Riemannian geometric modeling of underwater acoustic ray propagation ?application--Riemannian geometric model of convergence zone in deep ocean remote sound propagation br

Convergence-zone (CZ) sound propagation is one of the most important hydro-acoustic phenomena in thedeep ocean, which allows the acoustic signals with high intensity and low distortion to realize the long-rangetransmission. Accurate prediction and identification of CZ is of great significance in implementing remotedetection or communication, but there is still no standard definition in the sense of mathematical physics forconvergence zone. Especially for the issue of systematic error of computation introduced by the earth curvature,there is no exact propagation model. The curvature-correction methods always lead to the imprecision of theray phase. In previous research work, we realized that the Riemannian geometric meaning of the causticsphenomena caused by ray convergence is that the caustic points are equivalent to the conjugate points, whichform on geodesics with positive section curvature. In this work, we present a spherical layered acoustic raypropagation model for CZ based on the Riemannian geometric theory. With direct computation in the curvedmanifolds of the earth , a Riemannian geometric description of CZ is provided for the first time, on the basis ofcomprehensive analysis about its characteristics. And it shows that the mathematical expression of sectioncurvature adds an additional item after considering the earth curvature, which reflects the influenceof the earth curvature on the ray topology and CZ. By means of Jacobi field theory of Riemannian geometry,computational rule and method of the location and distance of CZ in deep water are proposed. Taking thetypical Munk sound velocity profile for example, the new Riemannian geometric model of CZ is compared withthe normal mode and curvature-correction method. Simulation and analysis show that the Riemanniangeometric model of CZ given in this paper is a mathematical form naturally considering the earth curvaturewith theoretical accuracy, which lays more solid scientific foundations for the study of convergence zone.Moreover, we find that the location of CZ moves towards sound source when the earth curvature is considered,and the width of CZ near the sea surface first increases and then decreases with sound propagation proceeding.The maximum width is about 20 km and the minimum is about 4 km.