An element by element spectral element method for elastic wave modeling*

Abstract

Abstract The spectral element method which combines the advantages of spectral method with those of finite element method, provides an efficient tool in simulating elastic waves equation in complex medium. Based on weak from the elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobotto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element examples are resented to in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are resented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and a spectral algorithms, the method can be used for complex models, including free surface boundaries and strong...