Simulation of wave propagation through an inhomogeneous turbulent medium with the aid of an integral formulation

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=xn. The algorithm for step n yields the pressure as a function of time and lateral position at x=xn+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=xn, 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, ‖xn−1−xn‖, 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 di...