Earth Resources Laboratory :: Abstracts

Finite difference seismic eave propagation using variable grid sizes

Antonio De Lilla

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on March 27, 1997 in partial fulfillment of the requirements for the degree of Master of Science

Abstract

Theoretical modeling has played an important role in understanding wave propagation in complex media. Finite difference is one of the most used methods to solve Partial Differential Equations numerically, and very often it requires enormous computational time and resources. In this thesis a variable finite difference method is developed, where a finer grid is used when model parameters are highly variable. In this scheme one can obtain accurate results with minimal computational requirements. In this study, a multigrid velocity-stress finite difference method is used to simulate the wave propagation across large models. The velocity-stress finite difference is formulated using a staggered grid, where a scheme is developed to relate the different-sized grids.

The variable grid scheme is first implemented in one dimension for the acoustic case. Different tests were carried out in order to obtain a validation of the method. Then, was developed a two-dimensional (2D) implementation of the multigrid finite difference method for elastic models. The (2D) implementation is tested using different models, both for acoustic and elastic media. The results obtained with the multigrid approach are in good agreement with the solutions obtained using the normal uniform grid finite difference.

Using the variable grid finite difference algorithm, we investigated the effect of interface irregularities on the reflection and scattering of elastic waves. We also examined the effects of interface roughness and the AVO (Amplitude Variation with Offset) analysis, commonly used in seismic exploration.