2.5-D Numerical Simulation of Acoustic Wave Propagation

Abstract

—Endeavors to simulate the 3-D seismic wave propagation effects in the 2-D environment have stimulated the development of 2.5-D simulation techniques. Liner (1991) has developed a damped 2.5-D acoustic wave equation using the 3-D Green's function for a constant density medium. This paper presents the finite-difference simulation and study of various numerical artifacts, using Liner's acoustic wave equation. Comparisons of second-order as well as fourth-order accurate 2.5-D and 2-D acoustic wave simulation results have been given. The snapshots at different times and zero off-set response of a salt dome model have been computed and strong reflections and diffraction phases have been reported. Also, the analysis of amplitude behaviors and computational time for Liner's (1991) and Williamson and Pratt's (1995) 2.5-D wave equations, with and without the last term (1/t 2),reveals that this last term is superfluous as suggested by Stockwell (1995). The effectiveness of Sponge transmissive as well as Clayton and Engquist (1980) absorbing boundary conditions has been studied. A modified Ricker wavelet, the second derivative of the convolution of Gaussian function and a polynomial window, has been used as a source. It has been found that the stability condition and the requirement of the number of grid points per wavelength to avoid grid dispersion are the same as for the 2-D acoustic cases.