Sound Speed Variations Research Articles

A computationally efficient model for determining sound speed in shallow tropical freshwater systems, with field validation

AbstractThe optimum performance of any underwater system depends on the propagation characteristics of the acoustic signals in the local water medium. Shallow tropical freshwater systems suffer from sub‐optimal performance of sonar systems deployed for any acoustic sensing because of random fluctuations of the water medium. The propagation characteristics depend largely on the sound speed variations defined by the site‐specific physical parameters such as water temperature, salinity and depth. The present study focuses on analysing the sound speed profile of a typical shallow freshwater system (Khadakwasla Lake; 18.43°N, 73.76°E), using regression models with the goal of deriving a computationally efficient model. To this end, a linear and polynomial regression model was developed, and their performance compared with the results of the model of Chen and Millero (), based on root mean square error (RMSE). In situ measurements of electrical conductivity, temperature and density (CTD) were carried out using a Valeport 602 CTD meter. Approximately 125 CTD samples were obtained during a 2‐day experimental study conducted at Khadakwasla Lake from 11 October 2017 to 12 October 2017. The data collection was undertaken throughout the day at multiple locations in the lake over a spatial distance of ~16 km. The Valeport 602 CTD meter uses the Chen and Millero () formula, considered the most conventional sound speed equation. The computational complexity of the proposed models was measured in terms of the number of addition and multiplication operations required. The validation of both models was carried out by varying the model input parameters within defined limits. The model inputs have been derived from an in situ experimental data collection process in a typical shallow tropical freshwater system. The linear regression model exhibited an RMSE of 4.15 m/s, while the polynomial regression model exhibited a good agreement with an RMSE of 0.5 m/s.

Investigation of liner cavitation considering coupling effect between engine vibration and acoustic field of water coolant passage

The engine vibration gives rise to pressure fluctuation of water coolant; therefore, the coupled system between engine structure and acoustic field of water coolant passage needs to be established to calculate the response of engine vibration and water coolant pressure fluctuation. A rectangular tank is used to evaluate water pressure induced by structural impact vibration. The dynamic characteristics of structural-acoustic coupled system are discussed by changing water depth. Considering the resonance effect, the relationship between natural frequencies of structure and acoustic field is examined by variation of sound speed. The equation of motion of engine structure coupled with acoustic field of water coolant passage is established to calculate coolant pressure fluctuation during engine working condition. The effect of piston slap forces on pressure fluctuation is evaluated. The influence of acoustic characteristics of water coolant passage on pressure fluctuation is discussed by varying sound speed.

Modeling Errors Compensation With Total Least Squares for Limited Data Photoacoustic Tomography

The limited data photoacoustic image reconstruction problem is typically solved using either weighted or ordinary least squares (LS), with regularization term being added for stability, which account only for data imperfections (noise). Numerical modeling of acoustic wave propagation requires discretization of imaging region and is typically developed based on many assumptions, such as speed of sound being constant in the tissue, making it imperfect. In this paper, two variants of total least squares (TLS), namely ordinary TLS and Sparse TLS were developed, which account for model imperfections. The ordinary TLS is implemented in the Lanczos bidiagonalization framework to make it computationally efficient. The sparse TLS utilizes the total variation penalty to promote recovery of high frequency components in the reconstructed image. The Lanczos truncated TLS and Sparse TLS methods were compared with the recently established state-of-the-art methods, such as Lanczos Tikhonov and Exponential Filtering. The TLS methods exhibited better performance for experimental data as well as in cases where modeling errors were present, such as few acoustic detectors malfunctioning and speed of sound variations. Also, the TLS methods does not require any prior information about the errors present in the model or data, making it attractive for real-time scenarios.

Correcting Multibeam Echosounder Bathymetric Measurements for Errors Induced by Inaccurate Water Column Sound Speeds

In this contribution a method for correcting bathymetric measurements affected by inaccurate water column sound speed profiles (SSPs) is presented. The method exploits the redundancy in the multibeam echosounder measurements obtained from the overlap of adjacent swaths by minimizing the difference between depths along overlapping swaths. Two optimization methods are used, i.e., Differential Evolution (DE) and Gauss-Newton (GN). While DE inverts for the sound speed by minimizing the depth variation, GN inverts for both bathymetry and sound speed by minimizing the squared sum of the differences between the modeled and measured travel times. The inversion method assumes a constant SSP in the water column. Applying the method to a salt wedge survey area with large variations in the water column sound speed indicates a good agreement between the original depth measurements and those derived after the inversion with the mean and standard deviation of the depth differences equaling 0.009m and 0.024m, respectively. This indicates that even with a simple parametrization of the sound speed in the water column, the correct bathymetry can be derived from the inversion. The SSP inversion method is also applied to an area with existing refraction artefacts. It corrects the bathymetry and reduces the mean and standard deviation of the depth standard deviation by a factor of around 2.75 compared to the case where the measured SSPs were used. Furthermore, the SSP inversion method neither manipulates the existing morphology nor introduces artificial bathymetric features in the areas where such refraction artefacts are not present. Considering constant SSPs, both DE and GN give almost identical results with GN being faster. However, GN is less flexible with regards to varying sound speed parameterizations.

A three-dimensional bistatic reverberation model of underwater explosion by interface scattering at variable sound speeds

Underwater reverberation is a main limitation of the sonar performance and thereby the reverberation level estimation becomes crucial. In this study, based on the Lambert law and ray theory, a model for predicting 3D bistatic reverberation performance by interface scattering at linear sound speed profile is established and then verified through the underwater explosion experiments. The Influences of source and receiver positions, and relative sound speed gradient on reverberation performance are further investigated. The results indicate that: (1) the proposed model can predict the short-range mean reverberation level effectively, with the deviation 2–4 dB and describe the whole reverberation level distribution in some details; (2) at the early reverberation phase, the interference effects between the interface scattering sounds are considerable and a dominating interface exists; the counterbalance between the losses by scattering, spreading and medium absorption results in the local high-intensity zones close to corresponding interfaces, respectively; (3) as the sound source moves towards some interface, associated local high-intensity zone gradually expands, while the other one shrinks; if the sound speed approaches are constant, an extra local high-intensity zone will appear between the previous two but with a lower magnitude.

Underwater Anchor-AUV Localization Geometries With an Isogradient Sound Speed Profile: A CRLB-Based Optimality Analysis

Existing works have explored anchor deployment for autonomous underwater vehicles (AUVs) localization under the assumption that sound propagates straightly underwater at a constant speed. Considering that the underwater acoustic waves propagate along bent curves at varying speeds in practice, it becomes much more challenging to determine a proper anchor deployment configuration. In this paper, taking the practical variability of underwater sound speed into account, we investigate the anchor-AUV geometry problem in a 3-D time-of-flight-based underwater scenario from the perspective of localization accuracy. To address this problem, we first rigorously derive the Jacobian matrix of measurement errors to quantify the Cramer–Rao lower bound (CRLB) with a widely-adopted isogradient sound speed profile. We then formulate an optimization problem that minimizes the trace of the CRLB subject to the angle and range constraints to figure out the anchor-AUV geometry, which is multivariate and nonlinear, and thus generally hard to handle. For mathematical tractability, by adopting tools from the estimation theory, we interestingly find that this problem can be equivalently transformed into a more explicit univariate optimization problem. By this, we obtain an easy-to-implement anchor-AUV geometry that yields satisfactory localization performance, referred to as the uniform sea-surface circumference (USC) deployment. Extensive simulation results validate our theoretical analysis and show that our proposed USC scheme outperforms both the cube and the random deployment schemes in terms of localization accuracy under the same parameter settings.

Combustion noise analysis of a turbulent spray flame using a hybrid DNS/APE-RF approach

Combustion generated noise of a turbulent spray flame has been investigated using a hybrid Computational Fluid Dynamics/Computational Aero-Acoustics (CFD/CAA) framework. In this two-step framework, the reacting flow-field of a flame is simulated using Direct Numerical Simulations (DNS) in the first step, while the acoustic wave propagation in a non-uniform mean flow is captured by solving the Acoustic Perturbation Equations extended to Reacting Flows (APE-RF) in the second step. The numerical approach used in this study is therefore, termed as the hybrid DNS/APE-RF approach. First, this hybrid DNS/APE-RF approach is used to simulate a benchmark experimental open turbulent non-premixed flame, and the results obtained for the non-premixed flame’s flow-field statistical quantities, as well as radiated sound intensities are extensively validated against experimental data. Next, the hybrid DNS/APE-RF approach is applied to an experimental open turbulent spray flame, for simulating its two-phase reacting flow-field along with its combustion generated acoustic field, to predict and analyze the noise radiation behavior. The DNS results of the spray flame are compared with measurements, in terms of droplet velocity statistics and gas-phase temperatures, and favorable agreement is observed. The computed acoustic power spectra of the spray flame exhibit a power law dependence of the form f−2.4 (where f is the frequency) in the frequency range 300 Hz < f < 1000 Hz. And, the computed noise spectra of the spray flame contain a nearly constant sound pressure level plateau, for frequencies greater than 1000 Hz and up to 3000 Hz. Acoustic refraction effects induced by sound speed variations in the flame, resulting in the attenuation of high-frequency noise radiated in the flame downstream direction, are also captured in the simulation. Noise radiation characteristics of the turbulent spray flame are found to resemble those of turbulent premixed and non-premixed flames.

Full Modeling of High-Intensity Focused Ultrasound and Thermal Heating in the Kidney Using Realistic Patient Models.

High-intensity focused ultrasound (HIFU) therapy can be used for noninvasive treatment of kidney (renal) cancer, but the clinical outcomes have been variable. In this study, the efficacy of renal HIFU therapy was studied using a nonlinear acoustic and thermal simulations in three patients. The acoustic simulations were conducted with and without refraction in order to investigate its effect on the shape, size, and pressure distribution at the focus. The values for the attenuation, sound speed, perfusion, and thermal conductivity of the kidney were varied over the reported ranges to determine the effect of variability on heating. Furthermore, the phase aberration was studied in order to quantify the underlying phase shifts using a second order polynomial function. The ultrasound field intensity was found to drop on average 11.1dB with refraction and 6.4dB without refraction. Reflection at tissue interfaces was found to result in a loss less than 0.1dB. Focal point splitting due to refraction significantly reduced the heating efficacy. Perfusion did not have a large effect on heating during short sonication durations. Small changes in temperature were seen with varying attenuation and thermal conductivity, but no visible changes were present with sound speed variations. The aberration study revealed an underlying trend in the spatial distribution of the phase shifts. The results show that the efficacy of HIFU therapy in the kidney could be improved with aberration correction. A method is proposed by that patient specific pre-treatment calculations could be used to overcome the aberration and therefore make ultrasound treatment possible.

Soft-Tissue Aberration Correction for Histotripsy.

Acoustic aberrations caused by natural heterogeneities of biological soft tissue are a substantial problem for histotripsy, a therapeutic ultrasound technique that uses acoustic cavitation to mechanically fractionate and destroy unwanted target tissue without damaging surrounding tissue. These aberrations, primarily caused by sound speed variations, result in severe defocusing of histotripsy pulses, thereby decreasing treatment efficacy. The gold standard for aberration correction (AC) is to place a hydrophone at the desired focal location to directly measure phase aberrations, which is a method that is infeasible in vivo. We hypothesized that the acoustic cavitation emission (ACE) shockwaves from the initial expansion of inertially cavitating microbubbles generated by histotripsy can be used as a point source for AC. In this study, a 500-kHz, 112-element histotripsy phased array capable of transmitting and receiving ultrasound on all channels was used to acquire ACE shockwaves. These shockwaves were first characterized optically and acoustically. It was found that the shockwave pressure increases significantly as the source changes from a single bubble to a dense cavitation cloud. The first arrival of the shockwave received by the histotripsy array was from the outer-most cavitation bubbles located closest to the histotripsy array. Hydrophone and ACE AC methods were then tested on ex vivo porcine abdominal tissue samples. Without AC, the focal pressure is reduced by 49.7% through the abdominal tissue. The hydrophone AC approach recovered 55.5% of the lost pressure. Using the ACE AC method, over 20% of the lost pressure was recovered, and the array power required to induce cavitation was reduced by approximately 31.5% compared to without AC. These results supported our hypothesis that the ACE shockwaves coupled with a histotripsy array with transmit and receive capability can be used for AC for histotripsy through soft tissue.

Studies on water column nutrient distribution and sound speed profile variations along coastal region of India

This study aim is to measure the water column nutrient and sound velocity variation along the coastal region of Poompuhar, Cuddalore, Mahabalipuram, Kalpakkam, Chennai and Pondicherry. Sound speed variation in the environment of the particular ocean depends on temperature, salinity, and pressure. Since temperature and salinity variations are large compared to pressure. In study locations the sound speed varies from 1445 to 1540m/s, temperature 27 to 290c and salinity 29 to 33psu. Water column nutrients like Nitrate, Nitrite, Phosphate, Silicate and Urea were analyzed to understand the physical and chemical concentration of study location. This nutrient has an inverse relationship with the temperature. Location-based nutrients analysis has been carried to identify the concentration each nutrients level in the particular location. The maximum concentration of nutrients observed in the study locations are silicate in Pondicherry (84%), Nitrite in Kalpakkam (4%), Nitrate in Cuddalore (16%), Phosphate in Chenn...

Measurements and modeling of mid-frequency propagation loss during the Korea Reverberation Experiment 2017 (KOREX-17)

Sound propagation in shallow water is significantly influenced by fluctuation of the water medium and scattering from rough ocean boundaries. To study the effect of the intensity fluctuations caused by the various environmental effects, mid-frequency propagation loss measurements along with the ocean environmental measurements were conducted on May 25–31, 2017, in shallow water off Geoje island, as part of the Korea Reverberation Experiment 2017 (KOREX-17). Continuous wave and linear frequency modulated signal with a center frequency of 3.5 kHz were transmitted by the Autonomous Reverberation Measurement System (ARMS). The Self Recording Hydrophone (SRH) was towed by the R/V Mirae at a speed of approximately 3 knots along two different tracks. Sound speed profiles were measured using the moored CTD chain near the source location, covering the water column between 3 and 50 m. CTD casts were also conducted at the beginning and end of each track. In this talk, the fluctuations of measured propagation losses were presented for both tracks. Finally, the effects of the sound speed variations on the propagation loss will be discussed in comparison with the model predictions obtained using the measured sound speed profiles.

Numerical Modeling of Ultrasound Propagation in Weakly Heterogeneous Media Using a Mixed-Domain Method.

A mixed-domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The present method is based on solving an integral equation derived from a Westervelt-like equation. One-dimensional problems are first studied to verify the MDM and to reveal its limitations. It is shown that this method is accurate for cases with small variation of sound speed. A 2-D case is further studied with focused ultrasound beams to validate the application of the method in the medical field. Results from the MATLAB toolbox k-Wave are used as the benchmark. Normalized root-mean-square (rms) error estimated at the focus of the transducer is 0.0133 when the coarsest mesh (1/3 of the wavelength) is used in the MDM. Fundamental and second-harmonic fields throughout the considered computational domains are compared and good agreement is observed. Overall, this paper demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities.

Stochastic matched-field localization of an acoustic source based on principles of Riemannian geometry.

Passive localization of acoustic sources is treated within a geometric framework where non-Euclidean distance measures are computed between a cross-spectral density estimate of received data on a vertical array and a set of stochastic replica steering matrices, rather than traditional replica steering vectors. A processing scheme involving matrix-matrix comparisons where steering matrices, as functions of the replica source coordinates, naturally incorporate environmental variability or uncertainty provides a general framework for considering the acoustic inverse source problem in an ocean waveguide. Within this context a subset of matched-field processors is examined, based on recent advances in the application of non-Euclidean geometry to statistical classification of data feature clusters. The matrices are interpreted abstractly as points in a Riemannian manifold, and an appropriately defined distance measure between pairs of matrices on this manifold defines a matched-field processor for estimating source location. Acoustic simulations are performed for a waveguide comprising both a depth-dependent sound-speed profile perturbed by linear internal gravity waves and a depth-correlated surface noise field, providing an example of the viability of this approach to passive source localization in the presence of sound-speed variability.

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.

Robust analysis method for acoustic properties of biological specimens measured by acoustic microscopy

We proposed a robust analysis method for the acoustic properties of biological specimens measured by acoustic microscopy. Reflected pulse signals from the substrate and specimen were converted into frequency domains to obtain sound speed and thickness. To obtain the average acoustic properties of the specimen, parabolic approximation was performed to determine the frequency at which the amplitude of the normalized spectrum became maximum or minimum, considering the sound speed and thickness of the specimens and the operating frequency of the ultrasonic device used. The proposed method was demonstrated for a specimen of malignant melanoma of the skin by using acoustic microscopy attaching a concave transducer with a center frequency of 80 MHz. The variations in sound speed and thickness analyzed by the proposed method were markedly smaller than those analyzed by the method based on an autoregressive model. The proposed method is useful for the analysis of the acoustic properties of bilogical tissues or cells.

Quantitative photoacoustic imaging in the acoustic regime using SPIM

While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this paper we present an approach for photoacoustic imaging, which in addition to the recovery of the absorption density parameter, the imaging parameter of standard photoacoustics, also allows us to reconstruct the spatially varying sound speed and density, respectively, of the medium. We provide analytical reconstruction formulas for all three parameters based in a linearized model based on single plane illumination microscopy (SPIM) techniques.

Variable sound speed in interacting dark energy models

We consider a self-consistent and physical approach to interacting dark energy models described by a Lagrangian, and identify a new class of models with variable dark energy sound speed. We show that if the interaction between dark energy in the form of quintessence and cold dark matter is purely momentum exchange this generally leads to a dark energy sound speed that deviates from unity. Choosing a specific sub-case, we study its phenomenology by investigating the effects of the interaction on the cosmic microwave background and linear matter power spectrum. We also perform a global fitting of cosmological parameters using CMB data, and compare our findings to ΛCDM.

A Green’s function parabolic equation description of infrasound propagation in an inhomogeneous and moving atmosphere

Accurate atmospheric infrasound propagation models must account for variations in local sound speed and ambient flow. This paper describes and demonstrates a method to extend the Green’s function parabolic equation (GFPE) to account for 3D high Mach number ambient flow in addition to an inhomogeneous atmosphere. Predictions of infrasonic propagation using the resulting GFPE model are then compared with predictions using other models.

Normal mode coupling through horizontally variable sound speed

In conjunction with construction of a normal mode model specifically designed to compute acoustic propagation in shallow water environments, the coupling associated with horizontally variable sound speed is predicted using a closed form solution in a modified Pekeris wave guide with a hard bottom. The code enables analysis of the correspondence between mode summation and the corresponding wave propagation as represented by ray propagation. The closed form solution is being used to provide insights into horizontal mode coupling and as a benchmark for verification of coupling in the shallow water normal mode solution.In conjunction with construction of a normal mode model specifically designed to compute acoustic propagation in shallow water environments, the coupling associated with horizontally variable sound speed is predicted using a closed form solution in a modified Pekeris wave guide with a hard bottom. The code enables analysis of the correspondence between mode summation and the corresponding wave propagation as represented by ray propagation. The closed form solution is being used to provide insights into horizontal mode coupling and as a benchmark for verification of coupling in the shallow water normal mode solution.

A High Order Compact Time/Space Finite Difference Scheme for the Wave Equation with Variable Speed of Sound

We consider fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound. We demonstrate that usually this is much more efficient than lower order schemes despite being implicit and only conditionally stable. Fast time marching of the implicit scheme is accomplished by iterative methods such as conjugate gradient and multigrid. For conjugate gradient, an upper bound on the convergence rate of the iterations is obtained by eigenvalue analysis of the scheme. The implicit discretization technique is such that the spatial and temporal convergence orders can be adjusted independently of each other. In special cases, the spatial error dominates the problem, and then an unconditionally stable second order accurate scheme in time with fourth order accuracy in space is more efficient. Computations confirm the design convergence rate for the inhomogeneous, variable wave speed equation and also confirm the pollution effect for these time dependent problems.