Modeling sea surface scattering by the time-domain finite-difference method

Abstract

A numerical scattering chamber based on the time-domain finite-difference solution of the two-way elastic wave equation is applied to a sea surface scattering problem, and excellent agreement is obtained in amplitude and phase with a reference solution obtained by an integral equation method. The sea surface roughness is one representation of a Pierson–Moskowitz spectrum for a wind speed of 15 m/s. The incident field is a 400-Hz continuous wave generated by a Gaussian tapered vertical array. This problem demonstrates a number of issues in numerical modeling of wave scattering. The spreading of Gaussian beams, even in homogeneous media, creates an asymmetry in the insonification of the surface footprint or scattering area. Because of beamspreading, Gaussian tapered vertical arrays do not generate Gaussian beams. Scattering from a rough, free, fluid surface can be accurately solved with careful treatment of the numerical boundary representing the free surface. Continuous wave (cw) scattering problems can be solved in the time domain. For the second-order, explicit, staggered finite-difference formulation used in this study, a spatial sampling of 20 points per acoustic wavelength was necessary for acceptable grid dispersion. However, to correctly compute the scattered field for the test model, it was sufficient to specify the free surface at a spatial sampling of only ten points per acoustic wavelength.