Direct and inverse scattering of classical waves at oblique incidence to stratified media via invariant imbedding equations
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Direct and inverse scattering problems in stratified media can be solved by first using invariant imbedding techniques to derive integro-differential equations and boundary conditions for the reflection kernels. These equations can be solved numerically to find the reflection kernels in the direct problem or the material parameter functions in the inverse problem. Previous work dealt with plane waves at normal incidence to stratified meda. This dissertation extends the method to the case of oblique incidence. Integro-differential equations are derived for lossless acoustic, electromagnetic, and elastic problems. Direct algorithms and complete inversion algorithms are given in each case. Numerical examples are provided. A final chapter gives examples of the use of Hamilton's quaternion analysis to factor three-dimensional wave equations.