Study and Implementation of the Finite Difference Method for Wave Propagation in Fluid and Elastic Media

Abstract

Two finite-difference methods for calculating wave propagation in two-dimensional fluid and elastic media has been implemented. The first is developed from the second order wave equations, while the other stems from a first order velocity-stress system that uses a staggered grid. The two methods are compared with regard to the implementation, and to the numerical results for different simulation parameters. In order to reduce artificial reflections from the model boundaries, it is important to consider the boundary conditions at the edges of the computational domain. Three different absorbing boundary methods are presented in this thesis: the Reynold's cite{Reynolds} absorbing boundary conditions, an attenuating layer, and the perfectly matched layer (PML) method. No concluding results of the PML method is available due to problems of numerical instability. Finally a study of how surface waves can be used to detect buried targets, has been done. The results are positive, in that they support the use of surface waves being a viable tool for detecting shallow buried objects in the seafloor.