Aspects of the theory of inversion as applied to geophysical problems.

[摘要] Inverse theory provides an important tool that the geophysicist can use toexplore the structure of the Earth. This thesis examines several new approaches to theinverse problem, and suggests ways of improving the conventional least-squarestechnique. Non least-squares inversion was applied to borehole temperature data fromSouth Africa, and when the norm of the inversion was controlled by the statistics ofthe misfit, It reduced by over 50% the number of iterations required for the inversionto converge upon a solution. Various damping schemes were also examined, and theuse of the misfit in controlling the damping is shown to provide the best solution ofthose studied (Cooper and Jones, in press).Improvements to the efficiency of the inverse process were also achieved bythe fitting of parabolic forms to portions of the misfit surface, using both the misfitvalue and the gradient of the surface. for gravity data. The presence of nearby minimaother than the one that the inversion has just converged to can also be detected inthis manner.The set of initial models that converged to a particular solution using leastsquaresinversion was studied for magnetic data, and it was noted to have a fractalnature. The fractal dimension of the set was found to be inversely proportional to thedamping of the inverse problem.The inverse process was pushed into a chaotic state by the modification of theleast-squares inversion equation. The chaotic state was studied, and exploited to

[发布机构] University of the Witwatersrand