ELASTIC WAVE-PROPAGATION SIMULATION IN HETEROGENEOUS MEDIA BY THE SPECTRAL MOMENTS METHOD

The second-order elastic wave propagation equations are solved using t he spectral moments method. This numerical method, previously develope d in condensed matter physics, allows the computation of Green's funct ions for very large systems, The elastic wave equations are transforme d in the Fourier domain for time derivatives, and the partial derivati ves in space are computed by second-order finite differencing. The dyn amic matrix of the discretized system is built from the medium paramet ers and the boundary conditions. The Green's function, calculated for a given source-receiver couple, is developed as a continued fraction w hose coefficients are related to the moments and calculated from the d ynamic matrix. The continued fraction coefficients and the moments are computed using a very simple algorithm, We show that the precise esti mation of the waveform for the successive waves arriving at the receiv er depends on the number of moments used. For long recording times, mo re moments are needed for an accurate solution. Efficiency and accurac y of the method is illustrated by modeling wave propagation in 1-D aco ustic and 2-D elastic media and by comparing the results obtained by t he spectral moments method to analytical solutions and classical finit e-difference methods.