Modeling broadband ocean acoustic transmissions with time-varying sea surfaces

Solutions to ocean acoustic scattering problems are often formulated in the frequency domain, which implies that the surface is "frozen" in time. This may be reasonable for short duration signals but breaks down if the surface changes appreciably over the transmission time. Frequency domain solutions are also impractical for source-receiver ranges and frequency bands typical for applications such as acoustic communications (e.g. hundreds to thousands of meters, 1-50 kHz band). In addition, a driving factor in the performance of certain acoustic systems is the Doppler spread, which is often introduced from sea-surface movement. The time-varying nature of the sea surface adds complexity and often leads to a statistical description for the variations in received signals. A purely statistical description likely limits the insight that modeling generally provides. In this paper, time-domain modeling approaches to the sea-surface scattering problem are described. As a benchmark for comparison, the Helmholtz integral equation is used for solutions to static, time-harmonic rough surface problems. The integral equation approach is not practical for time-evolving rough surfaces and two alternatives are formulated. The first approach is relatively simple using ray theory. This is followed with a ray-based formulation of the Helmholtz integral equation with a time-domain Kirchhoff approximation.