Abstract
Numerical methods based on Finite Difference and Finite Element approximations of the acoustic and elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms. Various numerical schemes based on Finite Difference and Finite Element Methods (FDM and FEM) are reported in the geophysical literature. We compare here the grid dispersion properties and stability conditions of the FDM and FEM that have become the most popular for wave propagation in the time domain. For FDM we use the classical results to compute grid dispersion curves, and for FEM we derive a novel approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of FEM for acoustic and elastic wave propagation modeling that overcomes the difficulties due to irregular node spacing within the element and the use of high order polynomials.
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