A dissertation submitted to the Faculty of Science, University of the
Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of
Doctor of Philosophy / Inverse theory provides an important tool that the geophysicist can use to
explore the structure of the Earth. This thesis examines several new approaches to the
inverse problem, and suggests ways of improving the conventional least-squares
technique. Non least-squares inversion was applied to borehole temperature data from
South Africa, and when the norm of the inversion was controlled by the statistics of
the misfit, It reduced by over 50% the number of iterations required for the inversion
to converge upon a solution. Various damping schemes were also examined, and the
use of the misfit in controlling the damping is shown to provide the best solution of
those studied (Cooper and Jones, in press).
Improvements to the efficiency of the inverse process were also achieved by
the fitting of parabolic forms to portions of the misfit surface, using both the misfit
value and the gradient of the surface. for gravity data. The presence of nearby minima
other than the one that the inversion has just converged to can also be detected in
this manner.
The set of initial models that converged to a particular solution using leastsquares
inversion was studied for magnetic data, and it was noted to have a fractal
nature. The fractal dimension of the set was found to be inversely proportional to the
damping of the inverse problem.
The inverse process was pushed into a chaotic state by the modification of the
least-squares inversion equation. The chaotic state was studied, and exploited to / AC2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/22950 |
| Date | January 1997 |
| Creators | Cooper, Gordon Robert John. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
Page generated in 0.002 seconds