Two-dimensional weighted residual method for scattering and diffraction of elastic waves by arbitrary shaped surface topography

This thesis studied the scattering and diffraction of P-waves on an arbitrary shaped canyon or valley. The analytical method defined the cylindrical-wave function to satisfy the zero stress-boundary condition along the half-space for semi-circular canyons by defining the wave potentials in terms of a single sine or cosine function only, instead of a combination of both. Combining this formulation with the use of the weighted residual method for the solution of the wave function, allows for a solution to an arbitrary shaped canyon and valley. The goal of this thesis is to generate a method that would have the flexibility to define any surface that could potentially represent the complexity of a real life canyon or valley.