Approximation to the Boundary Integral Equation and Applications to Modeling Acoustic Waves in Three Dimensional Structures.

Abstract : Approximations to the boundary integral equation (BIE) formulation for acoustic wave propagation permits simulation of acoustic waves in lavered earth models with three dimensional laver boundaries. The complete BIE solution is approximated by a series expansion analogous to the more familiar generalized ray expansion widely used in seismological modeling. A layer to layer propagation algorithm is presented which is efficient enough to perform three dimensional wave propagation on a modern minicomputer equipped with an processor. With an efficient propagation algorithm, iterative methods for computing the layer coupling are feasible. The ray expansion approach is most useful for approximating solutions on wave propagation problems in which multiple interaction between boundaries can be ignored. The approximate BIE method is applied to an acoustic model of a mountain in which a flat layered velocity structure is overlain by three dimensional topography. For the solution that includes primary reflection from the layered velocity structure and their corresponding interaction with the topography, amplitude variations between several profiles can be interpreted as they relate to the topography along the profile. Modeling these guided waves requires including waves that reflect from the subsurface velocity structure and interact with the free surface several times. These guided waves dominate the solution over the source-receiver geometry of interest. Peak amplitudes vary by a factor of 2 for stations spaced at 1 km; apparently the result of subtle changes in the interference of waves that have interacted with the free surface in different ways.