Three‐dimensional propagation modeling using the parabolic approximation

An algorithm has been developed for the propagation of sound in a three‐dimensionally varying ocean region. We start with the Helmholtz equation in cylindrical coordinates and apply the parabolic approximation in range (retaining variation in horizontal angle). The method involves the split‐step Fourier algorithm in depth and angle. In addition, an analytic continuation procedure in angle is used to facilitate implementation on a computer with finite memory. Initial computer results show identical answers compared to the two‐dimensional split‐step parabolic program when all angular variation is absent, and excellent agreement to an exact solution of the parabolic equation that contains an initial field that varies with angle. The numerical results of these calculations will be discussed.