New Statistical Methods for the Analysis of the Cratering on Venus

Abstract:

The sparse crater population (~1000 craters) on Venus is the most important clue of determining the planet's surface age and aids in understanding its geologic history. What processes (volcanism, tectonism, weathering, etc.) modify the total impact crater population? Are the processes regional or global in occurrence? The heated debate on these questions points to the need for better approaches.

We present new statistical methods for the analysis of the crater locations and characteristics. Specifically:

1) We produce a map of crater density and the proportion of no halo craters (inferred to be modified) by using generalized additive models, and smoothing splines with a spherical spline basis set. Based on this map, we are able to predict the probability of a crater has no halo given that there is a crater at that point. We also obtain a continuous representation of the ratio of craters with no halo as a function of crater density. This approach allows us to look for regions that appear to have experienced more or less modification, and are thus potentially older or younger.

2) We examine the randomness or clustering of distributions of craters by type (e.g. dark floored, intermediate). For example, for dark floored craters we consider two hypotheses: i) the dark floored craters are randomly distributed on the surface; ii) the dark floored craters are random given the locations of the crater population. Instead of only using a single measure such as average nearest neighbor distance, we use the probability density function of these distances, and compare it to complete spatial randomness to get the relative probability density function. This function gives us a clearer picture of how and where the nearest neighbor distances differ from complete spatial randomness. We also conduct statistical tests of these hypotheses. Confidence intervals with specified global coverage are constructed.

Software to reproduce the methods is available in the open source statistics software R. Both the methods and the code are extensible to similar marked spatial point process applications.