Non-stationary estimation in gravity prediction problems
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Date
1977-07
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University. Division of Geodetic Science
Abstract
This report investigates the impact that the assumptions of homogeneity and isotropy, when applied to potential related fields, have upon the stochastic processes which are applied to these fields. After seeing how these assumptions are incorporated into the statistical model to produce the familiar covariance function, the investigation centers on techniques which can be used to detect the presence of anisotropy in the field. The method found most useful is the two-dimensional covariance function, and some methods of representing this function are also investigated. Numerical studies are then carried out to see the effect the use of the 2-D covariance function has upon the results of prediction and collocation computations. It is found that, under certain circumstances, the 2-D function produces a result superior to that given by the general function. Recommendations are then given as to when the 2-D covariance function should be used in practical solutions, and suggestions made as to the possible areas of further research.