Coupling scattering from the sea surface to a one-way marching propagation model via conformal mapping: Validation

Abstract

Propagation models in underwater acoustics usually incorporate sea surface scattering effects in an ad hoc manner which in most cases requires making severe approximations. In particular, to include in a coherent manner in a marching acoustic propagation model the scattering that occurs at a rough sea surface poses a serious problem. Dozier [J. Acoust. Soc. Am. 75, 1415–1432 (1984)] introduced a rigorous approach in the framework of the split-step parabolic equation model, which used a sequence of conformal mappings to flatten segments of the sea surface locally. Each conformal mapping preserved the elliptic form of the wave equation. In each transformed space the parabolic approximation is made and the solution advanced one range step. The method has the attractive feature of handling surface roughness within a propagation model in a mathematically consistent manner, including refraction and multiple surface interactions when and where they occur. In this work the technique developed by Dozier is implemented in the realm of the finite element parabolic equation model [Collins, J. Acoust. Soc. Am. 93, 1736–1742 (1993)] and applied to the problem of forward scattering from both periodic and single realizations of randomly rough surfaces. The validity of the technique is examined by comparison with an exact solution to the scattering problem obtained through the method of moments for both types of surfaces. It is shown that the current technique provides the correct energy distribution of the forward-scattered field. The performance of this hybrid model suggests that it might be well suited as the reference solution for comparing with propagation models that include sea surface scattering in a more approximate manner.