Comparison of the WKBJ and truncated asymptotic methods for an acoustic medium

Abstract

A new time‐domain method for solving the 1‐D acoustic wave equation with smoothly varying density and bulk modulus is used to analyse the propagation of waves in a smoothly varying medium. The new ‘truncated asymptotic’ method is exact for a large class of inhomogeneities and hence does not require the usual restriction of geometrical optics, that the wavelength be much less than the material stratification length. The truncated asymptotic solution is used as a benchmark to analyse a two‐term WKBJ approximation for one of four classes of velocity functions. The velocity functions are such that the truncated asymptotic solutions are exact. For the case of small and intermediate velocity gradients, the WKBJ solution performs well when the length scale of the transition zone is of the same order, or larger, than the length of the applied wavelet. For steeper velocity gradients, the WKBJ solutions differs significantly from the exact truncated asymptotic solution. Copyright © 1990, Wiley Blackwell. All rights reserved