A comparison of phase screen and finite difference calculations for elastic waves in random media

Abstract

Phase screen and second‐order finite difference calculations of elastic wave propagation in two‐dimensional (2‐D) random media are compared to assess the accuracy and efficiency of the former method. The phase screen method is a forward propagation algorithm which depends only on the local S and P wave velocities. It differs from similar methods for scalar waves by treating P/S conversion. In its current formulation, the phase screen method does not treat modal propagation. Synthetic seismograms are generated by both methods at 640 evenly spaced receiver positions for identical realizations of 512 × 2750 velocity grid points. Comparisons are made for 2‐D random media characterized by exponential and zeroth‐order von Karman (self‐similar) autocorrelation functions of varying strength and correlation length. Constant and varying Poisson ratios are considered. Early arrivals compare more favorably since the phase screen method does not treat backscatter. The waveforms are compared by computing relative differences and cross correlations as a function of time offset. Temporal energy centroids of bandpass filtered synthetic seismograms are also computed and compared. Execution times are compared on a SUN 4/330, an ELXSI 6400, a Cray‐2, and an nCUBE parallel computer. The phase screen algorithm is roughly 2 orders of magnitude faster than the second‐order finite difference algorithm for 2‐D grids. An estimate, based on the number of operations in each algorithm, suggests that the phase screen method may be 3 orders of magnitude faster for comparable three‐dimensional problems.