Comparison of two different methods to include a beam pattern in parabolic equation models

Abstract

While it is straightforward to include the beam pattern of a sonar in ray models and normal mode models, things become more challenging for parabolic equation models. Two methods are compared in this paper. The first method uses an array starter for the parabolic equation model, derived by MacGillivray and Chapman as a generalization of Collins’ self-starter for a point source. Range propagation of the depth-dependent pressure field generated by this array starter then contains the effects of the beam pattern of the respective array. The second method inverts the computation direction so that the beam pattern can be applied to the simulation result for the complex sound pressure. This is done by performing a windowed Fourier transform into vertical wavenumber space at the sonar depth, thereby decomposing the sound pressure field into propagation angles allowing for multiplication with the beam pattern. This method is not limited to parabolic equation models. Both methods have been realized for WTD 71’s parabolic equation code PESSim (Parabolic Equation Sound Simulation). Using a homogeneous half-space with an analytic reference solution, the two methods are validated and compared. Both methods perform well while each has its advantages and disadvantages.