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针对压缩波声速n2线性分布、剪切波声速平方线性分布的变参数弹性海底沉积层中声场建模问题，建立了关于压缩波与剪切波本征函数的偏微分耦合方程组，基于微扰法，通过逐次微分给出了本征函数的近似解析解.理论分析表明，只有剪切波声速平方的梯度不为零的情况下，沉积层中的压缩波才会与剪切波产生耦合.压缩波与剪切波耦合的影响会带来本征值的变化，其对近场声传播的影响较小，但远距离声传播损失的预报在考虑耦合后与实测数据符合得更好.此外，耦合还会导致沉积层中本征函数及其导数的变化，使得耦合与非耦合情况下沉积层中质点位移场不同.通过与商用声场软件COMSOL计算结果的对比分析检验了本文方法的正确性，且本文方法计算时间远小于COMSOL软件运行时间.In the real ocean environment, the compressional and shear wave velocities in an elastic sediment layer vary with depth, leading to the coupling between compressional and shear waves. As the coupling will affect the underwater sound field, in this paper, a typical sound velocity distribution (where the compression wave velocity has an n2 linear distribution and the square of shear wave velocity has a linear distribution) is analyzed. Based on the wave equation in inhomogeneous elastic medium, coupled equations of wavenumber kernels of scalar and vector potential functions are established. Based on the perturbation method, approximate analytical solutions of integration kernels are acquired by successive differentiation. The comparison between theoretical prediction and experimental data, which are from the pressure sensor of ocean-bottom seismometer (OBS) consisting of three orthogonal hydrophones and one hydrophone, located at the bottom of the sea near Qingdao City, shows that the coupling between shear wave and compression wave has little effect on near-field sound propagation, while the prediction of long-range sound propagation needs to consider the influence of eigenvalue change caused by coupling. Theoretic analysis shows that there will be coupling between the two waves only if the gradient, σ, of the square of the shear wave velocity is nonzero. When α, the gradient of the reciprocal of the square of the compression wave velocity, becomes larger, and σ remains unchanged, the simulation results show that the change of the eigenvalue is very small when considering the coupling effect. Thus, transmission loss curves calculated by the coupled and uncoupled algorithm are almost the same. When σ becomes larger while α remains unchanged, the simulation results show that eigenvalues are changed to some extent if considering the coupling effect, and that the difference between transmission loss calculated by the coupled and uncoupled algorithms increases. That means the effect of σ value on coupling is greater than that of α value. In addition, the coupling between the compression wave and shear wave can lead the eigenfunctions and derivative eigenfunctions in the sediment to change. The horizontal displacement and vertical displacement are the Fourier-Bessel integral functions of eigenfunctions and derivative eigenfunctions. So the displacement field of particle in the sediment layer is different in the coupled case from that in the uncoupled cases. By comparing the transmission loss of sound pressure simulated by COMSOL software and that obtained from our proposed method, the correctness of the proposed method is verified. And the calculation time is much shorter than the calculation time by using COMSOL software.
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Keywords:
- elastic sediment /
- velocity changing /
- coupling /
- approximate analytical
[1] Godin O A, Chapman D M F 2001 J. Acoust. Soc. Am. 110 1890
[2] Godin O A, Chapman D M F 1999 J. Acoust. Soc. Am. 106 2367
[3] Chapman D M F, Godin O A 2001 J. Acoust. Soc. Am. 110 1908
[4] Greene J, Giard J, Potty G R, Miller J H 2011 International Symposium on Ocean Electronics Kochi, India, November 16-18, 2011 p211
[5] Soloway A G, Dahl P H, Odom R I 2015 J. Acoust. Soc. Am. 138 EL370
[6] Hall M V 1995 J. Acoust. Soc. Am. 98 1075
[7] Fryer G J 1981 J. Acoust. Soc. Am. 69 647
[8] Liu J Y, Tsai S H, Wang C C, Chu C R 2004 J. Sound Vib. 275 739
[9] Liu J Y, Tsai S H, Lin I C 2004 Ocean Eng. 31 417
[10] Ewing W M, Jardetzky W S, Press F 1957 Elastic Waves in Layered Media (New York: Mcgraw-Hill Book Company) pp328-330
[11] Karal F C, Keller J B 1959 J. Acoust. Soc. Am. 31 694
[12] Hook J F 1961 J. Acoust. Soc. Am. 33 302
[13] Scholte J G J 1961 Geophys. Prospect. 9 86
[14] Gupta R N 1966 B. Seismol. Soc. Am. 56 511
[15] Vidmar P J, Foreman T L 1979 J. Acoust. Soc. Am. 66 1830
[16] Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631
[17] Yang S E 2009 Theory of Underwater Sound Propagation (Harbin: Harbin Engineering University Press) pp24-25
[18] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2012 Computational Ocean Acoustics (New York: Springer New York) pp265-266
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[1] Godin O A, Chapman D M F 2001 J. Acoust. Soc. Am. 110 1890
[2] Godin O A, Chapman D M F 1999 J. Acoust. Soc. Am. 106 2367
[3] Chapman D M F, Godin O A 2001 J. Acoust. Soc. Am. 110 1908
[4] Greene J, Giard J, Potty G R, Miller J H 2011 International Symposium on Ocean Electronics Kochi, India, November 16-18, 2011 p211
[5] Soloway A G, Dahl P H, Odom R I 2015 J. Acoust. Soc. Am. 138 EL370
[6] Hall M V 1995 J. Acoust. Soc. Am. 98 1075
[7] Fryer G J 1981 J. Acoust. Soc. Am. 69 647
[8] Liu J Y, Tsai S H, Wang C C, Chu C R 2004 J. Sound Vib. 275 739
[9] Liu J Y, Tsai S H, Lin I C 2004 Ocean Eng. 31 417
[10] Ewing W M, Jardetzky W S, Press F 1957 Elastic Waves in Layered Media (New York: Mcgraw-Hill Book Company) pp328-330
[11] Karal F C, Keller J B 1959 J. Acoust. Soc. Am. 31 694
[12] Hook J F 1961 J. Acoust. Soc. Am. 33 302
[13] Scholte J G J 1961 Geophys. Prospect. 9 86
[14] Gupta R N 1966 B. Seismol. Soc. Am. 56 511
[15] Vidmar P J, Foreman T L 1979 J. Acoust. Soc. Am. 66 1830
[16] Westwood E K, Tindle C T, Chapman N R 1996 J. Acoust. Soc. Am. 100 3631
[17] Yang S E 2009 Theory of Underwater Sound Propagation (Harbin: Harbin Engineering University Press) pp24-25
[18] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2012 Computational Ocean Acoustics (New York: Springer New York) pp265-266
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