A new approach to the optimal modeling of sound propagation in the random ocean

Consideration is given to an optimal modeling problem for the general horizontally stratified ocean, which is assumed to be a random inhomogeneous medium. The random acoustic wave velocity potential p = p(x, y, z) in the ocean is described by the stochastic Helmholtz equation Δp + k²p = 0, where Δ is the standard Laplacian partial differential operator, and k = k(x, y, z) is the random wave number. Because of the random and inhomogeneous nature of the ocean, not only the amplitude and phase fluctuations of the sound wave but also its scattering have to be taken into account in the mathematical modeling of the random wave propagation. In this consideration, p is decomposed as p = p₀ + p_s, where p₀ is the deterministic component (the unperturbed part) of the velocity potential (which can be determined by some existing techniques) and p_s is the random component created essentially by a perturbation. A novel method for obtaining an optimal estimate of p_s is proposed. It is based on a PDL_g-spline theory and technique developed by the authors, so that p can be determined optimally and efficiently for the purpose of applications.