High-order finite element methods for seismic wave propagation
| dc.contributor.advisor | Sen, Mrinal K. | en |
| dc.contributor.advisor | Wheeler, Mary F. (Mary Fanett) | en |
| dc.creator | De Basabe Delgado, Jonás de Dios, 1975- | en |
| dc.date.accessioned | 2010-02-03T17:48:02Z | en |
| dc.date.accessioned | 2017-05-11T22:19:47Z | |
| dc.date.available | 2010-02-03T17:48:02Z | en |
| dc.date.available | 2017-05-11T22:19:47Z | |
| dc.date.issued | 2009-05 | en |
| dc.description | text | en |
| dc.description.abstract | 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. | en |
| dc.description.department | Computational Science, Engineering, and Mathematics | en |
| dc.format.medium | electronic | en |
| dc.identifier.uri | http://hdl.handle.net/2152/6864 | en |
| dc.language.iso | eng | en |
| dc.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. | en |
| dc.subject | Spectral Element Method | en |
| dc.subject | Interior-Penalty Discontinuous Galerkin Method | en |
| dc.subject | Seismic modeling | en |
| dc.subject | Grid dispersion | en |
| dc.subject | Stability | en |
| dc.subject | Synthetic seismograms | en |
| dc.title | High-order finite element methods for seismic wave propagation | en |