Average Sound Speed Research Articles

Spatial Ambiguity Correction in Coherence-Based Average Sound Speed Estimation.

Sound speed estimation can potentially correct the focusing errors in medical ultrasound. Maximizing the echo spatial coherence as a function of beamforming sound speed is a known technique to estimate the average sound speed. However, beamformation with changing sound speed causes a spatial shift of the echo signals resulting in noise and registration errors in the average sound speed estimates. We show that the spatial shift can be predicted and corrected, leading to superior sound speed estimates. Methods are presented for axial and 2-D location correction. Methods were evaluated using simulations and experimental phantom data. The location correction strategies improved the variance of sound speed estimates and reduced artifacts in the presence of strong backscatter variations. Limitations of the proposed methods and potential improvement strategies were evaluated.

Predictive Modeling of Future Full-Ocean Depth SSPs Utilizing Hierarchical Long Short-Term Memory Neural Networks

The spatial-temporal distribution of underwater sound speed plays a critical role in determining the propagation mode of underwater acoustic signals. Therefore, rapid estimation and prediction of sound speed distribution are imperative for facilitating underwater positioning, navigation, and timing (PNT) services. While sound speed profile (SSP) inversion methods offer quicker response times compared to direct measurement methods, these methods often focus on constructing spatial sound velocity fields and heavily rely on sonar observation data, thus imposing stringent requirements on data sources. To delve into the temporal distribution pattern of sound speed and achieve SSP prediction without relying on sonar observation data, we introduce the hierarchical long short-term memory (H-LSTM) neural network for SSP prediction. Our method enables the estimation of sound speed distribution without the need for on-site data measurement, significantly enhancing time efficiency. Compared to other state-of-the-art approaches, the H-LSTM model achieves a root mean square error (RMSE) of less than 1 m/s in predicting monthly average sound speed distribution. Its prediction accuracy has improved several-fold over alternative methods, which validates the robust capability of our proposed model in predicting SSP.

A Method for Full-Depth Sound Speed Profile Reconstruction Based on Average Sound Speed Extrapolation

The speed of sound in seawater plays a crucial role in determining the accuracy of multibeam bathymetric measurements. In deep-sea multibeam measurements, the challenge of inadequate longitudinal coverage of sound speed profiles arises from variations in seafloor topography, meteorological conditions, measurement equipment, and operational efficiency, resulting in diminished measurement precision. Building upon the EOF (Empirical Orthogonal Function), a method employed to analyze spatiotemporal data such as sound speeds, this paper addresses the limitations of the EOF method caused by the shallowest sampling depth of the sound speed profile samples. It proposes two methods for EOF reconstruction of measured sound speed profiles extended to full water depth by splicing measured sound speed profiles at non-full water depths with historical average sound speed profiles of the surveyed sea area. Specially, Method 2 introduces the latest metaheuristic optimization algorithm, CPO (Crested Porcupine Optimizer), which exhibited superior performance on multiple standard test functions in 2024. The study reconstructs randomly sampled measured sound speed profiles using the two proposed methods and commonly employed substitution and splicing methods, followed by a comparative analysis of the experimental outcomes. At a sampling depth of 200 m, Method 2 demonstrates performance superior to other methods, with RMSE, MAE, MAPE, and R2 values of 0.9511 m/s, 0.8492 m/s, 0.0566%, and 0.9963, respectively. Method 1 yields corresponding values of 0.9594 m/s, 0.8492 m/s, 0.0568%, and 0.9962, respectively. Despite its slightly inferior performance compared with Method 2, it offers substantial advantages over the substitution and splicing methods. Varying the sampling depth of measured sound speed profiles reveals that Methods 1 and 2 exhibit inferior reconstruction performance in shallow water compared with the substitution and splicing methods. Nevertheless, when the sampling depth surpasses the depth range of initial spatial modes with abrupt variations, both methods achieve notably higher reconstruction accuracy compared with the substitution and splicing methods, reaching a stabilized state. Sound ray tracing reveals that the reconstructed sound speed profiles from both methods meet the stringent accuracy standards for bathymetric measurements, achieving an effective beam ratio of 100%. The proposed methods not only provide rapid reconstruction of sound speed profiles, thereby improving the efficiency of multibeam bathymetric surveys, but also provide references for the reasonable determination of sampling depths of sound speed profiles to ensure reconstruction accuracy, demonstrating practical application value.

Ultrasound channel attention residual network for medical plane wave echo data-based average sound speed estimation

The average sound speed estimation is crucial for ultrasound imaging quality and diagnostic. In this article, the deep learning techniques were utilized and an innovative Ultrasound Channel Attention Residual Network (UCA-ResNet) was proposed. The UCA-ResNet incorporated a specially designed Ultrasound Channel Attention (UCA) block, which effectively enhanced relevant ultrasound channel features and convolutional channel features. For evaluation, the simulation, phantom, and in vivo experiments were conducted. In the simulation experiment, UCA-ResNet achieved remarkable results, with a mean absolute error (MAE) of 0.40 m/s, root mean square error (RMSE) of 1.25 m/s, standard deviation of error (SDE) of 1.25 m/s, and a one-time estimation time of 3.67 ms. Moreover, the phantom and in vivo experiments further validated the high accuracy and low computational cost of UCA-ResNet. The UCA-ResNet can accurately estimate the average sound speed using a single plane wave echo data while maintaining low computational cost. It has potential in enhancing medical ultrasound imaging quality and providing novel diagnostic insights. (Code and data will be available upon acceptance of the manuscript.)

Passive acoustic localization using dictionary learning

Ray-trace simulations are used to demonstrate the use of Dictionary Learning to improve passive localization of a source monitored with a vertical linear acoustic array. The learned dictionary, generated using historical sound velocity profile (SVP) data from a region of interest, is an over complete, sparse representation of the SVP training set. By minimizing an objective function that measures the differences between multipath reception intervals detected at a receiver for propagation through candidate and baseline SVP profiles, we show that an optimal SVP match to the “unknown” baseline can be reconstructed by an efficient dictionary search. Ray traces back-propagated through the reconstructed SVP according to beamformed receive angles computed with the baseline SVP are then found to well estimate the source position as the centroid of a cluster of multipath signal intersections. The accuracy for small unit-sparsity dictionaries of size up to 50 was evaluated on a randomly sampled, 30 SVP testing set obtained from an area close to that of the training set, demonstrating mean location errors less than 5% in both distance and depth. Five representative profiles spanning the range of observed sound speed variations were used to assess localization performance at source depths from 50 to 450 m and at source ranges from 2000 to 4500 m. Compared to using the average sound speed profile to estimate source position, using the learned dictionary produced a general performance increase in position accuracy.

Investigation of a method to estimate the average speed of sound using phase variances of element signals for ultrasound compound imaging

PurposeIn the receive beamforming of an ultrasonography system, a B-mode image is reconstructed by assuming an average speed of sound (SoS) as a constant value. In our previous studies, we proposed a method for estimating the average SoS based on the coherence factor (CF) and the reciprocal of phase variances of element signals in delay-and-sum (DAS) beamforming. In this paper, we investigate the accuracy of estimation of the average SoS for compound imaging.MethodsFor this purpose, two numerical simulations were performed with k-Wave software. Also, the estimation methods based on the CF and the reciprocal were applied to in vivo data from the common carotid artery, and B-mode images were reconstructed using the estimated average SoS.ResultsIn the first numerical simulation using an inhomogeneous phantom, the relationship between the accuracy and the transmission angles for the estimation was investigated, and the root mean squared errors (RMSEs) of estimates obtained based on the CF and the reciprocal of the phase variance were 1.25 ± 0.09, and 0.765 ± 0.17% at the transmission sequence of steering angles of (− 10°, − 5°, 0°, 5°, 10°), respectively. In the second numerical simulation using a cyst phantom, lateral resolutions were improved by reconstructing the image using the estimates obtained using the proposed strategy (reciprocal). By the proposed strategy, improvement of the continuity of the lumen–intima interface in the lateral direction was observed in the in vivo experiment.ConclusionConsequently, the results indicated that the proposed strategy was beneficial for estimation of the average SoS and image reconstruction.

Time spreading of a target echo from a short pulse in a waveguide

The normal mode approach has proven very useful for calculating reverberation in a shallow water waveguide. Generally the calculation is done as a function of range r, then the time dependence t is obtained via t = 2r/c, where c is some average sound speed. This assumes that all the multipath returns from a particular scattering point arrive at the same time. A better time dependence can be obtained by using mode group velocities [D. Ellis, J. Acoust. Soc. Am. 97, 2804–2814 (1995)]. For reverberation from a uniform bottom this only has a small effect compared to the simple approach. However, for a compact scattering feature or target, the time spreading for a short pulse can be quite significant. Analytical results for an isospeed waveguide have been previously obtained using an energy flux approach. Here, a model using modal group velocities is used to calculate the time dependence of an echo from a target or compact reverberation feature. The mode approach extends to a general sound speed profile. One can convolve the impulse response with the amplitude envelope of the transmitted pulse to obtain the echo time decay. [Work supported by Mount Allison University, and US Office of Naval Research.]

Ex vivo evaluation of the sensitivity of modified average speed of sound estimation method

The speed of sound (SoS), which is the propagation speed of longitudinal waves, is expected to be effective for the early detection and monitoring of diseases. Several methods that use handheld probes have been proposed to estimate the SoS. In this study, a modified average SoS estimation method, referred to as the improved focusing method, is proposed to increase the accuracy of average SoS estimation. In the proposed method, a plane wave was transmitted, and the center-element position-dependent variations in the SoS estimation were reduced. Ex vivo experiments were conducted using chicken liver to evaluate the applicability and sensitivity of the proposed method to actual tissues. The livers were subjected to continuous temperature changes to induce changes in the SoS. The results suggest that the improved focusing method measures the average SoS accurately as well as small SoS changes of approximately 1.5 m·s−1·°C−1.

First principles and mean field study on the magnetocaloric effect of YFe3 and HoFe3 compounds

In this work, the magnetothermal characteristics and magnetocaloric effect in YFe3 and HoFe3 compounds are calculated as function of temperature and magnetic field. These properties were investigated using the two-sublattice mean field model and the first-principles DFT calculation using the WIEN2k code. The two-sublattice model of the mean-field theory was used to calculate the temperature and field-dependences of magnetization, magnetic heat capacity, magnetic entropy, and the isothermal change in entropy ∆Sm. We used the WIEN2k code to determine the elastic constants and, subsequently, the bulk and shear moduli, the Debye temperature, and the density-of-states at Ef. According to the Hill prediction, YFe3 has bulk and shear moduli of roughly 99.3 and 101.2 GPa respectively. The Debye temperature is ≈ 500 K, and the average sound speed is ≈ 4167 m/s. In fields up to 60 kOe and at temperatures up to and above the Curie point for both substances, the trapezoidal method was used to determine ∆Sm. For instance, the highest ∆Sm values for YFe3 and HoFe3 in 30 kOe are approximately 0.8 and 0.12 J/mol. K, respectively. For the Y and Ho systems, respectively, the adiabatic temperature change in a 3 T field decreases at a rate of around 1.3 and 0.4 K/T. The ferro (or ferrimagnetic) to paramagnetic phase change in these two compounds, as indicated by the temperature and field dependences of the magnetothermal and magnetocaloric properties, ∆Sm and ∆Tad, is a second-order phase transition. The Arrott plots and the universal curve for YFe3 were also calculated and their features give an additional support to the second order nature of the phase transition.

Maximum entropy inference of seabed properties using waveguide invariant features from surface ships.

Acoustic data were recorded on two vertical line arrays (VLAs) deployed in the New England Mud Patch during the Seabed Characterization Experiment 2017 in about 75 m of water. The sound recorded during the passage of merchant ships permits identification of singular points for the waveguide invariant β for mode pairs (1,n):β1,n,for n=2,3,4,5, in the 15-80 Hz band. Using prior geophysical information and an acoustic data sample from the merchant ship KALAMATA, a geoacoustic model M of the seabed was developed. Then, using data samples from other merchant ships, a feature-ensemble maximum entropy method is employed to infer the statistical properties of geoacoustic parameter values for the sound speeds in a surface mud layer and a deep sand layer. Technical challenges include a sparsity of observed singular points, the unique identification of mode pairs for an observed singular point, and the deviation of the waveguide from horizontal stratification. A geoacoustic model M is developed that reproduced the observed β≈-1 for f < 20 Hz and mode cutoff features at about 15 Hz. The statistical low-frequency inference of the singular point structure from multiple ships provides evidence of an angle of intromission at the water sediment interface with an average sound speed ratio of about 0.986 and an average sound speed for the deeper sand layer of about 1775 m/s.

Local Sound Speed Estimation for Pulse-Echo Ultrasound in Layered Media.

Our previous methodology in local sound speed estimation utilized time delays measured by the cross correlation of delayed full-synthetic aperture channel data to estimate the average speed of sound. However, focal distortions in this methodology lead to biased estimates of the average speed of sound, which, in turn, leads to biased estimates of the local speed of sound. Here, we demonstrate the bias in the previous methodology and introduce a coherence-based average sound speed estimator that eliminates this bias and is computationally much cheaper in practice. Because this coherence-based approach estimates the average sound speed in the medium over an equally spaced grid in depth rather than time, we derive a refined model that relates the local and average speeds of sound as a function of depth in layered media. A fast, closed-form inversion of this model yields highly accurate local sound speed estimates. The root-mean-square (rms) error of local sound speed reconstruction in simulations of two-layer media is 4.6 and 2.5 m/s at 4 and 8 MHz, respectively. This work examines the impact of frequency, f -number, aberration, and reverberation on sound speed estimation. Phantom and in vivo experiments in rats further validate the coherence-based sound speed estimator.

3Pb5-2 Ex vivo evaluation on the accuracy of modified average sound speed estimation

3Pb5-2 Ex vivo evaluation on the accuracy of modified average sound speed estimation

A new underwater positioning model based on average sound speed

AbstractThe layout of seafloor datum points is the key to constructing the seafloor geodetic datum network, and a reliable underwater positioning model is the prerequisite for achieving precise deployment of the datum points. The traditional average sound speed positioning model is generally adopted in underwater positioning due to its simple and efficient algorithm, but it is sensitive to incident angle related errors, which lead to unreliable positioning results. Based on the relationship between incident angle and sound speed, the sound speed function model considering the incident angle has been established. Results show that the accuracy of positioning is easily affected by errors related to the incident angle; the new average sound speed correction model based on the incident angle proposed in this paper is used to significantly improve the underwater positioning accuracy.

Relation between statistical properties of sound speed distribution and average sound speed estimation

The speed of sound (SOS), which is the propagation speed of longitudinal waves, is a promising index for early detection and monitoring of diseases, and many measurement methods have been proposed. It has already been found that the average SOS can be easily and reasonably estimated for a homogeneous medium based on time-delay processing by utilizing the method using backscattered waves, which enables the use of handheld probes. However, the error caused by the application of the method to an inhomogeneous medium has not yet been clarified. In this study, we investigate the relationship between statistical properties of the SOS distribution and the measurement error through a simulation and a phantom experiment. As a result, it is revealed that if the spatial variation of the SOS distribution is below a certain level, the average SOS can be estimated under the assumption of a homogeneous medium.

Reliability evaluation of average sound speed estimation using backscattered waves of ultrasound

Reliability evaluation of average sound speed estimation using backscattered waves of ultrasound

Noninvasive multiparametric characterization of mammary tumors with transmission-reflection optoacoustic ultrasound

Development of imaging methods capable of furnishing tumor-specific morphological, functional, and molecular information is paramount for early diagnosis, staging, and treatment of breast cancer. Ultrasound (US) and optoacoustic (OA) imaging methods exhibit excellent traits for tumor imaging in terms of fast imaging speed, ease of use, excellent contrast, and lack of ionizing radiation. Here, we demonstrate simultaneous tomographic whole body imaging of optical absorption, US reflectivity, and speed of sound (SoS) in living mice. In vivo studies of 4T1 breast cancer xenografts models revealed synergistic and complementary value of the hybrid imaging approach for characterizing mammary tumors. While neovasculature surrounding the tumor areas were observed based on the vascular anatomy contrast provided by the OA data, the tumor boundaries could be discerned by segmenting hypoechoic structures in pulse-echo US images. Tumor delineation was further facilitated by enhancing the contrast and spatial resolution of the SoS maps with a full-wave inversion method. The malignant lesions could thus be distinguished from other hypoechoic regions based on the average SoS values. The reported findings corroborate the strong potential of the hybrid imaging approach for advancing cancer research in small animal models and fostering development of new clinical diagnostic approaches.

Ultrasound DMAS Beamforming for Estimation of Tissue Speed of Sound in Multi-Angle Plane-Wave Imaging

Various methods have been proposed to estimate the tissue speed of sound (SOS) of propagating medium using the curvature of received channel waveform or the analysis of resultant image quality. In our previous study, baseband delay-multiply-and-sum (DMAS) beamforming methods have been developed for multi-angle plane-wave (PW) imaging which relies on signal coherence among transmit events (Tx-DMAS) or receive channel (Rx-DMAS) or both (2D-DMAS) to suppress low-coherence clutters. In this study, we further extend our DMAS beamforming to quantify the level of signal coherence for determining the average SOS in multi-angle PW imaging. The signal coherence in multi-angle PW imaging is represented as the DMAS coherence factor (DCF) which can be easily estimated from the magnitude ratio of the pixel value of DMAS image to that of DAS image. By searching the beamforming velocity that provides the highest signal coherence of echo matrix, the average tissue SOS of the imaged object can be determined. For the PICMUS experimental dataset, the optimal beamforming velocity (Copt) estimated by the proposed DCF method does provide the best image quality. For the Prodigy dataset, the estimated tissue SOS is 1426 ± 6 m/s which is very close to the actual tissue SOS of 1427 m/s and the estimated SOS also corresponds to the Copt with the minimal −6-dB lateral width and the maximal contrast within an error of 10 m/s. Estimation of tissue SOS in the proposed DCF method is also robust even in the presence of transmit delay error due to deviation of SOS.

Attenuation of the human skull at broadband frequencies by using a carbon nanotube composite photoacoustic transducer.

The shockwave generated from a focused carbon nanotube (CNT) composite photoacoustic transducer has a wide frequency band that reaches several MHz in a single pulse. The objective of this study was to measure the transmission characteristics of a shockwave generated by a CNT composite photoacoustic transducer through Asian skulls and compare the results with numerical simulation ones. Three Korean cadaver skulls were used, and five sites were measured for each skull. The average densities and sound speeds of the three skulls were calculated from computed tomography images. The sound pressure after skull penetration was about 11% of the one before skull penetration. High-frequency energy was mostly attenuated. The average attenuation coefficients measured at the five sites of the three skulls were 3.59 ± 0.29, 5.99 ± 1.07, and 3.90 ± 0.86 np/cm/MHz. These values were higher than those previously measured at 270, 836, and 1402 kHz from other groups. The attenuation coefficients simulated by Sim4life were slightly smaller than the experimental values, with similar trends at most sites. The attenuation coefficients varied with measurement sites, skull shape, and thickness. These results may provide important data for future applications of shockwaves in noninvasive neurological treatments.

Effect of Sound-Speed Inhomogeneities in Sea Bottom on the Acoustic Wave Propagation in Shallow Water

The effect of volume inhomogeneities in the sea bottom upper layer (sediments) on the long-range sound propagation in shallow water is analyzed. The experimental basis for developing inhomogeneous bottom models are the data of 3D seismic survey on the spatial structure of sediments in the Kara Sea, where variations of ~10% in the average sound speed in the bottom are observed at ranges of ~1 km. The mode coupling due to bottom volume inhomogeneities is revealed within the normal mode approach. Coupled mode equations are derived not only for propagating modes but also for leaky modes and quasimodes; including these types of modes may be urgent in analysis of the waveguides where the sound speed in the bottom (c1) is less or approximately equal to the sound speed in water (c). Numerical simulations show that the coupling between energy-carrying modes is maximum at c1 ≈ c. Calculations of the attenuation of depth-averaged sound field intensity in a water layer, performed for the Kara Sea at ranges of up to 5 km, show that the mode coupling due to bottom volume inhomogeneities can be neglected, and the depth-averaged transmission loss can be calculated using the adiabatic approximation at frequencies below a few hundred hertz. When analyzing the depth-averaged intensity, the effects of mode coupling on bottom inhomogeneities can be observed only by implementing special conditions, for example, using mode arrays providing maximally pure (free of other modes) radiation of a specified mode.

Speed of sound evaluation considering spatial resolution in a scanning acoustic microscopy system capable of observing wide spatial area

The dependence of the speed of sound (SoS) in sliced rat organs on the spatial resolution was investigated through ultrasound analysis at high frequencies (80 and 250 MHz). The radio-frequency echo signals from target were acquired by a scanning acoustic microscopy system developed by the authors that can observe a sample with a transducer. The SoS was evaluated by correcting for the time of flight difference obtained from the wide area measurement. The dependency of the SoS on the spatial resolution was evaluated by applying different filtering methods. Stable analysis was possible after time correction, and fine textures reflecting the microstructure could be observed. The application of different filters to the results obtained at 250 MHz resulted in average SoS values that were similar to those obtained at 80 MHz. These results suggest that the primary targets evaluated 80 and 250 MHz are connective tissue and single cells, respectively.