Introduction to the spectral element method for three-dimensional seismic wave propagation

Details Introduction to the spectral element method for three-dimensional seismic wave propagation Introduction to the spectral element method for three-dimensional seismic wave propagation

Dec 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999geoji.139..806k&link_type=abstract

Geophysical Journal International, Volume 139, Issue 3, pp. 806-822.

Astronomy and Astrophysics

Astronomy

102

Attenuation, Finite Element Methods, Numerical Techniques, Seismic Modelling, Seismic Wave Propagation, Topography

Scientific paper

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.

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