Physics
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........13c&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF ROCHESTER, 1995.Source: Dissertation Abstracts International, Volume: 56-10, Section: B, page:
Physics
Scientific paper
The research presented in this thesis concerns a model for describing and analyzing spatial point patterns on the surface of a sphere. It was motivated by efforts to analyze data on the locations of impact craters on Venus that were collected by the satellite Magellan. This thesis first discusses tests of complete spatial randomness that were applied to the crater data. The tests showed that the distribution of impact craters on Venus is consistent with a spatially random process. To describe and model the mechanisms responsible for the crater distribution, the equilibrium resurfacing (ER) model was proposed (Phillips, et al 1992, J. Geophys. Res. (Planets), 97, 15,923-15,948). The model treats the observed pattern of craters as the result of two competing processes. One process adds new craters to the surface independently and uniformly over space and time. The second process removes craters through "resurfacing" events that erase craters within a circular patch on the planet surface. These events are idealized versions of volcanic and tectonic processes operating on Venus. The events are assumed to be of constant size and to occur independently and uniformly in space and time. The model has three parameters: the cratering rate, resurfacing event size and the resurfacing event rate. This thesis focuses on deriving the statistical properties of the ER model and developing methods for estimation and inference about its parameters. Expressions for the first and second order spatial intensities, the K-function, and the proportion of partially erased craters are obtained, along with the mean and variance of the total number of craters. A new method for parameter estimation that uses a likelihood-type estimation criterion based on inter-crater distances is proposed, and is shown to perform better than existing techniques via a simulation study. The estimation procedures are applied to the Venus crater data, along with tests of fit of the ER model. The results imply either a large value of the resurfacing patch size or a value close to 0. The large values are not consistent with the observed spatially random distribution of craters unless the patch size is close to being global. Neither large nor very small patch sizes are completely consistent with the observed proportion of damaged craters. Thus the ER model in its simplest form does not fully describe the situation on Venus. However, it may serve as a building block for more complicated and realistic models.
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