Three-Dimensional Wave Propagation Using Boundary Integral Equation Techniques.
Technical rept. May 84-May 85,
SIERRA GEOPHYSICS INC REDMOND WA
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The efficient numerical propagation of waves in complex three-dimensionally varying environments has been a problem of considerable geophysical interest over the past few years, yet has proven extremely difficult even for the case of acoustic wave propagation in two dimesional structures. This is primarily due to the fact that although the differential equations of motion are linear in the field quantities of interest, they are non-linear in terms of the boundary conditions for most realistic structures. This fundamental nonlinearity precludes construction of the solution for complex structures by superposition of the solutions for simple structures, and forces one into computationally costly schemes. Techniques for dealing with this fundamental nonlinearity have spanned the range from the crudest classical ray tracing approach to the computational-bound finite difference type methods. However, no single technique has ever proven entirely satisfactory for reasons of accuracy, completeness of solution, generality of application, cost or combinations thereof. For example, in cases where significant diffraction and interference effects require exact solutions, finite difference techniques have received widespread use.
- Numerical Mathematics