Riemannian Geometric Modeling of Underwater Acoustic Ray Propagation · Application——Riemannian Geometric Model of Convergence Zone in the Deep Ocean

Convergence-zone (CZ) sound propagation is one of the most important hydro-acoustic phenomenons in the deep ocean, that allows long-range transmission of acoustic signals with high intensity and low distortion. Accurate prediction and identification of CZ is of great significance for remote detection or communication, but there is still no standard definition in sense of mathematical physics for convergence zone. Especially on the issue of systematic error of computation introduced by the earth curvature, with no exact propagation model, curvature-correction methods always lead to imprecision of the ray phase. In previous research work, we realize that the Riemannian geometric meaning of the caustics phenomena caused by ray convergence is that the caustic points are equivalent to the conjugate points, which form on geodesics with positive section curvature. In this paper, we presents a spherical layered acoustic ray propagation model for CZ based on the Riemannian geometric theory. With direct computation in the curved manifolds of the earth instead of in the European space, a Riemannian geometric description of CZ is provided for the first time, on the basis of comprehensive analysis about it’s characteristics. And it shows that the mathematical expression of section curvature adds an additional item $\frac{{\hat c(l)\hat c'(l)}}{l}$ after considering the earth curvature, which reflects the influence of the earth curvature on the ray topology and CZ. By means of Jacobi field theory of Riemannian geometry, computational rule and methods of the location and distance of CZ in deep water are proposed. Taking the Munk sound speed profile as an typical example, the new Riemannian geometric model of CZ is compared with the normal mode and curvature-correction method. Simulation and analysis shows that the Riemannian geometric model of CZ given in this paper is a mathematical form naturally considering the earth curvature with theoretical accuracy, which lays more solid scientific foundations for research of convergence zone. Moreover, we find that the location of CZ moves towards sound source when considering the earth curvature, and the width of CZ near the sea surface increases first and then decreases with sound propagation. The maximum width is about 20 km and the minimum is about 4 km.