基于潜标的甚低频矢量声场建模与试验研究
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摘要
矢量水听器可以空间共点、同步地测量声场空间一点处的声压和质点振速的三正交分量,为水声信号的处理提供了更为全面的声场信息,也为解决水声问题提供了新的思路和方法。随着矢量水听器制作工艺以及矢量信号处理技术的不断发展和进步,关于矢量水听器的应用研究已成为水声研究领域的一项重要内容。然而对海洋矢量声场传播物理特性的研究却不多见,尤其是甚低频矢量声场及其试验研究工作就更少。潜标作为矢量水听器的一种工作平台,其水下工作期间必然受到诸如海流、潮汐、风浪等海洋环境的影响,使潜标体产生旋转、俯仰、倾斜等姿态变化,同时亦引起潜标体自身的振动,这种平台振动耦合问题亦引起了水声学者的重视。随着水声领域诸多方面对低频矢量水听器的需求,低频矢量水听器的水池校准研究逐渐提上日程,因而有必要研究水池矢量声场,以便为矢量水听器校准工作提供指导性意见。
本文在回顾了矢量水听器工程应用及矢量声系统研究、海洋矢量声场及海底参数反演研究,以及水池测试技术研究的基础上,以矢量水听器应用为背景,对浅海声传播矢量特性及海底参数反演、声学潜标综合监测技术和水池矢量声场进行了理论和试验研究。
结合海洋声场简正波理论,推导给出了浅海矢量声场中声压、质点振速和有功声强的简正波表达式,通过数值仿真研究了浅海甚低频矢量声场传播特性,包括声压、质点振速的传播规律,以及声压与质点振速间的相位关系,并以海试试验数据验证了声场仿真分析结果。根据海洋矢量场中声压信息与质点垂直振速信息可以互为补充,进行了基于声压和垂直振速联合处理的海底参数匹配场反演研究。仿真分析了不同条件下,四种代价函数利用宽带及单频信号进行匹配场反演时对海底密度与声速变化影响的灵敏度情况,最后结合浅海矢量声场海试数据进行了海底参数匹配场反演工作。
为研究潜标系统水下工作期间潜标体姿态和同步的潜标体振动情况,设计了潜标水下综合监测系统。介绍了综合监测系统的基本构成,给出了监测系统数据分析理论,分析了三套潜标水下综合监测海试数据,通过同步数据的研究分析可为矢量水听器悬挂装置、潜标体和锚系的优化设计提供依据；另外,以简化模型研究分析了矢量水听器悬挂系统一级与二级减振系统弹性元件的减振性能,并利用振动台进行了试验测试验证。
为便于低频矢量水听器水池校准工作的开展,研究了水池低频矢量声场。针对水池声场经典声压场数值仿真时存在计算速率低的问题,提出了一种水池声场快速计算方法,该方法将声场计算三重无穷级数展开转化为二重无穷级数展开,同时z方向的本征值通过x和y方向本征值确定。为避免数值溢出问题,给出了一种有效的解决措施。数值仿真和水池试验验证了该声场计算方法的快速性和正确性。最后将该快速算法推广至水池矢量声场质点振速场的计算,仿真分析了水池矢量场声压、质点振速的分布情况。
Vector hydrophone can simultaneously and colocatedly measure the acoustic pressure and three orthogonal components of particle velocity, which may provide more comprehensive information for further underwater acoustic signal processing and also inspire new thoughts and methods in solving undersea problems. With the development and improvement of the vector hydrophone's manufacture skill and vector signal processing, the related research on the application of vector hydrophone has become one of the most important issues in the field of underwater acoustics. However, the research on physical properties of vector acoustic field propagation is rarely reported, especially the theoretical study and experiment of VLF (very low frequency) vector acoustic field. Due to the influence of ocean current, tide, storm etc, subsurface buoy, as the platform of vector hydrophone, will suffer attitude changes including rotation, pitch, roll etc. Meantime, it also introduces self vibration and this vibration-coupling problem has caught more and more attention. With the demands of low frequency vector hydrophone in many aspects of underwater acoustic field, the calibration of low frequency vector hydrophone in the water tank is gradually calendared. So it is necessary to study the vector acoustic field in water tank in order to provide guidance for the calibration of vector hydrophone.
In this dissertation, after reviewing the research on engineering application of vector hydrophone and its suspension system, ocean vector acoustic field propagation and geoacoustic inversion, and measurement technology in the water tank, it focuses on the following aspects for further theoretical and experiment study, including vector properties of shallow water acoustic propagation, geoacoustic inversion, integrated monitoring technology of subsurface buoy and vector acoustic field in the water tank.
According to the normal mode theory, it derives the expressions of acoustic pressure, particle velocity and active acoustic intensity in shallow water vector acoustic field. Then the propagation properties of sound pressure, particle velocity and their mutual phase relation are study through numerical simulation and verified by sea trial data. The geoacoustic inversion via matched field processing on the basis of joint processing of acoustic pressure and vertical particle velocity is studied considering the information complementarity of them. The sensitivity of seabed density and sound speed for four cost functions used by matched field inversion (MFI) via both broadband and single frequency signal are compared in different conditions. Finally, the MFI inversion is conducted by use of the information of sound pressure and vertical particle velocity.
Underwater integrated monitoring system is designed to study the attitude and synchronous vibration of subsurface buoy. Basic structure of such integrated monitoring svstem is introduced, and the experiment data of three set of subsurface buoy are analyzed using correlation theory and spectral analysis theory. The analysis of synchronous data could provide some suggestion to improve the design of vector hydrophone suspension device, subsuface buoy and mooring system. In addition, damping performance of first order and second order suspension system are analyzed with a simplified model, which is verified vibration test.
The low frequency vector acoustic field in the water tank is studied to assist the calibration of low frequency vector hydrophone. In order to solve the low-speed calculation via classic pressure field expression, an efficient procedure for computation of the sound field in water tank is proposed, which converts a triple sum infinite expression to a double sum one and makes the eigenvalues in three orthogonal directions related to each other. In addition, another improved strategy is used to avoid the problem of computation overflow in PC implementation. Numerical simulation and tank trial have verified its effectiveness and correctness. Finally, this fast numerical solution is extended to calculate the particle velocity field and some numerical results are given for further use.
本文在回顾了矢量水听器工程应用及矢量声系统研究、海洋矢量声场及海底参数反演研究,以及水池测试技术研究的基础上,以矢量水听器应用为背景,对浅海声传播矢量特性及海底参数反演、声学潜标综合监测技术和水池矢量声场进行了理论和试验研究。
结合海洋声场简正波理论,推导给出了浅海矢量声场中声压、质点振速和有功声强的简正波表达式,通过数值仿真研究了浅海甚低频矢量声场传播特性,包括声压、质点振速的传播规律,以及声压与质点振速间的相位关系,并以海试试验数据验证了声场仿真分析结果。根据海洋矢量场中声压信息与质点垂直振速信息可以互为补充,进行了基于声压和垂直振速联合处理的海底参数匹配场反演研究。仿真分析了不同条件下,四种代价函数利用宽带及单频信号进行匹配场反演时对海底密度与声速变化影响的灵敏度情况,最后结合浅海矢量声场海试数据进行了海底参数匹配场反演工作。
为研究潜标系统水下工作期间潜标体姿态和同步的潜标体振动情况,设计了潜标水下综合监测系统。介绍了综合监测系统的基本构成,给出了监测系统数据分析理论,分析了三套潜标水下综合监测海试数据,通过同步数据的研究分析可为矢量水听器悬挂装置、潜标体和锚系的优化设计提供依据；另外,以简化模型研究分析了矢量水听器悬挂系统一级与二级减振系统弹性元件的减振性能,并利用振动台进行了试验测试验证。
为便于低频矢量水听器水池校准工作的开展,研究了水池低频矢量声场。针对水池声场经典声压场数值仿真时存在计算速率低的问题,提出了一种水池声场快速计算方法,该方法将声场计算三重无穷级数展开转化为二重无穷级数展开,同时z方向的本征值通过x和y方向本征值确定。为避免数值溢出问题,给出了一种有效的解决措施。数值仿真和水池试验验证了该声场计算方法的快速性和正确性。最后将该快速算法推广至水池矢量声场质点振速场的计算,仿真分析了水池矢量场声压、质点振速的分布情况。
Vector hydrophone can simultaneously and colocatedly measure the acoustic pressure and three orthogonal components of particle velocity, which may provide more comprehensive information for further underwater acoustic signal processing and also inspire new thoughts and methods in solving undersea problems. With the development and improvement of the vector hydrophone's manufacture skill and vector signal processing, the related research on the application of vector hydrophone has become one of the most important issues in the field of underwater acoustics. However, the research on physical properties of vector acoustic field propagation is rarely reported, especially the theoretical study and experiment of VLF (very low frequency) vector acoustic field. Due to the influence of ocean current, tide, storm etc, subsurface buoy, as the platform of vector hydrophone, will suffer attitude changes including rotation, pitch, roll etc. Meantime, it also introduces self vibration and this vibration-coupling problem has caught more and more attention. With the demands of low frequency vector hydrophone in many aspects of underwater acoustic field, the calibration of low frequency vector hydrophone in the water tank is gradually calendared. So it is necessary to study the vector acoustic field in water tank in order to provide guidance for the calibration of vector hydrophone.
In this dissertation, after reviewing the research on engineering application of vector hydrophone and its suspension system, ocean vector acoustic field propagation and geoacoustic inversion, and measurement technology in the water tank, it focuses on the following aspects for further theoretical and experiment study, including vector properties of shallow water acoustic propagation, geoacoustic inversion, integrated monitoring technology of subsurface buoy and vector acoustic field in the water tank.
According to the normal mode theory, it derives the expressions of acoustic pressure, particle velocity and active acoustic intensity in shallow water vector acoustic field. Then the propagation properties of sound pressure, particle velocity and their mutual phase relation are study through numerical simulation and verified by sea trial data. The geoacoustic inversion via matched field processing on the basis of joint processing of acoustic pressure and vertical particle velocity is studied considering the information complementarity of them. The sensitivity of seabed density and sound speed for four cost functions used by matched field inversion (MFI) via both broadband and single frequency signal are compared in different conditions. Finally, the MFI inversion is conducted by use of the information of sound pressure and vertical particle velocity.
Underwater integrated monitoring system is designed to study the attitude and synchronous vibration of subsurface buoy. Basic structure of such integrated monitoring svstem is introduced, and the experiment data of three set of subsurface buoy are analyzed using correlation theory and spectral analysis theory. The analysis of synchronous data could provide some suggestion to improve the design of vector hydrophone suspension device, subsuface buoy and mooring system. In addition, damping performance of first order and second order suspension system are analyzed with a simplified model, which is verified vibration test.
The low frequency vector acoustic field in the water tank is studied to assist the calibration of low frequency vector hydrophone. In order to solve the low-speed calculation via classic pressure field expression, an efficient procedure for computation of the sound field in water tank is proposed, which converts a triple sum infinite expression to a double sum one and makes the eigenvalues in three orthogonal directions related to each other. In addition, another improved strategy is used to avoid the problem of computation overflow in PC implementation. Numerical simulation and tank trial have verified its effectiveness and correctness. Finally, this fast numerical solution is extended to calculate the particle velocity field and some numerical results are given for further use.
引文
[1]罗超.基于矢量水听器阵的目标方位估计方法研究.西北工业大学硕士学位论文,2006.
[2]王友华.矢量水听器超复数模型及其DOA估计算法.复旦大学硕士学位论文,2008.
[3]朱韬.水下目标低频声散射特性研究.上海交通大学硕士论文,2008.
[4]姚直象.单矢量水听器信号处理研究.哈尔滨工程大学硕士论文,2005.
[5]吴祥兴.超低频矢量水听器技术研究.哈尔滨工程大学硕士论文,2005.
[6]孟春霞.单矢量水听器多目标方位估计方法研究.哈尔滨工程大学硕士学位论文,2005.
[7]陈洪娟.矢量传感器.哈尔滨：哈尔滨工程大学出版社,2006.
[8]吕云飞,张殿伦,邹吉武,兰华林,孙大军.基于潜标的海洋环境噪声测量系统.高技术通讯,2009,19(7)：760-763页.
[9]吕云飞.甚低频矢量水听器潜标探测系统关键技术研究.哈尔滨工程大学博士学位论文,2010.
[10]余赟,惠俊英,赵安邦,孙国仓,滕超.Pekeris波导中简正波的复声强及其应用.物理学报,2008,57(9)：5742-5748页.
[11]鹿力成,马力,陈耀明.浅海海底模型对低频声传播的影响.声学技术,2007,26(5)：787-793页.
[12]Zhang Yilu, John R. Potter, Paul James Seekings, Mandar Chitre, Venugopalan Pallayil. Rapid and robust single receiver geoacoustic inversion in shallow water. Oceans 2004 (IEEE/MTS), Kobe, Japan; 2004:9-12p.
[13]Sun Dajun, John Potter, Koay Teong Beng. Single receiver rapid geoacoustic inversion in shallow water. The 3rd International Workshop on Underwater Acoustic Technology, Harbin, China.2002:100-105p.
[14]V. A. Shchurov. Vector acoustics of the ocean. Vladivostok:Dalhauka,2006.
[15]V. A. Shchurov. Coherent and diffusive fields of underwater acoustic ambient noise. J. Acoust. Soc. Am,1991,90(2):991-1001p.
[16]V. A. Shchurov, V. I. Ilyichev, V. P. Kuleshov, M. V. Kuyanova. The interaction of energy flows of underwater ambient noise and a local source. J. Acoust. Soc. Am,1991,90(2): 1002-1004p.
[17]V. A. Shchurov, Shchurov V. A. Noise immunity of a combined hydroacoustic receiver. Acoustical Physics,2002,48(1):98-106p.
[18]Vladimir A. Shchurov, Marianna V. Kuyanova. Use of acoustic intensity measurements in underwater acoustics (modern state and prospects). Chinese Journal of Acoustics,1999, 18(4):315-326p.
[19]G. L. D'Spain, W. S. Hodgkiss, G. L. Edmonds. Energetics of the deep ocean's infrasonic sound field. J. Acoust. Soc. Am,1991,89(3):1134-1158p.
[20]Gerald L. D'Spain, William S. Hodgkiss. The simultaneous measurement of infrasonic acoustic particle velocity and acoustic pressure in the ocean by freely drifting swallow floats. J. Oceanic Eng,1991,16(2):195-207p.
[21]William S. Hodgkiss, Victor C. Anderson. Acoustic positioning for an array of freely drifting infrasonic sensors. J. Oceanic Eng,1983,8(3):116-119p.
[22]G. L. D'Spain, R. L. Culver, W. S. Hodgkiss, G. L. Edmonds. Freely drifting swallow float array May 1987 trip report. MPL technical memorandum 402, May,1988.
[23]D'Spain Gerald Lynden. Energetics of the ocean's infrasonic sound field. University of California, Ph.D.,1990.
[24]www.aphysci.com.
[25]赵羽.矢量阵阵处理研究.哈尔滨工程大学博士学位论文,2004.
[26]李思纯.基于矢量水听器的目标特征提取与识别技术研究.哈尔滨工程大学博士学位论文,2007.
[27]时胜国.矢量水听器及其在平台上的应用研究.哈尔滨工程大学博士学位论文,2007.
[28]孙贵青,李启虎,蔡惠智.声矢量传感器均匀直线阵.398-401页.
[29]孙贵青,杨德森,张揽月.基于矢量水听器的水下目标低频辐射噪声测量方法研究.声学学报,2002,27(5)：429-434页.
[30]杨德森,战国辰,刘星.低噪声水下目标辐射噪声测量的新方法研究.声学技术增刊,2001：245-247页.
[31]孙贵青,杨德森,张林,何元安,张揽月,洪连进.矢量水听器在水下目标低频辐射噪声测量中的应用.哈尔滨工程大学学报,2001,22(5)：5-9,19页.
[32]陈宗岐,于沨,刘文帅.利用矢量传感器测量舰船辐射噪声技术.舰船科学技术,2002,24(1)：19-22页.
[33]王之程,陈宗岐,于讽,刘文帅.舰船辐射噪声测量与分析.国防工业出版社,2004.
[34]赵玲.基于矢量水听器的海洋环境噪声测量装置及分析软件设计.哈尔滨工程大学硕士学位论文,2007.
[35]贾志富.同振球型声压梯度水听器的研究.应用声学,1997,16(3)：20-25页.
[36]Gordienko. V, Vector phase methods in acoustics. Moscow:Nauka,1989.
[38]C. B. Leslie, J. M. Kendall, J. L. Jones. Hydrophone for measuring particle velocity. J. Acoust. Soc. Am,1956,28(4):711-715p.
[39]Thomas B. Gabrielson. A simple neutrally buoyant sensor for direct measurement of particle velocity and intensity in water. J. Acoust. Soc. Am,1995,97(4):2227-2237p.
[40]Kevin J. Bastyr, Gerald C. Lauchle. Development of a velocity gradient underwater acoustic intensity sensor. J. Acoust. Soc. Am,1999,106(6):3178-3188p.
[41]陈洪娟.中频小型矢量水听器设计研究.哈尔滨工程大学博士学位论文,2005.
[42]刑世文.三维矢量水听器及其成阵研究.哈尔滨工程大学硕士学位论文,2009.
[43]姚直象.单矢量传感器及矢量阵信号处理研究.哈尔滨工程大学博士学位论文,2006.
[44]周士弘.分层介质波导中的声矢量场传播.哈尔滨工程大学学报,2004,25(1)：38-42页.
[45]Oleg E. Gulin, Yang Desen. On the certain semi-analytical models of low-frequency acoustic fields in terms of scalar-vector description. Chinese Journal of Acoustics,2004, 23(1):58-70p.
[46]彭汉书.浅海矢量声场特性及其应用研究.中国科学院声学研究所博士学位论文,2007.
[47]王德俊.矢量声场与矢量信号处理理论研究.哈尔滨工程大学博士学位论文,2004.
[48]惠俊英,孙国仓,赵安邦.Pekeris波导中简正波声强流及其互谱信号处理.声学学报,Vol.33,2008：300-304页.
[49]余赟,惠俊英,赵安邦等.Pekeris:波导中简正波的复声强及其应用.物理学报,Vol.57,No.9,2008：5742-5748页.
[50]孙国仓.浅海矢量声场及其信号处理.哈尔滨工程大学博士学位论文,2008.
[51]杨娟,惠俊英,王德俊等.低频矢量声场建模及其应用研究.声学技术,Vol.25,2006：16-21页.
[52]黄益旺,朴胜春,宋扬.楔形海域矢量场分析.哈尔滨工程大学学报,Vol.29,No.4,2008：390-394页.
[53]张海刚,杨士莪,朴胜春,任群言,马树青.声矢量场计算方法.哈尔滨工程大学学报,2010,31(4)：470-475页.
[54]K. B. Smith, G. L. D'Spain, W. S. Hodgkiss. Modeling acoustic particle velocity in range-dependent environments with a parabolic equation code. J. Acoust. Soc. Am,1993.
[55]www.onr.navy.mil/obs/reports/docs/05/oasmithk.pdf
[56]郭耀先.利用船舶噪音于ASIAEX南海实验中之地声参数反算.国立中山大学硕士论文,民国94.
[57]李秀林,李整林,李凤华,彭朝晖.浅海水平纵向相关与海底参数反演.自然科学进 展,2005,15(1)：38-45页.
[58]付金山.海底参数反演技术研究.哈尔滨工程大学硕士学位论文,2006.
[59]陈魏,马力,陈耀明.自适应下山模拟退火法反演海底等效地声参数.中国声学学会2006年全国声学学术会议,2006：121-122页.
[60]陈托.水平阵海底地层参数反演研究.哈尔滨工程大学硕士学位论文,2008.
[61]王占军.垂直阵的海底参数反演研究.哈尔滨工程大学硕士学位论文,2008.
[62]任群言.浅海环境下海底声参数获取技术研究.哈尔滨工程大学硕士学位论文,2009.
[63]鹿力成,马力,陈耀明,吴国清.浅海海底地声参数反演的差异进化算法.声学技术,2008,27(5)：58-59页.
[64]肖灵,张仁和,李风华,郭良浩.测量海底声学参数的匹配场反演方法.热带海洋学报,2001,20(4)：23-26页.
[65]Dosso S. E, Yeremy M. L, Ozard J. M, Chapman N. R. Estimation of ocean-bottom properties by matched-field inversion of acoustic field data. IEEE Journal of Ocean Engineering,1993,18:232-239p.
[66]M. I. TaroudakisBottom, M G Markaki. Geoacoustic inversion by matched field processing-a sensitivity study. Inverse Problems,2000,16:1679-1692p.
[67]Li Zhenglin, Zhang Renhe. A broadband geoacoustic inversion scheme. Chinese Physics letter,2004,21(2):1000-1103p.
[68]邱海宾,杨坤德.不同接收阵形时匹配场地声参数反演性能研究.声学技术,1-2页.
[69]李整林,鄢锦,李风华,郭良浩.由简正波群延时及幅度反演海底参数.声学学报,2002；27(6)：487-491页.
[70]李凤华,张仁和.由脉冲波形与传播损失反演海底声速与衰减系数.声学学报,2000,25(4)：298-302页.
[71]李整林,张仁和.简正波频散特征分析与海底参数反演.中国声学学会2005年全国声学学术会议,2005：10-12页.
[72]高伟,王宁,王好忠.2005黄海实验混响垂直相关统计反演海底参数术.声学学报,2008,33(2)：109-115页.
[73]http://www.arl.nus.edu.sg/web/research/geo.
[74]Junjie Shi, Dajun Sun, Cuie Zheng. Geoacoustic Inversion Based on Single Receiver Measurement. Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation, Aug.9-12, Changchun China,2009:4890-4894p.
[75]张学磊,李整林,黄晓砥.一种地声参数的联合反演方法.声学学报,2009,34(1)：54-59页.
[76]李整林,张仁和.基于等效海底模型的联合反演方法.中国声学学会2006年全国声学 学术会议,2006：153-155页.
[77]杨坤德.水声阵列信号的匹配场处理.西安：西北工业大学出版社,2008：1.
[78]Ingenito F. Measurement of mode attenuation coefficients in shallow water. J. Acoust. Soc. Am,1973,53(3):858-863p.
[79]Rubano L A. Acoustic propagation in shallow water over a low velocity bottom. J. Acoust. Soc. Am,1980,67(5):1608-1613p.
[80]唐俊峰.三维声场声速剖面反演研究.哈尔滨工程大学硕士学位论文,2003.
[81]李整林,张仁和,鄢锦,李凤华.由匹配场处理和传播损失反演海底参数.中国声学学会2002年全国声学学术会议,2002：141-142页.
[82]Yang Kunde, Ma Yuanliang. Multi-step Matched Field Inversion for Broadband Data from ASIAEX2001[J]. IEEE Journal of Ocean Engineering,2004,29(4):964-972p.
[83]Peng Hanshu, Li Fenghua. Geoacoustic inversion based on a vector hydrophone array. Chinese Physics Letter,2007,24(7):1977-1980p.
[84]李风华,彭汉书.矢量水听器阵列反演浅海地声参数.海洋中声传播、混响、环境噪声及舰船噪声,2007,26(5)：27-29页.
[85]彭汉书,李风华.单矢量水听器反演浅海海底吸收.中国声学学会2006年全国声学学术会议,2006：143-144页.
[86]彭汉书,李风华.由矢量水听器阵列反演浅海地声参数.声学技术,2008,27(2)：163-167页.
[87]李风华,孙梅,张仁和.由矢量水听器阵反演海底地声参数.哈尔滨工程大学学报,2010,31(7)：895-902页.
[88]Paulo Santos, Orlando Rodriguez, Paulo Felisberto, Sergio Jesus. Geoacoustic matched-field inversion using a vertical vector sensor array. Underwater acoustic and measurement:techniques and results conference, Greece,2009:1-6p.
[89]Paulo Santos, Paulo Felisberto, Sergio M. Jesus. Vector sensor arrays in underwater acoustic applications. Doctoral conference on computing, electrical and industrial systems, 2010:1-8p.
[90]P. Santos, O. C. Rodriguez, P. Felisberto, S. M. Jesus. Seabed geoacoustic characterization with a vector sensor array. J. Acoust. Soc. Am,2010,128(5):2652-2663p.
[91]Robert A. Koch. Proof of principle for geo-acoustic inversion of vector sensor array data. J. Acoust. Soc. Am,2010,127(3):1857p.
[92]Steven E. Crocker, James H. Miller, Paul C. Hines, John C. Osler. On the use of acoustic particle motion in geoacoustic inversion. J. Acoust. Soc. Am,2009,125(4):2747p.
[93]Kevin B. Smith. Acoustic inversion and 3-D studies employing acoustic vector sensors in shallow water.1-13p.[94]毛卫宁.矩形水池中瞬态声场的数值研究.电脑应用技术,1995,34：20-22页.
[95]毛卫宁,方世良,陆佶人.矩形水池中声能的衰变.声学技术,1995：165-167页.
[96]张文平,张天元,刘志刚,张洪田,柳贡民.四壁倾斜水池点源低频声场特性的理论计算及实验测量.声学学报,1996,21(2)：128-134页.
[97]陈亚林,杨坤德,马远良.消声水池声场的仿真计算.声学技术,2005,24(3)：132-136页.
[98]李明睿.消声水池声场仿真研究.声学与电子工程,2006(增刊)：78-81页.
[99]马大猷.室内稳态声场.声学学报,1994,19(1)：13-21页.
[100]马大猷.论室内声学.声学学报,2003,28(2)：97-101页.
[101]马大猷.现代声学理论基础.北京：科学出版社,2004：169-203页.
[102]马大猷.只有数学,缺少物理——莫尔斯受迫振动的理论.声学学报,2004,29(1)：1-5页.
[103]Model of the sound field in a rectangular cell. http://www.soton.ac.uk/%7 Eprb2 /acoustic%20model.htm.
[104]Ronald Lee. A study of a random sound field in a water tank. The American University, M. S.,1967.
[105]N. Cochard, P. Arzelies, J. L. Lacoume, Y. Gabillet. Noise source calibration in test tank. Oceans 98 Conference Proceedings,28th Sep.-1st Oct, Nice, France:134-137p.
[106]N. Cochard, J. L. Lacoume, P. Arzelies, Y. Gabillet. Underwater noise measurement in test tank. Oceans 2007 Europe, Aberdeen, Scotland:1-6p.
[107]Wei Wei, Robert Hickling. Measuring the Sound Power of a Moving Source. J. Acoust. Soc.Am,1995,97(1):116-120p.
[108]孙贵青,李启虎.声矢量传感器信号处理.声学学报,2004,29(6)：491-498页.
[109]Finn B. Jensen, William A. Kuperman, Michael B. Porter, Henric Schmidt. Computational ocean acoustics. New York, Springer-Verlag.1994:57-58p.
[110]刘伯胜,雷家煜.水声学原理.哈尔滨：哈尔滨工程大学出版社,1993：92-94页.
[111]杨士莪.水声传播原理.哈尔滨：哈尔滨工程大学出版社,1994：6-23页.
[112]M. B. Porter. The kraken normal mode program. Saclantcen Tech. Rep. Saclant.1991: 5-23p.
[113]何祚镛,赵玉芳.声学理论基础.北京：国防工业出版社,1981：56页.
[114]F. Jacobscn. Active and reactive, coherent and incoherent sound field. Journal of Sound and Vibration,1989,130:493-507p.
[115]孙贵青.矢量水听器检测技术研究.哈尔滨工程大学博士学位论文,2001.
[116]惠俊英.水下声信道.北京：国防工业出版社,1992.
[117]孙玉兰,朱练军,那健,王珂.潜标式水下目标噪声测量系统.测试技术学报,2002,16(z1)：505-508页.
[118]侯广利,张颖,孙继昌,张颖颖,王亚洲.一种潜标的水下姿态变化规律分析.海洋技术,2010,29(3)：38-43页.
[119]张贤达.现代信号处理.北京：清华大学出版社,2003：12-13页.
[120]杨德森,洪连进.矢量水听器原理及应用引论.北京：科学出版社,2009：93页.
[121]吕云飞,师俊杰,孙大军等.水池中低频矢量水听器灵敏度校准.压电与声光,2009,31(6)：814-816页.
[122]师俊杰,吕云飞,孙大军,张俊.水池声场的快速计算方法研究.声学技术,已录用.
[123]杜功焕,朱哲民,龚秀芬.声学基础.南京：南京大学出版社,2001：432-449页.
[124]B. Davies. Locating the zeros of an analytic function. J. Comput. Phys.1986,66:36-49.
[125]Vera V. Markovic, Bratislav D. Milovanovic, et. al. Efficient numerical solution for nonuniform sound field in a rectangular room. Acustica,1998,84(3):570-573p.
[126]Olivera R. Pronic, Vera V. Markovic, et. al. Determination of complex resonant frequencies in rooms by using electromegnetic acoustic anologies. Mediterranean Electrotechnical Conference, Melecon,1998:241-245p.
[127]张海澜.理论声学.北京：高等教育出版社,2007.
[128]万泉,蒋伟康.论莫尔斯的室内声场简正波理论解的完备性.振动与冲击,2009,28(2)：111-116页.
[2]王友华.矢量水听器超复数模型及其DOA估计算法.复旦大学硕士学位论文,2008.
[3]朱韬.水下目标低频声散射特性研究.上海交通大学硕士论文,2008.
[4]姚直象.单矢量水听器信号处理研究.哈尔滨工程大学硕士论文,2005.
[5]吴祥兴.超低频矢量水听器技术研究.哈尔滨工程大学硕士论文,2005.
[6]孟春霞.单矢量水听器多目标方位估计方法研究.哈尔滨工程大学硕士学位论文,2005.
[7]陈洪娟.矢量传感器.哈尔滨：哈尔滨工程大学出版社,2006.
[8]吕云飞,张殿伦,邹吉武,兰华林,孙大军.基于潜标的海洋环境噪声测量系统.高技术通讯,2009,19(7)：760-763页.
[9]吕云飞.甚低频矢量水听器潜标探测系统关键技术研究.哈尔滨工程大学博士学位论文,2010.
[10]余赟,惠俊英,赵安邦,孙国仓,滕超.Pekeris波导中简正波的复声强及其应用.物理学报,2008,57(9)：5742-5748页.
[11]鹿力成,马力,陈耀明.浅海海底模型对低频声传播的影响.声学技术,2007,26(5)：787-793页.
[12]Zhang Yilu, John R. Potter, Paul James Seekings, Mandar Chitre, Venugopalan Pallayil. Rapid and robust single receiver geoacoustic inversion in shallow water. Oceans 2004 (IEEE/MTS), Kobe, Japan; 2004:9-12p.
[13]Sun Dajun, John Potter, Koay Teong Beng. Single receiver rapid geoacoustic inversion in shallow water. The 3rd International Workshop on Underwater Acoustic Technology, Harbin, China.2002:100-105p.
[14]V. A. Shchurov. Vector acoustics of the ocean. Vladivostok:Dalhauka,2006.
[15]V. A. Shchurov. Coherent and diffusive fields of underwater acoustic ambient noise. J. Acoust. Soc. Am,1991,90(2):991-1001p.
[16]V. A. Shchurov, V. I. Ilyichev, V. P. Kuleshov, M. V. Kuyanova. The interaction of energy flows of underwater ambient noise and a local source. J. Acoust. Soc. Am,1991,90(2): 1002-1004p.
[17]V. A. Shchurov, Shchurov V. A. Noise immunity of a combined hydroacoustic receiver. Acoustical Physics,2002,48(1):98-106p.
[18]Vladimir A. Shchurov, Marianna V. Kuyanova. Use of acoustic intensity measurements in underwater acoustics (modern state and prospects). Chinese Journal of Acoustics,1999, 18(4):315-326p.
[19]G. L. D'Spain, W. S. Hodgkiss, G. L. Edmonds. Energetics of the deep ocean's infrasonic sound field. J. Acoust. Soc. Am,1991,89(3):1134-1158p.
[20]Gerald L. D'Spain, William S. Hodgkiss. The simultaneous measurement of infrasonic acoustic particle velocity and acoustic pressure in the ocean by freely drifting swallow floats. J. Oceanic Eng,1991,16(2):195-207p.
[21]William S. Hodgkiss, Victor C. Anderson. Acoustic positioning for an array of freely drifting infrasonic sensors. J. Oceanic Eng,1983,8(3):116-119p.
[22]G. L. D'Spain, R. L. Culver, W. S. Hodgkiss, G. L. Edmonds. Freely drifting swallow float array May 1987 trip report. MPL technical memorandum 402, May,1988.
[23]D'Spain Gerald Lynden. Energetics of the ocean's infrasonic sound field. University of California, Ph.D.,1990.
[24]www.aphysci.com.
[25]赵羽.矢量阵阵处理研究.哈尔滨工程大学博士学位论文,2004.
[26]李思纯.基于矢量水听器的目标特征提取与识别技术研究.哈尔滨工程大学博士学位论文,2007.
[27]时胜国.矢量水听器及其在平台上的应用研究.哈尔滨工程大学博士学位论文,2007.
[28]孙贵青,李启虎,蔡惠智.声矢量传感器均匀直线阵.398-401页.
[29]孙贵青,杨德森,张揽月.基于矢量水听器的水下目标低频辐射噪声测量方法研究.声学学报,2002,27(5)：429-434页.
[30]杨德森,战国辰,刘星.低噪声水下目标辐射噪声测量的新方法研究.声学技术增刊,2001：245-247页.
[31]孙贵青,杨德森,张林,何元安,张揽月,洪连进.矢量水听器在水下目标低频辐射噪声测量中的应用.哈尔滨工程大学学报,2001,22(5)：5-9,19页.
[32]陈宗岐,于沨,刘文帅.利用矢量传感器测量舰船辐射噪声技术.舰船科学技术,2002,24(1)：19-22页.
[33]王之程,陈宗岐,于讽,刘文帅.舰船辐射噪声测量与分析.国防工业出版社,2004.
[34]赵玲.基于矢量水听器的海洋环境噪声测量装置及分析软件设计.哈尔滨工程大学硕士学位论文,2007.
[35]贾志富.同振球型声压梯度水听器的研究.应用声学,1997,16(3)：20-25页.
[36]Gordienko. V, Vector phase methods in acoustics. Moscow:Nauka,1989.
[38]C. B. Leslie, J. M. Kendall, J. L. Jones. Hydrophone for measuring particle velocity. J. Acoust. Soc. Am,1956,28(4):711-715p.
[39]Thomas B. Gabrielson. A simple neutrally buoyant sensor for direct measurement of particle velocity and intensity in water. J. Acoust. Soc. Am,1995,97(4):2227-2237p.
[40]Kevin J. Bastyr, Gerald C. Lauchle. Development of a velocity gradient underwater acoustic intensity sensor. J. Acoust. Soc. Am,1999,106(6):3178-3188p.
[41]陈洪娟.中频小型矢量水听器设计研究.哈尔滨工程大学博士学位论文,2005.
[42]刑世文.三维矢量水听器及其成阵研究.哈尔滨工程大学硕士学位论文,2009.
[43]姚直象.单矢量传感器及矢量阵信号处理研究.哈尔滨工程大学博士学位论文,2006.
[44]周士弘.分层介质波导中的声矢量场传播.哈尔滨工程大学学报,2004,25(1)：38-42页.
[45]Oleg E. Gulin, Yang Desen. On the certain semi-analytical models of low-frequency acoustic fields in terms of scalar-vector description. Chinese Journal of Acoustics,2004, 23(1):58-70p.
[46]彭汉书.浅海矢量声场特性及其应用研究.中国科学院声学研究所博士学位论文,2007.
[47]王德俊.矢量声场与矢量信号处理理论研究.哈尔滨工程大学博士学位论文,2004.
[48]惠俊英,孙国仓,赵安邦.Pekeris波导中简正波声强流及其互谱信号处理.声学学报,Vol.33,2008：300-304页.
[49]余赟,惠俊英,赵安邦等.Pekeris:波导中简正波的复声强及其应用.物理学报,Vol.57,No.9,2008：5742-5748页.
[50]孙国仓.浅海矢量声场及其信号处理.哈尔滨工程大学博士学位论文,2008.
[51]杨娟,惠俊英,王德俊等.低频矢量声场建模及其应用研究.声学技术,Vol.25,2006：16-21页.
[52]黄益旺,朴胜春,宋扬.楔形海域矢量场分析.哈尔滨工程大学学报,Vol.29,No.4,2008：390-394页.
[53]张海刚,杨士莪,朴胜春,任群言,马树青.声矢量场计算方法.哈尔滨工程大学学报,2010,31(4)：470-475页.
[54]K. B. Smith, G. L. D'Spain, W. S. Hodgkiss. Modeling acoustic particle velocity in range-dependent environments with a parabolic equation code. J. Acoust. Soc. Am,1993.
[55]www.onr.navy.mil/obs/reports/docs/05/oasmithk.pdf
[56]郭耀先.利用船舶噪音于ASIAEX南海实验中之地声参数反算.国立中山大学硕士论文,民国94.
[57]李秀林,李整林,李凤华,彭朝晖.浅海水平纵向相关与海底参数反演.自然科学进 展,2005,15(1)：38-45页.
[58]付金山.海底参数反演技术研究.哈尔滨工程大学硕士学位论文,2006.
[59]陈魏,马力,陈耀明.自适应下山模拟退火法反演海底等效地声参数.中国声学学会2006年全国声学学术会议,2006：121-122页.
[60]陈托.水平阵海底地层参数反演研究.哈尔滨工程大学硕士学位论文,2008.
[61]王占军.垂直阵的海底参数反演研究.哈尔滨工程大学硕士学位论文,2008.
[62]任群言.浅海环境下海底声参数获取技术研究.哈尔滨工程大学硕士学位论文,2009.
[63]鹿力成,马力,陈耀明,吴国清.浅海海底地声参数反演的差异进化算法.声学技术,2008,27(5)：58-59页.
[64]肖灵,张仁和,李风华,郭良浩.测量海底声学参数的匹配场反演方法.热带海洋学报,2001,20(4)：23-26页.
[65]Dosso S. E, Yeremy M. L, Ozard J. M, Chapman N. R. Estimation of ocean-bottom properties by matched-field inversion of acoustic field data. IEEE Journal of Ocean Engineering,1993,18:232-239p.
[66]M. I. TaroudakisBottom, M G Markaki. Geoacoustic inversion by matched field processing-a sensitivity study. Inverse Problems,2000,16:1679-1692p.
[67]Li Zhenglin, Zhang Renhe. A broadband geoacoustic inversion scheme. Chinese Physics letter,2004,21(2):1000-1103p.
[68]邱海宾,杨坤德.不同接收阵形时匹配场地声参数反演性能研究.声学技术,1-2页.
[69]李整林,鄢锦,李风华,郭良浩.由简正波群延时及幅度反演海底参数.声学学报,2002；27(6)：487-491页.
[70]李凤华,张仁和.由脉冲波形与传播损失反演海底声速与衰减系数.声学学报,2000,25(4)：298-302页.
[71]李整林,张仁和.简正波频散特征分析与海底参数反演.中国声学学会2005年全国声学学术会议,2005：10-12页.
[72]高伟,王宁,王好忠.2005黄海实验混响垂直相关统计反演海底参数术.声学学报,2008,33(2)：109-115页.
[73]http://www.arl.nus.edu.sg/web/research/geo.
[74]Junjie Shi, Dajun Sun, Cuie Zheng. Geoacoustic Inversion Based on Single Receiver Measurement. Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation, Aug.9-12, Changchun China,2009:4890-4894p.
[75]张学磊,李整林,黄晓砥.一种地声参数的联合反演方法.声学学报,2009,34(1)：54-59页.
[76]李整林,张仁和.基于等效海底模型的联合反演方法.中国声学学会2006年全国声学 学术会议,2006：153-155页.
[77]杨坤德.水声阵列信号的匹配场处理.西安：西北工业大学出版社,2008：1.
[78]Ingenito F. Measurement of mode attenuation coefficients in shallow water. J. Acoust. Soc. Am,1973,53(3):858-863p.
[79]Rubano L A. Acoustic propagation in shallow water over a low velocity bottom. J. Acoust. Soc. Am,1980,67(5):1608-1613p.
[80]唐俊峰.三维声场声速剖面反演研究.哈尔滨工程大学硕士学位论文,2003.
[81]李整林,张仁和,鄢锦,李凤华.由匹配场处理和传播损失反演海底参数.中国声学学会2002年全国声学学术会议,2002：141-142页.
[82]Yang Kunde, Ma Yuanliang. Multi-step Matched Field Inversion for Broadband Data from ASIAEX2001[J]. IEEE Journal of Ocean Engineering,2004,29(4):964-972p.
[83]Peng Hanshu, Li Fenghua. Geoacoustic inversion based on a vector hydrophone array. Chinese Physics Letter,2007,24(7):1977-1980p.
[84]李风华,彭汉书.矢量水听器阵列反演浅海地声参数.海洋中声传播、混响、环境噪声及舰船噪声,2007,26(5)：27-29页.
[85]彭汉书,李风华.单矢量水听器反演浅海海底吸收.中国声学学会2006年全国声学学术会议,2006：143-144页.
[86]彭汉书,李风华.由矢量水听器阵列反演浅海地声参数.声学技术,2008,27(2)：163-167页.
[87]李风华,孙梅,张仁和.由矢量水听器阵反演海底地声参数.哈尔滨工程大学学报,2010,31(7)：895-902页.
[88]Paulo Santos, Orlando Rodriguez, Paulo Felisberto, Sergio Jesus. Geoacoustic matched-field inversion using a vertical vector sensor array. Underwater acoustic and measurement:techniques and results conference, Greece,2009:1-6p.
[89]Paulo Santos, Paulo Felisberto, Sergio M. Jesus. Vector sensor arrays in underwater acoustic applications. Doctoral conference on computing, electrical and industrial systems, 2010:1-8p.
[90]P. Santos, O. C. Rodriguez, P. Felisberto, S. M. Jesus. Seabed geoacoustic characterization with a vector sensor array. J. Acoust. Soc. Am,2010,128(5):2652-2663p.
[91]Robert A. Koch. Proof of principle for geo-acoustic inversion of vector sensor array data. J. Acoust. Soc. Am,2010,127(3):1857p.
[92]Steven E. Crocker, James H. Miller, Paul C. Hines, John C. Osler. On the use of acoustic particle motion in geoacoustic inversion. J. Acoust. Soc. Am,2009,125(4):2747p.
[93]Kevin B. Smith. Acoustic inversion and 3-D studies employing acoustic vector sensors in shallow water.1-13p.[94]毛卫宁.矩形水池中瞬态声场的数值研究.电脑应用技术,1995,34：20-22页.
[95]毛卫宁,方世良,陆佶人.矩形水池中声能的衰变.声学技术,1995：165-167页.
[96]张文平,张天元,刘志刚,张洪田,柳贡民.四壁倾斜水池点源低频声场特性的理论计算及实验测量.声学学报,1996,21(2)：128-134页.
[97]陈亚林,杨坤德,马远良.消声水池声场的仿真计算.声学技术,2005,24(3)：132-136页.
[98]李明睿.消声水池声场仿真研究.声学与电子工程,2006(增刊)：78-81页.
[99]马大猷.室内稳态声场.声学学报,1994,19(1)：13-21页.
[100]马大猷.论室内声学.声学学报,2003,28(2)：97-101页.
[101]马大猷.现代声学理论基础.北京：科学出版社,2004：169-203页.
[102]马大猷.只有数学,缺少物理——莫尔斯受迫振动的理论.声学学报,2004,29(1)：1-5页.
[103]Model of the sound field in a rectangular cell. http://www.soton.ac.uk/%7 Eprb2 /acoustic%20model.htm.
[104]Ronald Lee. A study of a random sound field in a water tank. The American University, M. S.,1967.
[105]N. Cochard, P. Arzelies, J. L. Lacoume, Y. Gabillet. Noise source calibration in test tank. Oceans 98 Conference Proceedings,28th Sep.-1st Oct, Nice, France:134-137p.
[106]N. Cochard, J. L. Lacoume, P. Arzelies, Y. Gabillet. Underwater noise measurement in test tank. Oceans 2007 Europe, Aberdeen, Scotland:1-6p.
[107]Wei Wei, Robert Hickling. Measuring the Sound Power of a Moving Source. J. Acoust. Soc.Am,1995,97(1):116-120p.
[108]孙贵青,李启虎.声矢量传感器信号处理.声学学报,2004,29(6)：491-498页.
[109]Finn B. Jensen, William A. Kuperman, Michael B. Porter, Henric Schmidt. Computational ocean acoustics. New York, Springer-Verlag.1994:57-58p.
[110]刘伯胜,雷家煜.水声学原理.哈尔滨：哈尔滨工程大学出版社,1993：92-94页.
[111]杨士莪.水声传播原理.哈尔滨：哈尔滨工程大学出版社,1994：6-23页.
[112]M. B. Porter. The kraken normal mode program. Saclantcen Tech. Rep. Saclant.1991: 5-23p.
[113]何祚镛,赵玉芳.声学理论基础.北京：国防工业出版社,1981：56页.
[114]F. Jacobscn. Active and reactive, coherent and incoherent sound field. Journal of Sound and Vibration,1989,130:493-507p.
[115]孙贵青.矢量水听器检测技术研究.哈尔滨工程大学博士学位论文,2001.
[116]惠俊英.水下声信道.北京：国防工业出版社,1992.
[117]孙玉兰,朱练军,那健,王珂.潜标式水下目标噪声测量系统.测试技术学报,2002,16(z1)：505-508页.
[118]侯广利,张颖,孙继昌,张颖颖,王亚洲.一种潜标的水下姿态变化规律分析.海洋技术,2010,29(3)：38-43页.
[119]张贤达.现代信号处理.北京：清华大学出版社,2003：12-13页.
[120]杨德森,洪连进.矢量水听器原理及应用引论.北京：科学出版社,2009：93页.
[121]吕云飞,师俊杰,孙大军等.水池中低频矢量水听器灵敏度校准.压电与声光,2009,31(6)：814-816页.
[122]师俊杰,吕云飞,孙大军,张俊.水池声场的快速计算方法研究.声学技术,已录用.
[123]杜功焕,朱哲民,龚秀芬.声学基础.南京：南京大学出版社,2001：432-449页.
[124]B. Davies. Locating the zeros of an analytic function. J. Comput. Phys.1986,66:36-49.
[125]Vera V. Markovic, Bratislav D. Milovanovic, et. al. Efficient numerical solution for nonuniform sound field in a rectangular room. Acustica,1998,84(3):570-573p.
[126]Olivera R. Pronic, Vera V. Markovic, et. al. Determination of complex resonant frequencies in rooms by using electromegnetic acoustic anologies. Mediterranean Electrotechnical Conference, Melecon,1998:241-245p.
[127]张海澜.理论声学.北京：高等教育出版社,2007.
[128]万泉,蒋伟康.论莫尔斯的室内声场简正波理论解的完备性.振动与冲击,2009,28(2)：111-116页.