The flattened surface parabolic equation

A simple surface flattening transformation is applied to the problem of underwater acoustic scattering from an irregular sea surface. The flattened surface elliptic wave equation is factored to obtain a parabolic equation that has the same high angle capability as recent parabolic equation models. The flattened surface parabolic equation contains an additional surface slope term, but includes forward scattering from the irregular sea surface. The transformation creates additional volume irregularities and irregularities in the water–sediment interface that the range and depth mesh need to resolve. The surface flattening transformation is easy to implement in a parabolic equation model. It compares very well with results obtained using boundary integral equations. An example is given of scattering at 400 Hz from a sea surface with wave heights of 3 m or nearly a wavelength.