三维浅海环境下全海深声速剖面快速反演研究
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摘要
声速剖面反演是采用分布积分探头技术快速获取逐点测量所不能得到的大面积海域等效声速剖面的一种有效方法。基于声传播时间的声速剖面反演由于具有计算速度较快、受海底声学参数影响小以及射线声学适用于三维复杂声场的计算等优点而被广泛应用。这种反演模型的关键点在于特征声线搜索和声传播时间测定的精确性。在三维浅海环境下，不平整海底的反射使得声线发生水平方向上的偏转，从而导致声线在三维空间传播，这在以往的基于声传播时间的声速剖面反演模型中都没有考虑，给反演结果带来了不必要的误差。为提高声速剖面反演的精度，本文首先对三维空间特征声线搜索和传播时间计算进行了深入研究，然后采用最快特征声线传播时间作为代价函数反演了南海某海域声速剖面。另外，声速剖面反演是多维优化问题，正演模型的计算速度是限制反演速度的主要瓶颈。本文采用微扰近似方法将实际声传播时间表示为背景声速下的声传播时间与扰动项之和，从而使得声速剖面反演由原来的非线性优化问题转化为经验正交函数系数所满足的线性方程组求解形式，使得反演速度得到了提高。本文的主要创新点如下：
1、提出了三维空间特征声线搜索和声传播时间计算模型
研究了不平整海底反射时声线的传播规律，提出了不平整海底浅海环境下的射线传播模型，开发了声场计算软件，在三维空间求解最快特征声线轨迹和传播时间。与理论解和其它模型的对比表明，当传播距离为100km时，该软件计算的声传播时间精度能达到10~(-6)s。
2、通过不同的方法分别提高声速剖面反演的精度和速度
通过考虑声线在不平整海底反射所引起的水平偏转来减小声传播时间的计算误差进而有效地提高声速剖面反演的精度；采用微扰法快速反演声速剖面，在降低部分反演精度的条件下，将反演时间由10小时缩短为数十秒，实现了海洋环境信息的实时监测。
3、基于最快特征声线传播时间的声速剖面反演算法性能研究
仿真计算了经验正交函数阶数与反演精度之间的关系。仿真结果证明，在声速变化不是很复杂的情况下，3阶经验正交函数足以用来反演声速剖面，继续增加阶数反演精度会略有提高，但是意义不大。
通过理论推导和仿真研究了基于声传播时间的声速剖面反演对海底深度、声源水平位置以及基阵倾斜等参数失配的敏感性问题。结果表明，参数失配给反演所带来的额外误差与声传播时间近似成反比，当这些参数失配相对较小时，对声速剖面反演的精度影响不大。
除此之外，本文还研究了以下主要内容：
1、声速剖面外延
针对用经验正交函数表示声速剖面受限于样本声速的测量深度的问题，本文并未采取传统的海洋数据同化的方法，而是采用多项式对温度进行拟合，盐度取平均，然后根据声速经验公式求声速的方法对残缺样本声速数据进行合理地外延。
2、未知声源参数和声速剖面联合反演
针对声源水平位置和爆炸时刻不完整的情况，通过增加声传播时间方程个数的方法对声速剖面和未知的声源参数进行联合反演以获取整个实验海域的时间平均和空间综合意义上的声速剖面。
Sound speed profile (SSP) inversion is an effective method of obtaining the equivalentSSP rapidly in a large area by distributed acoustic detectors, which can hardly be realized bymanual mearsurment. Because of many advantages, such as fast calculation speed, being notinfluenced greatly by the acoustic parameters of seabed, and being suitable for the calculationof sound field in three-dimensional (3D) environments, SSP inversion based on ray traveltime was applied widely in recent years. The key procedure for this model is the accuratedetermination of eigenray and precise measurement of corresponding transmission time.Horizontal deflection often occurs when acoustic ray reflects from irregular seabed in shallowwater, and leads to3D ray tracing. This phenomenon was not usually considered in givenmodels, thus additonal error will be introduced. In this paper a new method for eigenrayseeking in3D environment had been presented firstly, and the shortest travel time ofeigenrays are used to construct a cost function to invert SSP for some area of South China Sea.In addition, SSP inversion is a problem of multi-dimensional optimization and the calculationspeed of transmission time is the main obstacle to restrict the inversion efficience. To improvethe algorithm speed of inversion, ray travel time is expressed as the sum given by referencedSSP and perturbation terms, and inversion procedure is transfered from non-linearoptimization to the solution of system of linear equations of empirical orthogonal functions(EOFs) by perturbation approximation. The primary innovations are as follows:
1. The model for eigenray seeking in3D environments and travel time calculation hasbeen developed.
The rule of horizontal deflection when a ray reflects from irregular seabed has beenrevealed; the model of ray tracing in shallow water with irregular seabed has been built andsound field calculation software for eigenray seeking in3D environments and travel timecalculation has been developed. Accuracy of the results is compared with other models andtheoretical values. It indicates that the precision of sound travel time given by this modelreaches to the quantity of10-6seconds when the horizontal travel range is up to100km.
2. The precision and speed of SSP inversion have been improved dramatically bydifferent methods.
The error of sound travel time calculation had been reduced, and the precision of SSPinversion has been improved effectively by considering the horizontal deflection induced byray reflection from irregular seabed. The calculation time has been reduced from10hours to several tens of seconds and satisfies real-time monitoring of SSP with only a few precisionloss by perturtbation approximation.
3. The algorithmic performance of SSP inversion based on the shortest travel time of theeigenray had been researched deeply.
Relationship between the precision of inversion and the number of EOFs used fornumerical simulation had been studied. It shows that the first3orders of EOFs are enough touse for inversion of SSP, the precision of inversion will not be improved obviously whennumber of used EOFs increases.
The problems of parameter mismatching including the depth of seabed, the horizontallocation of source and the inclination of array have been researched by theoretical calculationand numerical simulation. The results indicate that the additional errors introduced bymismatched parameters are inversely proportional to transmission time and the influence onSSP inversion can be neglected when the mismatched parameters are relatively small.
Moreover, the following contents are also included in the thesis：
1. When calculate the values of SSP and EOFs, in order to overcome the difficulty thatno sufficient measuring data about sound speed in larger depth, instead of the method ofconventional ocean data assimilation, the sound speed profiles exceeding the measurementdepth have been extended by empirical formula, using reasonable estimated values oftemperature and salinity.
2. Joint inversion of unknown parameters of source and SSP has been developed.
As to the problem of incomplete parameters of source location, explosive moment, theyare inverted at the same time with SSP, using more equations of sound transmission time fordifferent recievers.
1、提出了三维空间特征声线搜索和声传播时间计算模型
研究了不平整海底反射时声线的传播规律，提出了不平整海底浅海环境下的射线传播模型，开发了声场计算软件，在三维空间求解最快特征声线轨迹和传播时间。与理论解和其它模型的对比表明，当传播距离为100km时，该软件计算的声传播时间精度能达到10~(-6)s。
2、通过不同的方法分别提高声速剖面反演的精度和速度
通过考虑声线在不平整海底反射所引起的水平偏转来减小声传播时间的计算误差进而有效地提高声速剖面反演的精度；采用微扰法快速反演声速剖面，在降低部分反演精度的条件下，将反演时间由10小时缩短为数十秒，实现了海洋环境信息的实时监测。
3、基于最快特征声线传播时间的声速剖面反演算法性能研究
仿真计算了经验正交函数阶数与反演精度之间的关系。仿真结果证明，在声速变化不是很复杂的情况下，3阶经验正交函数足以用来反演声速剖面，继续增加阶数反演精度会略有提高，但是意义不大。
通过理论推导和仿真研究了基于声传播时间的声速剖面反演对海底深度、声源水平位置以及基阵倾斜等参数失配的敏感性问题。结果表明，参数失配给反演所带来的额外误差与声传播时间近似成反比，当这些参数失配相对较小时，对声速剖面反演的精度影响不大。
除此之外，本文还研究了以下主要内容：
1、声速剖面外延
针对用经验正交函数表示声速剖面受限于样本声速的测量深度的问题，本文并未采取传统的海洋数据同化的方法，而是采用多项式对温度进行拟合，盐度取平均，然后根据声速经验公式求声速的方法对残缺样本声速数据进行合理地外延。
2、未知声源参数和声速剖面联合反演
针对声源水平位置和爆炸时刻不完整的情况，通过增加声传播时间方程个数的方法对声速剖面和未知的声源参数进行联合反演以获取整个实验海域的时间平均和空间综合意义上的声速剖面。
Sound speed profile (SSP) inversion is an effective method of obtaining the equivalentSSP rapidly in a large area by distributed acoustic detectors, which can hardly be realized bymanual mearsurment. Because of many advantages, such as fast calculation speed, being notinfluenced greatly by the acoustic parameters of seabed, and being suitable for the calculationof sound field in three-dimensional (3D) environments, SSP inversion based on ray traveltime was applied widely in recent years. The key procedure for this model is the accuratedetermination of eigenray and precise measurement of corresponding transmission time.Horizontal deflection often occurs when acoustic ray reflects from irregular seabed in shallowwater, and leads to3D ray tracing. This phenomenon was not usually considered in givenmodels, thus additonal error will be introduced. In this paper a new method for eigenrayseeking in3D environment had been presented firstly, and the shortest travel time ofeigenrays are used to construct a cost function to invert SSP for some area of South China Sea.In addition, SSP inversion is a problem of multi-dimensional optimization and the calculationspeed of transmission time is the main obstacle to restrict the inversion efficience. To improvethe algorithm speed of inversion, ray travel time is expressed as the sum given by referencedSSP and perturbation terms, and inversion procedure is transfered from non-linearoptimization to the solution of system of linear equations of empirical orthogonal functions(EOFs) by perturbation approximation. The primary innovations are as follows:
1. The model for eigenray seeking in3D environments and travel time calculation hasbeen developed.
The rule of horizontal deflection when a ray reflects from irregular seabed has beenrevealed; the model of ray tracing in shallow water with irregular seabed has been built andsound field calculation software for eigenray seeking in3D environments and travel timecalculation has been developed. Accuracy of the results is compared with other models andtheoretical values. It indicates that the precision of sound travel time given by this modelreaches to the quantity of10-6seconds when the horizontal travel range is up to100km.
2. The precision and speed of SSP inversion have been improved dramatically bydifferent methods.
The error of sound travel time calculation had been reduced, and the precision of SSPinversion has been improved effectively by considering the horizontal deflection induced byray reflection from irregular seabed. The calculation time has been reduced from10hours to several tens of seconds and satisfies real-time monitoring of SSP with only a few precisionloss by perturtbation approximation.
3. The algorithmic performance of SSP inversion based on the shortest travel time of theeigenray had been researched deeply.
Relationship between the precision of inversion and the number of EOFs used fornumerical simulation had been studied. It shows that the first3orders of EOFs are enough touse for inversion of SSP, the precision of inversion will not be improved obviously whennumber of used EOFs increases.
The problems of parameter mismatching including the depth of seabed, the horizontallocation of source and the inclination of array have been researched by theoretical calculationand numerical simulation. The results indicate that the additional errors introduced bymismatched parameters are inversely proportional to transmission time and the influence onSSP inversion can be neglected when the mismatched parameters are relatively small.
Moreover, the following contents are also included in the thesis：
1. When calculate the values of SSP and EOFs, in order to overcome the difficulty thatno sufficient measuring data about sound speed in larger depth, instead of the method ofconventional ocean data assimilation, the sound speed profiles exceeding the measurementdepth have been extended by empirical formula, using reasonable estimated values oftemperature and salinity.
2. Joint inversion of unknown parameters of source and SSP has been developed.
As to the problem of incomplete parameters of source location, explosive moment, theyare inverted at the same time with SSP, using more equations of sound transmission time fordifferent recievers.
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