A method of seeking eigen-rays in shallow water with an irregular seabed

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1 32 2 Vol Journal of Harbin Engineering University Dec 20 doi /j issn TB566 A A method of seeking eigen-rays in shallow water with an irregular seabed ZHANG Wei YANG Shi'e TANG Yunfeng HUANG Yiwang Science and Technology on Underwater Acoustic Laboratory Harbin Engineering University Harbin 5000 China Abstract For three dimensional 3D shallow water sound propagation if the horizontal deflexion of a ray introduced by reflection on an irregular seabed is not taken into account there will be a serious error in the source bearing Therefore the research of an eigen-ray model for shallow 3D water is of great significance for underwater a- coustics In this paper a compensation and scanning method was applied to seek eigen-rays and respective transmission time was calculated based on the ray model in shallow water with an irregular seabed The results contrasting with the theoretical transmission time indicate that the method of seeking eigen-rays proposed in this paper is feasible In the computation program reflection points were directly derived from ray equations avoiding ray tracing step by step and nearly doubling computing speed Keywords eigen ray 3D shallow water transmission time horizontal deflexion zhangwei667@ 63 com 93- x 0 y 0 z 0 x r y r z r c z x y

2 2 545 Z = h x y Snell s 6 2 μ 2 v 2 s 2 s 2 = ncos θ 2 c z 0 c z = cos θ 0 = n z cos θ 2 z θ 2 θ 2 Snell zj+ μ x j+ - x j - j dz = 0 { z j 槡 n 2 - μ 2 j - v 2 j 3 zj+ v y j+ - y j - j dz = 0 z j 槡 n 2 - μ 2 j - v 2 j θ θ 0 z z 0 x j y j z j x j + y j + z j + j μ a = μ 2 v a = v 2 s a = - s 2 u j v j s j n x y z I = n μ j v j s j R = n μ j + v j + s j + 3 I = N I N - N N I tan π t = g ln 4 + θ 0 2 R = - N I N - N N I 5 tan π 4 + θ' W = s j - b μ j - b 2 v j μ j+ = b W - b 2 b v j - b 2 μ j + μ j + b s j /F v j+ = b 2 W + v j + b 2 s j + b b v j - b 2 μ j /F { s j+ = - W + b 2 v j + b 2 s j + b μ j + b s j /F x y z μ v z u x y z 3 x u y u z u x = x u x y z x a y a z a μ a v a s a m αu j v j s j x x m x r x r x u u j = ncos θcos α x m y m z m x r v j = ncos θsin α 4 x { r y y r ' z s j = nsin θ z r ' x m - y m - z m - x r 3 z z h x y b b 2 F = + b 2 + b 2 z 2 N = t = F b b 2 - c z sinθ z dz 7 z 7 sinθ 0 θ 0 θ' g 7 6 g x r z r 2 z z rn ' z rn + ' x y z x y z

3 α = atan y r - y 0 ± β x r - x 0 dβ β β 2 β n β n β n + 2 x r y y rn ' y rn + ' 2 y rn ' y rn + ' Δy n = y rn ' - y r α = α ± arctan Δy n / x rn - x Δy n εy α 0 Fig The trajectory of eigen rays β n ' β n + ' 3 β n ' β n + ' dβ' Table The transmission time of eigen rays and error β ' β 2 ' β m ' 2 α 0 min z r - z r ' /s /s /s /ms /ms εz ms Z = x y c z = Z m /s 0 m 0 m 5 m 00 m c = m 0 m 5 m - 0 c 0 + gz c 0 = 530 m /s g = - 0 ~ 0 50 m 6 4 km 0 m m

4 2 547 Table 2 2 The angles and transmission time of eigen rays for 3D / / / / /s Fig The projection in the vertical direction of eigen rays Table 3 /s /s Fig 3 The projection in the horizontal direction of eigen rays km m s s 2 2 Bellhop The contrast of transmission time between 2D and 3D congeneric eigen rays 4

5 MERCER J A FELTON W J BOOKER J R Three-dimensional eigenrays through ocean mesoscale structure J J Acoustic Soc Am TINDLE C T BOLD G E Improved ray calculations in shallow water J J Acoustic Soc Am HARRISON C H Three dimensional ray paths in basins troughs and near seamounts by use of invariants J J Acoustic Soc Am YANG Shi'e Theory of underwater sound propagation M Harbin Harbin Engineering University Press J od of improving quantum-behaved particle swarm optimization J Computing Technology and Automation WANG Shuquan A new method of three-dimensional eigen ray-tracing J Acta Acustica croprocessors J NAN Mingxing YANG Tingwu DING Fenglei Three-dimensional ray tracing in ocean front region J Technical Acoustics J JIANG Wei LI Taibao A three dimensional sound ray tracing method by deploying regular tetrahedrons J Acta Acustica HUANG Y Q ZHANG J Z A sound ray tracing algorithm in three-dimensional heterogeneous media based on wave front travel times interpolation J Chinese Journal of A- coustics TAPPERT F D TANG X Ray chaos and eigenrays J J Acoustic Soc Am J YANG Chuanjiang LIU Qing HUANG Zhen One meth- 3 M J LIU Bosheng LEI Jiayu The theory of underwater acoustic M Harbin Harbin Engineering University Press SUN Wanqin GE Liang A finite automaton-based two-dimensional sound ray tracing method J Acta Armamentari J J TANG Junfeng YANG Shi'e Sound speed profile in ocean WANG Baihe FENG Xi'an HUANG Jianguo et al A new inverted by using travel time J Journal of Harbin Engineering University method for eigen rays searching in stratified ocean J Mi D HUANG Yiwang Long-rang source localization by matched field in shallow water D Harbin Harbin Engineering University

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