Date of Award
Doctor of Philosophy
The examination of inverse problems represents a fascinating, diverse and difficult area of study. Almost any problem in mathematics, physics and engineering has an associated inverse problem. The method of quasi-solutions allows one to reformulate inverse problems as a function minimization involving the associated forward problem. The function to minimize is known as a penalty function or cost function and is defined as the least squares difference between some measured quantity and a quantity computed by the forward solver. This strategy avoids the need to construct the inverse operator. The forward problem is often well posed and can be solved quickly and accurately by various numerical solution techniques. The cost function, however, is typically a complicated multidimensional, multimodal surface. These properties make it difficult to locate the global minimum where the quasi-solution exists.;The simulated annealing algorithm performs well at minimizing functions with multiple local minima and hence has been employed in the quasi-solution of the inverse problem. Regularization techniques in the area of inverse problems attempt to better condition the problem by removing the local minimum from the cost function. Focus in this work has been placed on finding the global minimum of the multimodal cost function rather than strongly regularizing the penalty function. Two physical applications are chosen to test the feasibility of the proposed inversion method.;The first application involves the mise-a-la-masse electromagnetic prospecting technique from geophysics. This technique attempts to recover the size, shape and orientation of buried conductive ore bodies based on surface measurements. Here, a finite difference method is employed to solve the potential equation in a 3D semi-infinite medium.;The second application focuses on the scattering of acoustic waves by a 2D inhomogeneous medium. In this field, acoustic waves scattered from incident waves are used to reconstruct the index of refraction of the inhomogeneity. The incident waves are time harmonic plane waves which lie in the resonance region. A special hybrid partial differential equation/integral equation solution technique is employed to solve the direct problem.
Moseley, Douglas John, "Computational Solution Of Inverse Problems With Simulated Annealing" (1995). Digitized Theses. 2567.