A New Technique to Synthesize Seismography with More Flexibility: the Legendre Spectral Element Method with Overlapped Elements

Abstract

The classic spectral element method (SEM) is important for seismographical simulation. However, waves subjected to irregular interfaces or surfaces are difficult to simulate accurately using SEM with quadrangular/hexahedral elements. In this paper we propose a new technique to solve this problem. The technique reconstructs some new elements near the surface/interface to substitute for any element crossing the interface, thus making the boundary of some new elements an accurate fit to the interface/surface. Numerical comparisons with the classic SEM show that the technique has improved flexibility when dealing with interface problems without losing accuracy and efficiency. The technique also enables us to vary the size and shape of an element smoothly as the velocity in a medium varies so that this removes the inaccuracy resulting from the high local variation of the grid in the classic SEM. Therefore, the technique widens the application of the classic SEM in seismographic simulation.