Truncated Total Least Squares Regularization Method for Ocean Acoustic Tomography Inverse Problem

Acoustic travel time tomography will be applied on the atmosphere to directly provide spatially averaged values of meteorological quantities (temperature and wind field) which are needed for the evaluation of numerical models as well as to complete in situ point measurements and conventional studies of the atmospheric surface layer over natural surfaces. Sound waves propagate through the atmosphere with different sound velocities according to the distribution of air temperature and wind vector and become, therefore, an information carrier about the medium properties. In the presented study acoustic travel time data were measured between sources and receivers placed around an array of 200×260 m2 as initial values for the tomographic reconstruction. Thereby, a frequently applied procedure of ray tomography, the simultaneous iterative reconstruction technique, characterized by simple handling and small computational requirements, was used. Additionally, a special system of equations for the isolation of the temperature and wind influence on the sound speed was solved. To estimate the sound ray propagation and to simulate acoustic travel times during various meteorological conditions a ray tracing model based on a modified version of Snell’s law corresponding to the influence of wind vector will be introduced.

Ocean Acoustic Tomography (OAT) is an efficient and economical marine acoustic observation technique. Targeted observation is an appealing procedure to reduce the uncertainty of ocean environment prediction through additional observation. This study aimed to assess the validity of OAT as an observation method for targeted observation. OAT based on Niche Genetic Algorithm was employed to extract sound speed and temperature profiles from acoustic transmission time, utilizing data from the 2019 Yellow Sea experiment. The inversion results were compared with measurement data, which are found to be accurate and reliable. To further evaluate OAT as targeted observation method, the vertical bias structure of OAT was added on synchronous measurement data in the sensitive area of targeted observation to simulate OAT observation in sensitive area. This simulated data was then incorporated into a 3D-Var assimilation system to improve the short-term prediction of the target region. Comparing the predictions derived with the measurement data at the verification time, it shows that the simulated OAT observation improved the quality of target region prediction, indicating that OAT can be an effective observation method for targeted observation. An Observing System Simulation Experiment was conducted to assess the impact of OAT characteristics on prediction improvement. The results show that both adding observation nodes and extending the observation duration have positive effects, while extending the observation duration performs better.

An ocean environment monitoring scheme is designed to be placed in South China Sea, aiming at mesoscale eddy observation. In this paper, we use acoustic moorings combined with PIES (pressure inverted echo sounder) array to inverse three-dimensional sound speed field to infer the structure of mesoscale eddy. Ocean Acoustic Tomography (OAT) with acoustic moorings is widely used for inversion. Single Empirical Orthogonal Function Reconstruction (sEOF-R) is used for inversion with PIES array. We combine them together using convex optimization for empirical orthogonal function parameters inversion. The simulation results show that our proposed method achieves lower RMSE and performs better in the structure estimation of mesoscale eddy than methods with only one kind of equipment and existing methods to combine data from different kinds of equipment.

The travel time measurements used in ocean acoustic tomography are based on the use of wideband waveforms. Because of this, the effects of source or receiver motion must be modeled as time compression/expansion and not as simple frequency shifts. Equivalent situations occur when there is a frequency error between the clocks used to generate an ocean acoustic tomography wideband signal and the clock used to digitize the associated reception, and when the clock used to digitize the reception is not “properly” matched to the structure of the transmitted waveform. The common thread is that you have uniformly spaced samples at one set of times but you really need them at a different uniform spacing at a different set of times. The obvious solution is to interpolate. This paper describes the effects of some simple interpolaton techniques on the processing of the wideband waveforms used in making ocean acoustic tomography travel time measurements.

In shallow water acoustic tomography, broadband mid-frequency acoustic waves (1 to 5 kHz) follow multiple ray-like paths to travel through the ocean. Travel-time (TT) variations associated to these raypaths are classically used to estimate sound speed perturbations of the water column using the ray theory. In this shallow water environment, source and receiver arrays, combined with adapted array processing, provide the measurement of directions-of-arrival (DOA) and directions-of-departure (DOD) of each acoustic path as new additional observables to perform ocean acoustic tomography. To this aim, the double-beamforming technique is used to extract the TT, DOA, and DOD variations from the array-to-array acoustic records. Besides, based on the first order Born approximation, we introduce the time-angle sensitivity kernels to link sound speed perturbations to the three observable variations. This forward problem is then inversed by the maximum a posteriori method using both the extracted-observable variations and the proposed sensitivity kernels. Inversion results obtained on numerical data, simulated with a parabolic equation code, are presented. The inversion algorithm is performed with the three observables separately, namely TT, DOA, and DOD. The three observables are then used jointly in the inversion process. The results are discussed in the context on ocean acoustic tomography.

Acoustic travel time tomography uses the dependence of sound speed on temperature and flow properties along the propagation path to measure these parameters. An algorithm is introduced that is capable of resolving the two-dimensional flow field within a specified measuring area. Different flow fields have been simulated to explore the reconstruction properties of the algorithm. Furthermore, an experiment within the Barrel of Ilmenau has been carried out, which demonstrates that the acoustic tomographic method is able to detect flow fields in a closed convection chamber. The simulations reveal that the vector tomographic algorithm can resolve the flow field characteristics speed and direction. Furthermore it is demonstrated that the distribution of sound sources and receivers has to be homogeneous around the measuring site. For the reconstruction of flow distributions, this requirement is even more important compared to temperature reconstructions, since information along inclined sound ray paths within each grid cell are needed to reconstruct the flow vector properly.

In the image reconstruction of the electrical capacitance tomography (ECT) system, the application of the total least squares theory transforms the ill-posed problem into a nonlinear unconstrained minimization problem, which avoids calculating the matrix inversion. But in the iterative process of the coefficient matrix, the ill-posed problem is also produced. For the effect on the final image reconstruction accuracy of this problem, combined with the principle of the ECT system, the coefficient matrix is targeted and updated in the overall least squares iteration process. The new coefficient matrix is calculated, and then, the regularization matrix is corrected according to the adaptive targeting singular value, which can reduce the ill-posed effect. In this study, the total least squares iterative method is improved by introducing the mathematical model of EIV to deal with the errors in the measured capacitance data and coefficient matrix. The effect of noise interference on the measurement capacitance data is reduced, and finally, the high-quality reconstructed images are calculated iteratively.

Chapter 1 - Fundamental Knowledge

Accurate knowledge of the spatial and temporal evolution of the three-dimensional ocean sound speed profile (SSP) is crucial for underwater source localization. Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations based on acoustic measurements between multiple source-receiver pairs (e.g., eigenrays arrival times). This study investigates the estimation of range-dependent SSPs using a classical model-based OAT method (i.e., ray-based ocean acoustic tomography), for various configurations of source and receiver configurations using autonomous platforms in a highly-dynamic upper ocean environment. A regional oceanographic simulation of the De Soto Canyon circulation in the Gulf of Mexico is used to construct 3D sound speed variations spanning a month long which exhibits significant sub-mesoscale variability. Two main aspects affecting OAT performance in the presence of high 3D SSPs variability are investigated: (1) The influence of the input acoustic data (i.e., source-receivers configuration and platform motion, arrival-times accuracy...) and (2) the actual implementation of the OAT scheme (i.e., selection of complexity reduction basis, linearized forward model assumptions as well as the use of iterative solvers) on SSPs estimations errors. Practical implications for the design of OAT experiments in the dynamic upper ocean will be discussed. [Work supported by the Office of Naval Research.]

Acoustic travel-time tomography of the atmosphere is a nonlinear inverse problem which attempts to reconstruct temperature and wind velocity fields in the atmospheric surface layer using the dependence of sound speed on temperature and wind velocity fields along the propagation path. This paper presents a statistical-based acoustic travel-time tomography algorithm based on dual state-parameter unscented Kalman filter (UKF) which is capable of reconstructing and tracking, in time, temperature, and wind velocity fields (state variables) as well as the dynamic model parameters within a specified investigation area. An adaptive 3-D spatial-temporal autoregressive model is used to capture the state evolution in the UKF. The observations used in the dual state-parameter UKF process consist of the acoustic time of arrivals measured for every pair of transmitter/receiver nodes deployed in the investigation area. The proposed method is then applied to the data set collected at the Meteorological Observatory Lindenberg, Germany, as part of the STINHO experiment, and the reconstruction results are presented.

An ocean acoustic tomography (OAT) experiment was conducted during May to September 2008 in the Luzon Strait where the Kuroshio sporadically intrudes and strong internal tides and waves occur. Although the reciprocal sound transmissions between two acoustic stations were remarkably disturbed by these waves, ocean current signals proportional to the travel time differences, were successfully retrieved by low‐pass filtering out the high frequency wave components under these conditions. The drift of internal clock occurring during the observation is corrected through the procedure that the travel time differences for rays passing the upper 500 m layer are determined relative to those for rays passing near the underwater sound channel (USC) axis of depth about 1000 m. The observed currents relative to currents near the USC axis agree with the moored upward looking ADCP (acoustic Doppler current profiler) data. This study suggests a potential ability of OAT for the operational measurement of ocean currents.

Coastal acoustic tomography (CAT) which was proposed by Hiroshima University in 1990s as a shallow-sea application of ocean acoustic tomography (OAT) is developed as a mirror-type CAT (MCAT) for measuring deep strait throughflows in Indonesian archipelago seas in real time. MCAT system is composed of a land station (M0) connected to a 100 m submarine cable edged by a 5 kHz subsurface transceiver and triangular-arrayed bottom-moored stations (M1, M2, and M3). Reciprocal data are first obtained among three station pairs (M1M2, M2M3, and M3M1). Data received at M1 from M2 and M3 are transferred to the land station (M0) by the first mirror reflection, resulting in travel time summations (t21 + t10, t31 + t10) (t21: travel time from M2 to M1). Data obtained at the offshore stations M2 and M3 are transferred to the nearshore station M1 by the first mirror reflection, resulting in travel time summations (t12 + t21, t13 + t31, t23 + t31, and t32 + t21). All the first mirror data at M1 are also transferred to M0 by the second mirror reflection, adding a travel time by t10 for the above four travel time summations. Finally, travel time differences are calculated for M0M1, M1M2, M2M3, and M3M1 by subtracting the summation data at M0. They are converted to path-average currents along the four transmission lines, succeeding in strait throughflow estimate. The mirror reflection function of MCAT can develop in an underwater transfer system of sound from moving sources by adding a hydrophone.

Ocean current profiling using ocean acoustic tomography (OAT) was conducted in the Kuroshio Current southeast of Taiwan from August 20 to September 15, 2009. Sound pulses were transmitted reciprocally between two acoustic stations placed near the underwater sound channel axis and separated by 48 km. Based on the result of ray simulation, the received signals are divided into multiple ray groups because it is difficult to resolve the ray arrivals for individual rays. The average differential travel times from these ray groups are used to reconstruct the vertical profiles of currents. The currents are estimated with respect to the deepest water layer via two methods: An explicit solution and an inversion with regularization. The strong currents were confined to the upper 200 m and rapidly weakened toward 500 m in depth. Both methods give similar results and are consistent with shipboard acoustic Doppler current profiler results in the upper 150 m. The observed temporal variation demonstrates a similar trend to the prediction from the Hybrid Coordinate Ocean Model.

Early attempts at understanding scintillations in sound transmission through the ocean assumed that ocean fine structure is homogeneous and isotropic. It is, in fact, dominated by internal waves, which are neither homogeneous nor isotropic. Sound Transmission Through a Fluctuating Ocean (Flatté et al., Cambridge University Press, Cambridge, England 1979) combined recently developed internal-wave models with path-integral methods to predict the fluctuations of resolved acoustic multipaths. At that time, Ocean Acoustic Tomography (Munk et al., Cambridge University Press, Cambridge, England 1995), which uses ray travel times to determine large-scale ocean structure, had just been proposed. The wideband acoustic sources and receivers required to make travel-time measurements for tomography also provided the technology needed to quantify acoustic fluctuations. Conversely, internal-wave-induced scattering limits travel-time measurement precision. Tomography experiments at 25-km range provided some of the earliest tests of path-integral predictions. Subsequent tomography experiments provided data at ever-increasing ranges and decreasing frequencies. The Acoustic Thermometry of Ocean Climate project made measurements at megameter ranges with 1400-m vertical line array receivers. The next step is a modular distributed VLA capable of spanning the full water column that is under development to enable separation of acoustic modes using spatial filtering and to fully characterize deep-water acoustic time fronts.

This talk will describe some of the origins of what became known as ocean acoustic tomography, and how it has evolved in the intervening years. Some published mis-conceptions about its beginnings are somewhat interesting. The possibilities of its having a more central role in the determining the evolution of the ocean in future climate raise fascinating technical problems that probably have equally fascinating solutions.