基于字典学习的声速剖面重构和反演

声速剖面（Sound Speed Profile,SSP） 是海洋环境观测的重要要素之一,引入遥感参数进行SSP 反演可以实时获取声速数据。反演首先需要依托精确的基函数对声速场进行降维表示,本文提出一种利用非线性基函数-学习字典（Learned Dictionaries,LDs） 提高降维精度的方案,并使用在多源信息融合上表现良好的自组织竞争型神经网络算法（Self-organizing Map,SOM） 对南海海域进行SSP 反演。实验结果使用均方根误差（Root Mean Square Error,RMSE）作为精度评估。实验结果显示：LDs 较传统基函数-经验正交函数（Empirical Orthogonal Functions,EOFs） 的降维精度在使用三阶基函数时提升0.13 m/s,五阶基函数提升0.07 m/s。使用五阶基函数进行反演,LDs 的反演精度为3.01 m/s,低于EOFs 的反演精度2.47 m/s。其原因为反演误差在机器学习训练基函数时被放大,导致所求得反演系数欠优。LDs 基函数较之传统的EOFs 能够有效突破正交性的限制,更精确地表示声速的扰动,达到了更高的降维精度,为声学信号处理任务的基函数学习提供一种方案。     

声速剖面EOF重构的实测数据采样深度研究

经验正交函数（experiential orthogonal functions,EOF）是重构声速剖面（sound speed profile,SSP）的一种有效方法,利用部分实测数据结合历史剖面资料可以重构当前位置的声速剖面。针对实测数据的采样深度难以确定这一问题,本文介绍了一种基于历史声速剖面资料的实测数据采样深度选取方法,根据EOF空间函数的方差贡献率确定数据量,进而采用EOF算法重构全海深声速剖面。实验结果表明：采用该方法得到的数据重构的声速剖面与实测声速剖面具有较好的一致性,基于常梯度声线跟踪法得到的水深数据能够满足0.25%倍水深限差,有效波束比达到了100%,为实际测量作业中声剖数据的采样深度提供了参考。     

多波束测量声速剖面EOF表示阶次选取研究

经验正交函数(EOF)是描述声速剖面的有效基函数,通常只需要前几阶EOF即可较为精确地表示声速剖面。但使用EOF重构的声速剖面进行多波束测量声速改正时,选取的阶次未必满足多波束测深精度要求。针对此问题,首先介绍了EOF表示声速剖面的原理及流程,然后以北海某区域实测声速剖面数据为例,分析了不同阶次EOF拟合声速剖面误差以及不同阶次EOF拟合声速剖面对多波束测深的影响,最后结合NOAA对多波束测量声速剖面误差造成的水深限差要求确定EOF阶次,实现了在满足多波束测深精度的同时,合理确定EOF阶次的目的。     

一种基于声速剖面展开的内波监测新方法

声速剖面时空分布的获取是利用声学方法监测内波的核心问题。在反演算法中，声速剖面通常是采用展开的方式用若干个参数来表示的。这就导致了有时很难从反演结果中直接获得内波的相关信息。本文的目标是找到一种通过展开系数直接获取内波特性的方法。通过推导内波水动力方程，可以从较少的声速剖面样本中提取出水动力简正模态（Hydrodynamic Normal Modes，HNMs）作为声速剖面展开的正交基。较之广泛采用的正交经验函数（Empirical Orthogonal Functions, EOFs），HNMs直接与内波活动相关，具有更明确的物理含义。然后，基于HNMs对声速剖面的时间序列进行展开，获得展开系数。最后，从前两阶展开系数的时间导数中可以获取内波活动的信息。将方法应用于受内波影响而具有明显时空扰动的南海北陆架区温度链数据，结果表明：只用前两节模态就可以在较好的精度范围内重构声速剖面。前两阶系数的时间导数具有独特的双震荡结构可以用于探测内孤立波。从展开系数也可以获得幅度以及波长信息。理论推导和实验分析证明了本文方法在内波监测中的有效性。HNMs方法使用便利且对样本的依赖性较小，可以在内波活跃海域作为EOFs的有效补充用于声速剖面的展开。     

基于遥感数据和表层声速的全海深声速剖面反演

海洋声速剖面严重影响着水下声传播特性,近实时地获取声速剖面对水下声通信、水下定位、鱼群探测等都有重要意义。单经验正交函数回归（single Empirical Orthogonal Function regression,sEOF-r）方法通过建立声速剖面的经验正交系数与海面遥感数据之间的线性回归关系来反演声速剖面。但是,海洋是一个复杂的动力系统,声速与海面遥感数据并不是简单的线性关系,因此,本文基于Argo历史网格数据,通过自组织映射（Self-Organizing Map,SOM）生成海平面高度异常（Sea Level Anomaly,SLA）、海表面温度（Sea Surface Temperature,SST）等海表遥感数据以及表层声速仪测量的表层声速与声速剖面异常之间的非线性映射;然后利用近实时的海表遥感数据和表层声速反演三维海洋声速场。声速剖面反演的结果表明,在多源信息融合的优势下,本文方法的反演性能最稳定且精度最高,声速剖面的平均反演精度比经典sEOF-r方法提高约2 m/s,比未考虑表层声速的经典SOM方法提高约1 m/s。     

海洋声速场的经验正交函数描述及声速剖面预报

针对位于东海外缘台湾东北部冲绳海槽张裂带以西的深海海域声速场的统计资料,分析利用少于５号经验正交函数描述声速场。探索利用经验正交函数、海表和温跃层水温对海水声速剖面进行预报的方法。研究结果对于声速场数据库的建设、海洋声速场的预报和水下声层技术具有重要的意义。     

基于Argo 观测资料的南海北部海域声速场 时空特征分析

利用近5 年的Argo剖面序列,通过经验正交函数（EOF） 分析,分析了南海北部海域声速垂直结构的时空变化特征 和声速场水平分布特征。分析表明：EOF 的前6 个模态反映了海区声速结构的主要变化,可以很好地表示声速剖面。第1 模 态具有明显的年变化周期,主要受海洋混合层季节性变化影响;第2 模态与第1 模态时间函数具有明显的反向变化特征,主 要对次表层进行调制;第3 模态主要影响次表层以下声速变化;表层声速分布与深层声速分布有明显的差异,表层声速主要 受海水温度变化的影响,深层声速分布与南海环流系统关系密切;冷涡的存在会引起声速场的低值中心。     

南海北部内波活动下的声速剖面重构方法研究

在内波条件下,水声信道稳定性变差,声速剖面的重构具有一定难度。与其他方法相比,经验正交分解法优点在于能用少量参数进行重构,而不需要引入大量的参数。利用南海北部陆坡测量的温度链数据,采用经验正交分解法对声速剖面进行重构。结果表明:在内波剧烈的南海北部海域,通过经验正交分解法重构声速剖面具有可行性,其前3个模态累计贡献率达到96.7%。分析样本的周期覆盖率对重构结果的影响后发现,当样本覆盖完整的海洋潮汐活动周期时,基于EOF分析对本组声速剖面的重构均方根误差小于1.1 m/s,重构声速剖面结果理想;而当采集的样本不能覆盖完整周期时,误差较大。     

EOF重构声速剖面对深水多波束的声速改正分析

声速误差是多波束水深地形测量主要误差源之一,通常采用现场声速剖面测量的方式加以改正,但在深远海多波束水深地形测量时,现场获取全深度的声速剖面并非易事。针对这一问题,利用东南印度洋海洋调查工作中采集到的17个站位的CTD数据,将所有站位声速剖面拓展到全深度,采用经验正交函数分析法(Empirical Orthogonal Functions,EOF)构建调查区声速剖面场,可获得声速剖面场内任意一点的声速值。然后通过EOF重构声速剖面场获得的声速值对测区内多波束水深地形数据进行改正,并与实测声速剖面对多波束水深地形数据的改正结果进行对比,结果表明,5000 m水深范围内2种声速改正结果相差很小,EOF重构法对深水多波束的声速改正满足水深测量的要求。     

声速剖面EOF表示的第一模态解析

为实现对声速剖面EOF表示后第一模态时间系数和空间函数变化规律的解析,提出了一种简化的声速剖面变化模型,即"拐点"深度值和声速值的变化;声速梯度的变化和表层海水温度周期性变化所引起的海水声速变化,通过将4种因素所引起的第一模态空间函数的变化规律与实际声速剖面簇第一模态空间函数的变化规律对比,分析引起实测声速剖面变化的主要因素,最后,分别用深海和浅海实测声速剖面数据对其进行验证。     

System-orthogonal functions for sound speed profile perturbation

Empirical orthogonal functions (EOFs) are typically derived from direct measurements of the sound speed profile (SSP) and they are orthogonal in regard to the statistics of the SSP uncertainty. Viewed from the output end of a particular sonar system, however, the effect of an error in one EOF is usually coupled with the effect of the error in another due to the strongly nonlinear relation between the SSP parameters and the system response. In this paper, a new set of basis functions, orthogonal in regard to sonar performance measure, is developed to characterize SSP perturbations. The performance measure used is the Cramer-Rao bound (CRB) for SSP expansion coefficients derived from a full-field random Gaussian signal model; a closed-form, analytical solution is obtained for both the range-independent and adiabatically range-dependent environments. The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients. Compared to the EOFs, the new set of basis functions depends on both the statistics of the sound speed uncertainty and the sound waveguide propagation property; it incorporates the measurement noise as well. The development makes possible the investigation of the relative significance of the individual basis functions in system response; it also provides a novel framework for optimum acoustic parameterization in adaptive rapid environmental assessment.     

Rapid environmental assessment in the South China Sea: Improved inversion of sound speed profile using remote sensing data

Complex perturbations in the profile and the sparsity of samples often limit the validity of rapid environmental assessment (REA) in the South China Sea (SCS). In this paper, the remote sensing data were used to estimate sound speed profile (SSP) with the self-organizing map (SOM) method in the SCS. First, the consistency of the empirical orthogonal functions was examined by using k-means clustering. The clustering results indicated that SSPs in the SCS have a similar perturbation nature, which means the inverted grid could be expanded to the entire SCS to deal with the problem of sparsity of the samples without statistical improbability. Second, a machine learning method was proposed that took advantage of the topological structure of SOM to significantly improve their accuracy. Validation revealed promising results, with a mean reconstruction error of 1.26 m/s, which is 1.16 m/s smaller than the traditional single empirical orthogonal function regression (sEOF-r) method. By violating the constraints of linear inversion, the topological structure of the SOM method showed a smaller error and better robustness in the SSP estimation. The improvements to enhance the accuracy and robustness of REA in the SCS were offered. These results suggested a potential utilization of REA in the SCS based on satellite data and provided a new approach for SSP estimation derived from sea surface data.     

Ocean acoustic tomography as a data assimilation problem

The ocean acoustic tomographic (OAT) approach to sound speed field estimation is generalized to include a variety of sources of information of interest such as an oceanographic model of the sound speed field, direct local sound speed measurements, and a full field acoustic propagation model as well as measurements. The inverse problem is presented as a four-dimensional field estimation problem using a variational approach commonly used in oceanographic data assimilation. The current OAT approach is shown to be a special case of the general framework. The matched-field tomography (MFT) approach is also discussed within this context. A simple implementation of this novel approach is then investigated in the absence of a suitable oceanographic model, and acoustic propagation is accounted for using a standard parabolic equation model. The inverse equations derived are validated numerically through a simple inversion example, and some issues on environmental mismatch and computations are discussed. The developments then provide a basic framework for ongoing data-model melding in acoustically focused oceanographic sampling (AFOS) network     

Remote sensing of ocean sound speed profiles by a perceptron neuralnetwork

A method is developed to estimate ocean sound speed profiles through synthesis of remotely measured environmental data and historical statistics of sound speed obtained at a remotely sensed location. Sound speed profiles are represented by an expansion of empirical orthogonal functions (EOF) of the historical sound speed variation, while the remotely sensed environmental data provide real-time information to determine the expansion coefficients. Environmental inputs are limited to sea surface temperature available from satellite infrared sensors, acoustic time-of-flight and ocean bottom temperature measurable from bottom mounted acoustic and thermal transducers. A multilayer perceptron neural network is implemented to learn the functional transformation from the measured environmental input to the desired EOF coefficient output on a set of representative sound speed profiles. Sea surface temperature, time-of-year, and time-of-flight from the acoustic multipath that maximally samples the vertical sound speed are found to be the dominant inputs. The trained network is computationally efficient and produces estimates for untrained environmental inputs with a mean error of 1.1-4.4 m/s     

黄海冷水团声层析监测数值模拟

海洋冷水团是海洋学家关注多年的问题 ,其监测方法亟待解决。本文将简正波波数层析法用于冷水团监测 ,并对简正波波数层析用于反演黄海冷水团声速剖面进行了数值模拟。数值模拟结果表明 ,简正波波数层析可以用于反演平均声速剖面 ,特别在监测与距离有关海洋环境的声速结构方面大有潜力。     

Modal Inversion Analysis for Geoacoustic Properties of the New Jersey Continental Shelf in the SWAT Experiments

In this paper, inversion for bottom sediment properties at a site on the New Jersey continental shelf is studied as part of the Shallow Water Acoustic Technology (SWAT) project. A source towed at a constant water depth over a range of some tens of kilometers transmitted low-frequency continuous wave (cw) signals, which were measured on a bottom-moored vertical line array of receivers. For the along-shelf geometry, the zeroth-order asymptotic Hankel transform is then applied to the acoustic field at 50 Hz measured on the resulting synthetic aperture horizontal array created at each receiver depth. The resulting horizontal wave number spectra, which have peaks corresponding to the mode eigenvalues, are observed to have slightly different values at different receiver depths, and therefore, stochastic mode inversion is exploited to utilize all of the observed peak position information. The estimated sound-speed profile (SSP) for the upper 10 m of sediment is then compared with an inversion result obtained using midfrequency (2–16 kHz) chirp sonar pulses reflected at normal incidence from the sediment. Although obtained using totally different inversion techniques, both estimated profiles are shown to be in good agreement in the top 10 m of sediment. The acoustic field simulated using the inverted SSP also agrees well with the measured acoustic field at each receiver depth. Furthermore, simulated sound fields which use this profile as input data are shown to be effective in predicting the measurements obtained at a different frequency (125 Hz) and for a different (cross-shelf) geometry.      

Assessment of acoustic iterative inverse method for bubble sizing to experimental data

Comparative study was carried out for an acoustic iterative inverse method to estimate bubble size distributions in water. Conventional bubble sizing methods consider only sound attenuation for sizing. Choi and Yoon [IEEE, 26(1), 125–130 (2001)] reported an acoustic iterative inverse method, which extracts the sound speed component from the measured sound attenuation. It can more accurately estimate the bubble size distributions in water than do the conventional methods. The estimation results of acoustic iterative inverse method were compared with other experimental data. The experimental data show good agreement with the estimation from the acoustic iterative inverse method. This iterative technique can be utilized for bubble sizing in the ocean.     

Inversion Method for Sound Velocity Profile of Eddy in Deep Ocean

The modal wave number tomography approach is used to obtain sound speed profile of water column in deep ocean. The approach consists of estimation of the local modal eigenvalues from complex pressure field and use of these data as input to modal perturbative inversion method for obtaining the local sound speed profile. The empirical orthonormal function (EOF) is applied to reduce the parameter search space. The ocean environment used for numerical simulations includes the Munk profile as the unperturbed background speed profile and a weak Gaussian eddy as the sound speed profile perturbation. The results of numerical simulations show the method is capable of monitoring the oceanic interior structure.