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A propagation simulation algorithm is described whereby, at the beginning of step n, the pressure associated with a progressive wave is specified as a function of time and lateral position along a planar surface, x=x[sub n]. The algorithm for step n yields the pressure as a function of time and lateral position at x=x[sub n+1]. The basic mathematical formulation employs an integral equation that predicts the waveforms at arbitrary positions to the right of the first surface. The medium between the point and the surface, x=x[sub n], is turbulent. The integral over the surface involves the Green's function for a point source in the actual medium. Although the exact Green's function is extremely difficult to compute, it is argued that a good approximation for moderate step sizes, |x[sub n-1]-x[sub n]|, results if the Green's function is taken to be that which results from a ray-acoustics approximation. Moreover, because the first caustic for a point source Green's function is not encountered for a distance considerably longer than the distance between successive caustics for a nominally parallel group of rays within a ray tube, the difficulties of explicitly taking caustics into account is circumvented with this algorithm.