreading level (less than 12mm/yr) of the Arctic Gakkel ridge. PCA will provide an objective measurement of this correlation.