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Finite difference seismic eave propagation using variable grid sizesby 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.
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