Sound Speed Errors Research Articles

A Co-Localization Algorithm for Underwater Moving Targets with an Unknown Constant Signal Propagation Speed and Platform Errors.

Underwater mobile acoustic source target localization encounters several challenges, including the unknown propagation speed of the source signal, uncertainty in the observation platform's position and velocity (i.e., platform systematic errors), and economic costs. This paper proposes a new two-step closed-form localization algorithm that jointly estimates the angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA) to address these challenges. The algorithm initially introduces auxiliary variables to construct pseudo-linear equations to obtain the initial solution. It then exploits the relationship between the unknown and auxiliary variables to derive the exact solution comprising solely the unknown variables. Both theoretical analyses and simulation experiments demonstrate that the proposed method accurately estimates the position, velocity, and speed of the sound source even with an unknown sound speed and platform systematic errors. It achieves asymptotic optimality within a reasonable error range to approach the Cramér-Rao lower bound (CRLB). Furthermore, the algorithm exhibits low complexity, reduces the number of required localization platforms, and decreases the economic costs. Additionally, the simulation experiments validate the effectiveness of the proposed localization method across various scenarios, outperforming other comparative algorithms.

A differential-based method for correcting ultra-short baseline positioning results

The primary factors influencing the positional accuracy of an ultra-short baseline (USBL) system are errors in sound speed, delay, installation deviation, and the bending of sound rays. Premised on the USBL positioning model, an error contribution model including ranging error, delay error, sound speed error and array element installation deviation was constructed. In parallel, an indirect difference correction method with additional coefficients was proposed based on the geometric correlation of the error function model. Specifically, a reference beacon was deployed on the seabed, and differential correction was achieved by directly computing target coordinates, integrating them with the positional data from the reference beacon. The proposed method demonstrated efficacy in mitigating errors associated with gradual variations or pronounced geometric correlations, including discrepancies in sound speed, bending of sound rays, and deviations in the installation of array elements. The correction method was applied to the USBL positioning, and the simulation results show that the proposed method notably enhanced both accuracy and consistency in positioning, particularly in shallow water environments characterised by significant sound speed errors. The sea trial data from the R/V Dayang Yihao in the Western Pacific demonstrate that the proposed method can effectively mitigate the errors induced by sound ray bending in deep-sea environments. The mean absolute error (MAE) and standard deviation (STD) were reduced by 51.3% and 55.3%, respectively, compared with the results of the USBL direct solution.

Improvement of Seafloor Positioning Through Correction of Sound Speed Profile Temporal Variation

Dear Editor, This letter proposes a high-precision seafloor transponder positioning method based on the correction of sound speed profile (SSP) temporal variation. In the proposed method, the ocean sound speed error is modeled as the temporal variation of a background SSP, and the linearized expression of the acoustic travel time with respect to the sound speed coefficient is derived based on the ray acoustic model. Moreover, the proposed method introduces the constraint of acoustic ranging observations between seafloor transponders and determines the weights of travel time and ranging observations using Akaike's Bayesian information criterion (ABIC) to reduce the positioning error caused by the correlation between sound speed and position parameters. The experimental results in the South China Sea show that the proposed method performs better than the global navigation satellite system-acoustic ranging combined positioning solver (GARPOS) [1], in terms of rigid distance errors and long baseline positioning accuracy.

Augmented Underwater Acoustic Navigation with Systematic Error Modeling Based on Seafloor Datum Network

Underwater acoustic navigation technology is an important approach to achieving high precision ocean navigation. One of the critical issues of the technology is to correct systematic errors, which are related to time delays and time-varying sound speed errors. In this study, we propose an augmented underwater acoustic navigation with systematic error model based on seafloor datum network. The proposed algorithm first selects data sets of piece-wise systematic error modeling by extracting the main periodic term of systematic errors based on the Fourier transform. Before that, the wavelet transform is used for denoising to better extract the main periodic term. Then the systematic error correction model is constructed by using the polynomial fitting method. After that, an augmented observation equation of underwater acoustic navigation with systematic error correction is constructed. Finally, an adaptive robust Kalman filter is developed for underwater acoustic navigation. The proposed algorithm is verified by an experiment in the South China Sea. The three-dimensional root mean square values of underwater acoustic navigation are 1.010 and 1.502 m in the operating range of 2.7 and 8.7 km. The results demonstrate that the proposed algorithm can efficiently reduce the influence of systematic error, thus improving underwater acoustic navigation accuracy.

Adaptive subarray coherence based post-filter using array gain in medical ultrasound imaging

This paper presents an adaptive subarray coherence-based post-filter (ASCBP) applied to the eigenspace-based forward–backward minimum variance (ESB-FBMV) beamformer to simultaneously improve image quality and beamformer robustness. Additionally, the ASCBP can separate close targets. The ASCBP uses an adaptive noise power weight based on the concept of the beamformer’s array gain (AG) to suppress the noise adaptively and achieve improved images. Moreover, a square neighborhood average was applied to the ASCBP in order to provide more smoothed square neighborhood ASCBP (SN-ASCBP) values and improve the speckle quality. Through simulations of point phantoms and cyst phantoms and experimental validation, the performance of the proposed methods was compared to that of delay-and-sum (DAS), MV-based beamformers, and subarray coherence-based post-filter (SCBP). The simulated results demonstrated that the ASCBP method improved the full width at half maximum (FWHM) by 57 % and the coherent interference suppression power (CISP) by 52 dB compared to the SCBP post-filter. Considering the experimental results, the SN-ASCBP method presented the best enhancement in terms of generalized contrast to noise ratio (gCNR) and contrast ratio (CR) while the ASCBP showed the best improvement in FWHM among other methods. Furthermore, the proposed methods presented a striking performance in low SNRs. The results of evaluating the different methods under aberration and sound speed error illustrated the better robustness of the proposed methods in comparison with others.

Improved techniques to resolve the water column sound speed structure for multibeam ray-tracing

Multibeam bathymetry surveys conducted in highly stratified environments are routinely affected by sound speed errors. The approach proposed here aims to combine measured with synthetic sound speed profiles in order to minimize sound speed errors. The adequacy of synthetic profiles derived from a regional hydrodynamic model and spatiotemporal interpolation is therefore investigated. Ray-tracing comparisons at the 65° launch angle between measured and synthetic profiles demonstrates that the expected depth bias for modeled profiles will be in excess of 1% of water depth. Spatiotemporally interpolating hourly sampled profiles decreases the depth bias up to a factor of three for higher beam angles. Residual sounding depth biases are observed and ascribed to a residual surface sound speed error.

Modeling the effects of internal waves on synthetic aperture sonar resolution

Synthetic aperture sonar (SAS) beamforming is performed under the assumption of a constant sound speed within the water column or by utilizing a measured sound speed profile. Water column features, such as internal waves or internal wave boluses that cause a sound speed structure different than that assumed, can break the constant sound speed assumption resulting in image defocusing and loss of resolution. The resultant loss of resolution can be quantified using the point spread function (PSF). An ellipse fitting technique was applied to SAS images collected by the Norwegian Defence Research Establishment (FFI) using the HISAS system. In conjunction with the analysis conducted on real data, a ray tracing method was applied to model the broadening effects on the PSF for sound speed differences caused by internal wave boluses. A wavenumber beamforming algorithm was also applied to artificial echo data, in which sound speed errors were introduced. It is hoped that the two models can be used in conjunction with SAS data to determine the sound speed within an internal wave feature from the observed loss in resolution.

Assessing the Robustness of Frequency-Domain Ultrasound Beamforming Using Deep Neural Networks.

We study training deep neural network (DNN) frequency-domain beamformers using simulated and phantom anechoic cysts and compare to training with simulated point target responses. Using simulation, physical phantom, and in vivo scans, we find that training DNN beamformers using anechoic cysts provided comparable or improved image quality compared with training DNN beamformers using simulated point targets. The proposed method could also be adapted to generate training data from in vivo scans. Finally, we evaluated the robustness of DNN beamforming to common sources of image degradation, including gross sound speed errors, phase aberration, and reverberation. We found that DNN beamformers maintained their ability to improve image quality even in the presence of the studied sources of image degradation. Overall, the results show the potential of using DNN beamforming to improve ultrasound image quality.

Seafloor geodetic network establishment and key technologies

Seafloor geodetic network construction involves the development of geodetic station shelter, network configuration design, location selection and layout, surveying strategy, observation model establishment and optimization, data processing strategy and so on. This paper tries to present main technological problems involved in the seafloor geodetic network construction, and seek the technically feasible solutions. Basic conceptions of developing seafloor geodetic station shelters for shallow sea and deep-sea are described respectively. The overall criteria of seafloor geodetic network construction for submarine navigation and those of network design for crustal motion monitoring are both proposed. In order to enhance application performances of the seafloor geodetic network, the seafloor network configuration should prefer a symmetrical network structure. The sea surface tracking line measurements for determining the seafloor geodetic station position should also adopt an approximately symmetrical configuration, and we recommend circle tracking line observations combined with cross-shaped line (or double cross-shape line) observations for the seafloor positioning mode. As to the offset correction between the Global Navigation Satellite System antenna phase center and the acoustic transducer, it is recommended to combine the calibration through external measurements and model parameter estimation. Besides, it is suggested to correct the sound speed error with a combination of observation value correction and parameterized model correction, and to mainly use the model correction to reduce the influence of acoustic ray error on the seafloor positioning. Following the proposed basic designs, experiments are performed in shallow sea area and deep-sea area respectively. Based on the developed seafloor geodetic shelter and sufficient verification in the shallow sea experiment, a long-term seafloor geodetic station in the deep-sea area of 3000 m depth was established for the first time, and the preliminary positioning result shows that the internal precision of this station is better than 5 cm.

Thermoacoustic Range Verification in the Presence of Acoustic Heterogeneity and Soundspeed Errors– Accuracy and Robustness Relative to Live Ultrasound Images

Lack of online range verification limits efficacy of particle therapy for many tumor sites. Real-time thermoacoustic range verification could enable more aggressive treatment planning and hypofractionation for tumor sites that can be imaged with ultrasound during treatment. Our objective was to experimentally demonstrate accuracy and robustness of thermoacoustic range estimates relative to ultrasound images despite acoustic heterogeneity and discrepancies between assumed and true soundspeed. Prior results were for weak acoustic scatterers with known soundspeeds. 250 ns pulses of 0.26 Gy of 16 MeV protons and 2.3 Gy of 60 MeV helium ions were delivered to water and oil targets, respectively. Thermoacoustic signals with DC-4 MHz bandwidth were detected by a 96-channel ultrasound array placed 6-10 cm distal to the Bragg peak. One-way beamforming with an assumed soundspeed was performed to estimate range. The same soundspeed and transducer array were used to generate ultrasound images via two-way ultrasound beamforming. An air gap phantom displaced the Bragg peak by 6.5 mm to demonstrate accuracy. The scanner’s soundspeed setting was altered by ±5% to demonstrate robustness to soundspeed errors. Tissue mimicking gelatin and a 5 mm thick bone sample were introduced to demonstrate robustness to acoustic heterogeneity. Single ion pulse measurements sufficed during the helium run, but signal averaging was required for protons. Estimates of the entry point agreed with the air-target interface in ultrasound images and range estimates agreed with Monte Carlo simulations to within 300 μm microns, even when TA emissions traveled through a strong acoustic scatterer. Estimated Bragg peak locations were translated 6.5 mm by the air gap phantom and correctly identified scenarios when the beam stopped inside bone, but did not accurately estimate range in bone. Soundspeed errors dilate and acoustic heterogeneities deform ultrasound images. Thermoacoustic range estimates are transformed similarly and are robust relative to ultrasound images of underlying anatomy. When the target can be visualized with ultrasound during treatment, thermoacoustic range verification may enable real-time motion management and range verification. Therapeutic systems deliver higher (200+ MeV) energy protons using pulse durations exceeding 5 μs and generate thermoacoustic emissions with sonar bandwidths (DC-100 kHz). Therefore, custom acoustic hardware will be required to detect low frequency thermoacoustic emissions and also generate high-resolution ultrasound images.Abstract 3713; Table 1Experimentwaterwater & bonewater & air gapsafflower oilIonprotonprotonproton4HeBeam Energy (MeV)16.0±0.1516.0±0.1516.0±0.1560.7±0.4Bragg curve FWHM (μm)390240390230distal HWTM (μm)1609016080Monte Carlo Range (mm)2.471.948.952.51Thermoacoustic Range (mm)2.65±0.091.36±0.616.59±0.042.76±0.04N8887 Open table in a new tab

Thermoacoustic range verification in the presence of acoustic heterogeneity and soundspeed errors - Robustness relative to ultrasound image of underlying anatomy.

To demonstrate robustness of thermooacoustic range verification to acoustic heterogeneity and discrepancies between assumed and true propagation speed, i.e., soundspeed errors. A beam sweeper was used to deliver 250ns pulses that deposited 0.26Gy of 16MeV protons and 2.3Gy of 60MeV helium ions into water and oil targets, respectively. Thermoacoustic signals were detected by a 96-channel ultrasound array with a 1-4MHz sensitivity band (-6dB), bandpass filtered and backprojected to create thermoacoustic images in the plane of the ultrasound array. The same soundspeed and transducer array were used to estimate range and generate the ultrasound images onto which Bragg peak locations were overlaid. An air-gap phantom that displaced the Bragg peak by 6.5mm demonstrated accuracy. Robustness to soundspeed errors was demonstrated in a waterbath as the assumed propagation speed scanner setting was altered by . Tissue-mimicking gelatin and a bone sample were introduced to demonstrate robustness to acoustic heterogeneity relative to ultrasound images of the underlying morphology. Single ion pulse measurements sufficed during the helium run, but signal averaging was required for protons. Range and entry point into the target were estimated from data collected by transducers placed at least 6cm distal to the Bragg peak. When ultrasound images depicted the air-target interface where the beam enters, estimates of the entry point agreed with ultrasound images and range estimates agreed with Monte Carlo simulations to within 300μm, even when thermoacoustic emissions traveled through a strongly scattering bone sample. Estimated Bragg peak locations were translated 6.5mm by the air-gap phantom and correctly identified scenarios when the beam stopped inside the bone. Soundspeed errors dilate and acoustic heterogeneities deform ultrasound images. When thermoacoustic receivers are co-located with the ultrasound imaging array, the same transformations shift thermoacoustic range estimates. Therefore, thermoacoustic range verification is robust relative to ultrasound images of underlying anatomy. When the treatment target is visible in ultrasound, e.g., prostate, online thermoacoustic range estimates could verify that the treatment spot is inside the target.

Linear approximation of underwater sound speed profile: Precision analysis in direct and inverse problems

Sound speed is one of the key sources of uncertainty in an underwater environment. The wave equation for a complex sound speed profile (SSP) cannot be analytically solved and numerical solutions generally involve high computational costs. A relatively simple way is to approximate the SSP by assuming it as horizontally stratified, vertically multi-layered and linearly varied with respect to water depth in each layer. This approximative model leads to a fast computation of the sound propagation. However, the error of SSP results in an inaccurate sound field computation, thus the model accuracy in terms of error propagation in both direct and inverse problems should be investigated. Rapidly developing numerical techniques are currently able to accurately simulate the sound propagation in a complex configuration, such that the difference between a real case with a complex SSP and its approximation can be precisely quantified. In this paper, the sound propagation with a complex SSP is simulated via a full wave numerical approach, known as the spectral element method. The efficiency of SSP linear approximation with various layer number (corresponding to different sound speed error) is quantified via transmission loss forecast (direct problem) and sound source localization error (inverse problem), respectively. The precision analysis is able to guide the choice of optimal approximate model for different scenarios, which is a trade-off between the computational cost and the model accuracy.

A Robust Method for Ultrasound Beamforming in the Presence of Off-Axis Clutter and Sound Speed Variation

Previously, we introduced a model-based beamforming algorithm to suppress ultrasound imaging artifacts caused by clutter sources, such as reverberation and off-axis scattering. We refer to this method as aperture domain model image reconstruction (ADMIRE). In this study, we evaluated the algorithm’s limitations and ability to suppress off-axis energy using Field II-based simulations, experimental phantoms and in vivo data acquired by a Verasonics ultrasound system with a curvilinear transducer (C5-2). We compared image quality derived from a standard delay-and-sum (DAS) beamformer, DAS with coherence factor (CF) weighting, ADMIRE and ADMIRE plus CF weighting. Simulations, phantoms and in vivo scan results demonstrate that ADMIRE substantially suppresses off-axis energy, while preserving the spatial resolution of standard DAS beamforming. We also observed that ADMIRE with CF weighting further improves some aspects of image quality. We identified limitations of ADMIRE when suppressing off-axis clutter in the presence of strong scattering, and we suggest a solution. Finally, because ADMIRE is a model-based beamformer, we used simulated phantoms to test the performance of ADMIRE under model-mismatch caused by gross sound speed deviation. The impact of sound speed errors largely mimics DAS beamforming, but ADMIRE never does worse than DAS itself in resolution or contrast. As expected the CF weighting used as a post processing technique provides a boost in contrast but decreases CNR and speckle SNR. The results indicate that ADMIRE is robust in terms of model-mismatch caused by sound speed variation, especially when the actual sound speed is slower than the assumed sound speed. As an example, the image contrast obtained using DAS, DAS + CF, ADMIRE and ADMIRE + CF in the presence of −5% gross sound speed error are 24.9 ± 0.71 dB, 39.1 ± 1.2 dB, 43.2 ± 2.3 dB and 52.5 ± 2.9 dB, respectively.

Computing navigation corrections for co-registration of repeat-pass synthetic aperture sonar images

Interferometric processing of repeat-pass Synthetic Aperture Sonar (SAS) data requires a precise co-registration of the images in order to exploit the phase information for applications such as differential interferometry or coherent change detection. Co-registration of SAS images is made difficult by changing environmental conditions and positioning ambiguities that give rise to warping functions which are not well modeled by affine or polynomial transformations, resulting in non-negligible residual misregistration errors. The objective of this presentation will be to examine these warping functions in greater detail to gain a better physical understanding of the estimated along- and across-track displacements. A non-linear least-squares optimization is used to determine the corrections to be applied to the repeat-pass data that will yield a repeat-pass image that is co-registered with the original. These corrections include sway, heave and yaw as well as sound speed errors and element-level surge adjustments. Repeat-pass SAS data collected a Kongsberg HISAS 1020 system is used to demonstrate this optimization, showing good agreement with modeled and real data for most parameters, while determining surge estimates are shown to be particularly challenging. An examination of the resulting repeat-pass coherence will also be performed.

A Bayesian Method for Localization by Multistatic Active Sonar

The question of localizing a target with multistatic active sonar is reexamined from the perspective of finding a peak in a probability distribution function. The probability distribution function is constructed using straightforward Bayesian principles. Both a position estimate and a covariance matrix can be found, provided that an implementation of a numerical algorithm for finding a local maximum is available. The localization method developed herein can account for transmitter and receiver location errors, sound-speed errors, time errors, and bearing errors. A Monte Carlo test is conducted to compare the accuracy of the proposed method to that of a more conventional method used as a baseline. In each iteration, a transmitter, several receivers, and a target are positioned randomly within a square region, and the target is localized by both methods. The proposed method is generally more accurate than the baseline method, within the range of parameters considered here. The degree of improvement over the baseline is greater with a larger region area, with a larger bearing measurement error, and with a smaller time-of-arrival measurement error, and slightly greater with a larger number of receivers.

Eigenspace-based minimum variance beamformer combined with Wiener postfilter for medical ultrasound imaging

In this paper, a new beamformer which combines the eigenspace-based minimum variance (ESBMV) beamformer with the Wiener postfilter is proposed for medical ultrasound imaging. The primary goal of this work is to further improve the medical ultrasound imaging quality on the basis of the ESBMV beamformer. In this method, we optimize the ESBMV weights with a Wiener postfilter. With the optimization of the Wiener postfilter, the output power of the new beamformer becomes closer to the actual signal power at the imaging point than the ESBMV beamformer. Different from the ordinary Wiener postfilter, the output signal and noise power needed in calculating the Wiener postfilter are estimated respectively by the orthogonal signal subspace and noise subspace constructed from the eigenstructure of the sample covariance matrix.We demonstrate the performance of the new beamformer when resolving point scatterers and cyst phantom using both simulated data and experimental data and compare it with the delay-and-sum (DAS), the minimum variance (MV) and the ESBMV beamformer. We use the full width at half maximum (FWHM) and the peak-side-lobe level (PSL) to quantify the performance of imaging resolution and the contrast ratio (CR) to quantify the performance of imaging contrast. The FWHM of the new beamformer is only 15%, 50% and 50% of those of the DAS, MV and ESBMV beamformer, while the PSL is 127.2dB, 115dB and 60dB lower. What is more, an improvement of 239.8%, 232.5% and 32.9% in CR using simulated data and an improvement of 814%, 1410.7% and 86.7% in CR using experimental data are achieved compared to the DAS, MV and ESBMV beamformer respectively. In addition, the effect of the sound speed error is investigated by artificially overestimating the speed used in calculating the propagation delay and the results show that the new beamformer provides better robustness against the sound speed errors. Therefore, the proposed beamformer offers a better performance than the DAS, MV and ESBMV beamformer, showing its potential in medical ultrasound imaging.

Synthetic aperture focusing for medical endoscopic ultrasonography

A new approach for synthetic aperture focusing (SAF) to enhance both signal to noise ratio (SNR) and resolution in endoscopic ultrasonography is presented in this paper. The technique uses the rotation feature of single element transducer probe, and transmits and receives the echoes at different time and locations during the rotary scanning. Based on theoretical simulation, axial and lateral matched-filters are developed according to the coded and linear frequency modulated characteristics of the echoes to implement axial and lateral compression. The effects of SNR and resolution enhancements by the new SAF approach are demonstrated by both Field II simulation and sample experiment. Data for 6 point targets are simulated and the performance of SAF is compared with those from conventional imaging method and Delay-and-Sum (DS) method. Pigskin samples are examined by a single element transducer at 8 MHz. The effects of sound speed errors and rotary scanning speed errors on both SNR and resolution are calculated to show the robustness of SAF algorithm. Both simulation and experimental results indicated that new SAF can improve SNR and resolution of ultrasound images by 9.38 dB and 51% respectively as compared with the conventional method. It therefore has potential for future clinical and research applications.

EFFECTS OF A DEEP MIXED SHELL ON SOLARg-MODES,p-MODES, AND NEUTRINO FLUX

A mixed-shell model that reflects g-modes away from the Sun's center is developed further by calibrating its parameters and evaluating a mixing mechanism: buoyancy. The shell roughly doubles g-mode oscillation periods and would explain why there is no definitive detection of their periods. But the shell has only minor effects on most p-modes. The model provides a mechanism for causing short-term fluctuations in neutrino flux and makes plausible the correlations between this flux and solar activity levels. Relations are derived for a shell heated asymmetrically by transient increases in nuclear burning in small "hot spots." The size of these spots and the timing of a heating event are governed by sets(ℓ) of standing asymptotic g-modes, coupled by a maximal principle that greatly enhances their excitation and concentrates power toward the equator, assisting the detection of higher-ℓ sets. Signals from all sets, except one, in the range 2 ⩽ ℓ ⩽ 8 are identified by difference periods between consecutive radial states using the method of Garcia et al. and reinterpreting their latest spectrum. This confirms two detections of sets in a similar range of ℓ by their rotation rates. The mean radius of shell mixing is rm = 0.16 R☉, which improves an earlier independent estimate of 0.18 by the author. The shell may cause the unexplained dip in measured sound speed at its location. Another sound speed error, centered near 0.67 R☉, and reversing flows in the same place with a period originally near 1.3 yr suggest that the g-modes are depositing there about 3% of the solar luminosity. That implies the shell at rm is receiving a similar magnitude of power, which would be enough energy to mix the corresponding shell in a standard solar model in ≪107 yr.

An efficient sound speed estimation method to enhance image resolution in ultrasound imaging

Most of clinical ultrasound imaging systems use a pre-determined sound speed, mostly 1540 m/s, in transmit- and receive-beamforming while actual sound speed varies depending on tissue composition and temperature. Sound speed errors, particularly in receive-beamforming, lead to resolution degradation and sensitivity loss in ultrasound imaging. In this paper, we propose a sound speed estimation method in which an optimal sound speed, the speed that makes the echo signal delays at the transducer elements be best matched to the theoretical delays, is estimated by maximizing the beamformed echo signal amplitude with respect to the sound speed and the reflector displacement from the central axis of the ultrasound beam. Since the sound speed can be estimated from the echo signals on several scan lines, the proposed method does not require excessive computation. Experimental imaging studies of phantoms and porcine tissue with a 6 MHz 128-element linear probe and a 3 MHz 128-element convex probe have shown that spatial resolution, particularly in the lateral direction, can be improved by the proposed method.

Full-field tomography and Kalman tracking of the range-dependent sound speed field in a coastal water environment

The monitoring, assessment and prediction of dynamic processes in shallow water constitute an attractive challenge. The availability of targeted observations enable high-resolution ocean forecasting to develop the 4D environmental picture. In particular, range-resolving acoustic tomography data constitute an effective way to reduce the non-uniform distribution and sparsity of standard hydrographic observations. In this paper a Kalman filtering scheme is investigated for tracking the time variations of a range-dependent sound-speed field in a vertical slice of a shallow water environment from full-field acoustic data and a propagation model taking into account the acoustic properties of the seafloor and subseafloor. The basic measurement setup for each radial of a tomography system consists of a broadband, multifrequency sound source and a vertical receiver array spanning most of the water column. The state variables represent the main features of the sound-speed field in a low dimensional parameterization scheme using empirical orthogonal functions. To test the algorithm acoustic data are synthesized from ocean model predictions obtained in support of the MREA/BP07 experiment southeast of the island of Elba, Italy. Bottom geoacoustic parameters obtained from previous acoustic inversion experiments are input to a normal mode propagation model as a background dataset. Additional data such as sea-surface temperature data from satellite or in situ hydrographic observations provide a priori approximate information about the range dependency of the subsurface structure and an estimation of the sea-surface sound speed. The evolution of the entire sound-speed field in the vertical slice is then sequentially estimated by the inversion processor. The results show that the daily space and time variations of the simulated sound-speed field can be effectively tracked with an extended Kalman filter. The depth-integrated sound-speed error (RMS) remains lower than 0.3 m/s (0.09 °C) when the benchmark environment is completely determined in the parameter space and lower than 0.7 m/s (0.22 °C) for an approximate environment parameterization.