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UBC Theses and Dissertations

Some new approaches to gravity modelling Green, William Robert


Geophysical inversion methods are most effective when applied to linear functionals; it is therefore advantageous to employ linear models for geophysical data. A two-dimensional linear model consisting of many horizontal prisms has been developed for interpretation of gravity profiles. A Backus-Gilbert inversion which finds the acceptable model "nearest" to an initial estimate can be rapidly computed; iterative application of the technique allows a single-density model to be developed at modest expense of computer time. Gravity data from the Guichon Creek batholith were inverted as a test of the method, with results comparable to a standard polygon model. The entropy of these linear models is a useful property which can be minimized to find an optimum "structured" or "compact" model. Since a numerical optimization is used, computations become prohibitively long for any large number of parameters. Several simple models have been found by minimizing the entropy of an intial model under the constraints imposed by a known gravity profile. Similar results can be obtained by using a simpler objective function. It is also possible to maximize model entropy; this procedure tends to evenly distribute the anomalous mass beneath the profile, while minimum entropy tries to concentrate mass in as few prisms of the model as possible.

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