Introduction to the spectral element method for three-dimensional seismic wave propagation
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ID: 294501
1999
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Abstract
We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the flexibility of a finite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wavefield on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simplifies the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/reflectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.
| Reference Key |
openalex_W2148631859
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|---|---|
| Authors | Dimitri Komatitsch, Jeroen Tromp |
| Journal | geophysical journal international |
| Year | 1999 |
| DOI |
10.1046/j.1365-246x.1999.00967.x
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| URL | |
| Keywords | Keywords not found |
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