A convolution algorithm for standard parabolic-equation modeling

Abstract

The split-step Fourier algorithm for solving the acoustic parabolic equation involves two Fourier transforms, one forward and the other inverse. These may, of course, be replaced by a convolution. For the standard parabolic equation, the particular form of one of the convolved factors allows the convolution integral to be solved using a single Fourier transform. Application of this technique results in a limitation on the allowed range step. When applicable, however, the convolution algorithm reduces computer run times to about 60% of those required by the standard split-step Fourier algorithm. Examples are presented and limitations are discussed.