The finite-element method is a general technique for constructing approximate solutions to boundary-value problems. The method involves dividing the domain of interest into a finite number of simple subdomains, the finite elements, and using variational concepts to construct an approximation of the solution over the collection of finite elements.
There has been limited previous work on simulation of earthquake ground motion using finite-element methods. The first application is perhaps due to Lysmer and Drake [30], who demonstrated a finite element method for seismology to simulate Love and Rayleigh waves in a 2-D nonhorizontally layered structures idealized from an alluvial valley and a path from the Central Valley in California to the Sierra Navada, respectively. Toshinawa and Ohmachi [45] used a 3-D finite element method to model Love wave propagation in the Kanto plain, Japan, for waves with periods of about 10 seconds. They found that the 3-D simulation produced synthetics with larger amplitude and duration than 2-D simulation and that the 3-D synthetics agreed better with the data. In the same year, Li et al [28] used a finite element method to evaluate the effects of site conditions on the 3-D seismic response of alluvial basins on the Connection Machine CM-2. Results for a shallow truncated semi-ellipsoidal valley subjected to oblique incident SV-waves illustrate conversion from body waves to surface waves at the valley confluence and the large amplitude and long duration of surface ground motion, as well as spatial variation within the valley, compared to the surrounding rock and to one-dimensional models of the valley. Waves with near critical incident angles produce an especially large response.
Without having the disadvantages of FDM and BEM, FEM has the potential to simulate effectively the seismic ground motion in large realistic basins. Therefore a complete 3-D FEM is needed.