Harvard Seismology: Wave Propagation in 3D media

We have developed and implemented a spectral element method which we use to simulate the propagation of elastic and anelastic seismic waves in complex local, regional, and global Earth models. We also use this method to evaluate site effects and seismic risk in 3D basins (Tokyo, Boston...). In a spectral element method, spatial derivatives are evaluated using the weak form of the wave equation, on a grid made of elements on which a Gauss-Lobatto-Legendre quadrature rule is used. We therefore have to solve an ordinary differential equation in time, for which temporal derivatives are evaluated by a standard finite difference method, namely a Newark scheme written in a predictor/multicorrector algorithm.

Active participants in this project are Dimitri Komatitsch and Jeroen Tromp.

Recent Developments

Effects of free-surface topography variation are accounted for by adapting the grid to the shape of the surface
A non-structured grid is used in depth to drastically reduce the cost of the simulation in regions where a coarser mesh can be used (when a significantly higher velocity is present)
The accuracy of the method is shown by several tests on 3D models with topography for which solutions computed using other methods were available
The acoustic/elastic coupling is solved using a potential in the homogeneous fluid region
Successful runs on crust-less PREM, computed using a Global Pseudo-Spectral method, match the Normal Mode Synthetics. See these results.

Publications

The Spectral Element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures, Dimitri Komatitsch and Jean-Pierre Vilotte, Bull. Seis. Soc. Am., vol. 88(2), pp 368-392 (1998).
The Spectral Element method for elastic wave equations: application to 2D and 3D seismic problems, Dimitri Komatitsch, Jean-Pierre Vilotte, Rossana Vai, José-Manuel Castillo-Covarrubias and Francisco-José Sánchez-Sesma, Int. J. Num. Meth. Eng. (1999), in press. This work is the result of a collaboration with Prof. Paco Sánchez-Sesma of the Instituto de Ingenieria of the University of Mexico (UNAM).

Last modified: August 17, 1998