Purely numerical methods based on the Finite Element Method (FEM) are becoming
increasingly popular in seismic modeling for the propagation of acoustic and
elastic waves in geophysical models. These methods o er a better control on the accuracy
and more geometrical
exibility than the Finite Di erence methods that have
been traditionally used for the generation of synthetic seismograms. However, the
success of these methods has outpaced their analytic validation. The accuracy of the
FEMs used for seismic wave propagation is unknown in most cases and therefore
the simulation parameters in numerical experiments are determined by empirical
rules. I focus on two methods that are particularly suited for seismic modeling: the
Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin
Method (IP-DGM).
The goals of this research are to investigate the grid dispersion and stability
of SEM and IP-DGM, to implement these methods and to apply them to subsurface
models to obtain synthetic seismograms. In order to analyze the grid dispersion
and stability, I use the von Neumann method (plane wave analysis) to obtain a
generalized eigenvalue problem. I show that the eigenvalues are related to the grid
dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to
the number of degrees of freedom inside one element.
The grid dispersion results indicate that SEM of degree greater than 4 is
isotropic and has a very low dispersion. Similar dispersion properties are observed
for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis
functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes
per wavelength to be used. On the other hand, the stability analysis shows that,
in the elastic case, the size of the time step required in IP-DGM is approximately
6 times smaller than that of SEM. The results from the analysis are con rmed by
numerical experiments performed using an implementation of these methods. The
methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE
salt dome model. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6864 |
| Date | 03 February 2010 |
| Creators | De Basabe Delgado, Jonás de Dios, 1975- |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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