Sound Speed Estimation Research Articles

Passive Cavitation Mapping by Cavitation Source Localization From Aperture-Domain Signals-Part I: Theory and Validation Through Simulations.

Passive cavitation mapping (PCM) algorithms for diagnostic ultrasound arrays based on time exposure acoustics (TEA) exhibit poor axial resolution, which is in part due to the diffraction-limited point spread function of the imaging system and poor rejection by the delay-and-sum beamformer. In this article, we adapt a method for speed of sound estimation to be utilized as a cavitation source localization (CSL) approach. This method utilizes a hyperbolic fit to the arrival times of the cavitation signals in the aperture domain, and the coefficients of the fit are related to the position of the cavitation source. Wavefronts exhibiting poor fit to the hyperbolic function are corrected to yield improved source localization. We demonstrate through simulations that this method is capable of accurate estimation of the origin of coherent spherical waves radiating from cavitation/point sources. The average localization error from simulated microbubble sources was 0.12 ± 0.12mm ( 0.15 ± 0.14λ0 for a 1.78-MHz transmit frequency). In simulations of two simultaneous cavitation sources, the proposed technique had an average localization error of 0.2mm ( 0.23λ0 ), whereas conventional TEA had an average localization error of 0.81mm ( 0.97λ0 ). The reconstructed PCM-CSL image showed a significant improvement in resolution compared with the PCM-TEA approach.

Cavitating flow behind a backward facing step

Flow topology and unsteady cavitation dynamics in the wake of a backward facing step was investigated using high speed videography and time-resolved X-ray densitometry, along with static and dynamic pressure measurements. The measurements are used to inform the understanding of underlying mechanisms of observed flow dynamics as they are related to shock wave induced instabilities. The differences in cavity topology and behavior at different cavitation numbers are examined to highlight flow features such as the pair of cavitating spanwise vortices in the shear layer and propagating bubbly shock front. The shock speeds at different cavitation conditions are estimated based on void-fraction measurements using the X-T diagram and compared to those computed using the one-dimensional Rankine Hugoniot jump condition. The two speeds(computed and measured) are found to be comparable. The effect of compressibility of the bubbly mixture is determined by estimating the local speed of sound using homogeneous ‘frozen model’ and homogeneous ‘equilibrium model’. The current estimation of sound speed suggests that expression used to determine the local speed of sound is closer to the classic ‘frozen model’ than the ‘equilibrium model’ of speed of sound.

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

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

Deep Learning for Ultrasonic Crack Characterization in NDE

Machine learning for nondestructive evaluation (NDE) has the potential to bring significant improvements in defect characterization accuracy due to its effectiveness in pattern recognition problems. However, the application of modern machine learning methods to NDE has been obstructed by the scarcity of real defect data to train on. This article demonstrates how an efficient, hybrid finite element (FE) and ray-based simulation can be used to train a convolutional neural network (CNN) to characterize real defects. To demonstrate this methodology, an inline pipe inspection application is considered. This uses four plane wave images from two arrays and is applied to the characterization of cracks of length 1-5 mm and inclined at angles of up to 20° from the vertical. A standard image-based sizing technique, the 6-dB drop method, is used as a comparison point. For the 6-dB drop method, the average absolute error in length and angle prediction is ±1.1 mm and ±8.6°, respectively, while the CNN is almost four times more accurate at ±0.29 mm and ±2.9°. To demonstrate the adaptability of the deep learning approach, an error in sound speed estimation is included in the training and test set. With a maximum error of 10% in shear and longitudinal sound speed, the 6-dB drop method has an average error of ±1.5 mmm and ±12°, while the CNN has ±0.45 mm and ±3.0°. This demonstrates far superior crack characterization accuracy by using deep learning rather than traditional image-based sizing.

Prediction of Sound Speed in Natural-Gas Mixtures Using the CP-PC-SAFT Equation of State

An equation of state based on the perturbed-chain statistical associating fluid theory (PC-SAFT) for estimates of sound speed in natural-gas mixtures is successfully applied in this work. Prediction results of the speed of sound for five binary and six multicomponent systems (dataset includes 1000 data points taken from literature) containing hydrocarbons, nitrogen, and carbon dioxide in a wide range of temperatures (250–415 K) and pressures (0.1–60 MPa) are presented. The fitting parameters of the binary interaction were not used in the calculations. The results of modeling for the speed of sound are shown to be in good agreement with the literature data.

Phase speed in water-saturated sand and glass beads at MHz frequencies.

Measurements of the phase velocity of compressional sound waves in water-saturated granular materials are reported for the 1.0-2.0 MHz frequency range. The sound speed estimates are based on travel times through granular layer thicknesses ranging from 8 to 17 mm. Three types of granular media were used: 336 μm median diameter glass beads and two natural sands with median diameters of 219 and 406 μm. These grain sizes and frequency range correspond to 0.5<ka<1.2, where k is the wavenumber and a the grain radius. To remove trapped air, the samples were boiled under pressure before transfer to the measurement tank. The results are compared to previously reported experimental results and to the Schwartz and Plona [J. Appl. Phys. 55(11), 3971-3977 (1984)] multiple scattering prediction, confirming negative dispersion for ka > 0.5. Scaling the data by a factor depending on porosity and grain density reduces the spread among the available phase speed estimates by nearly a factor of 2, from 12.5% to 6.9%.

Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of partial differential equations to the loss function. Our PINNs is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a trainable hyperparameter, which is optimized to achieve the best performance of the network. The adaptive activation function changes dynamically, involved in the optimization process. The usage of the adaptive activation function significantly improves the convergence, evidently observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

On global smooth solutions of 3-D compressible Euler equations with vanishing density in infinitely expanding balls

In this paper, we are concerned with the global smooth solution problem for 3-D compressible isentropic Euler equations with vanishing density in an infinitely expanding ball. It is well-known that the classical solution of compressible Euler equations generally forms the shock as well as blows up in finite time due to the compression of gases. However, for the rarefactive gases, it is expected that the compressible Euler equations will admit global smooth solutions. We now focus on the movement of compressible gases in an infinitely expanding ball. Because of the conservation of mass, the fluid in the expanding ball becomes rarefied meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. We will confirm this interesting phenomenon from the mathematical point of view. Through constructing some anisotropy weighted Sobolev spaces, and by carrying out the new observations and involved analysis on the radial speed and angular speeds together with the divergence and rotations of velocity, the uniform weighted estimates on sound speed and velocity are established. From this, the pointwise time-decay estimate of sound speed is obtained, and the smooth gas fluids without vacuum are shown to exist globally.

1Pb5-6 Relation between statistical properties of sound speed distribution and average sound speed estimation

1Pb5-6 Relation between statistical properties of sound speed distribution and average sound speed estimation

Extending Retrospective Encoding for Robust Recovery of the Multistatic Data Set.

Robust recovery of multistatic synthetic aperture data from conventional ultrasound sequences can enable complete transmit-and-receive focusing at all points in the field of view without the drawbacks of virtual-source synthetic aperture and further enables more advanced imaging applications, such as backscatter coherence, sound speed estimation, and phase aberration correction. Recovery of the multistatic data set has previously been demonstrated on a steered transmit sequence for phased arrays using an adjoint-based method. We introduce two methods to improve the accuracy of the multistatic data set. We first modify the original technique used for steered transmit sequences by applying a ramp filter to compensate for the nonuniform frequency scaling introduced by the adjoint-based method. Then, we present a regularized inversion technique that allows additional aperture specification and is intended to work for both steered transmit and walking aperture sequences. The ramp-filtered adjoint and regularized inversion techniques, respectively, improve the correlation of the recovered signal with the ground truth from 0.9404 to 0.9774 and 0.9894 in steered transmit sequences and 0.4610 to 0.4733 and 0.9936 in walking aperture sequences.

A Computationally Efficient Mean Sound Speed Estimation Method Based on an Evaluation of Focusing Quality for Medical Ultrasound Imaging

Generally, ultrasound receive beamformers calculate the focusing time delays of fixed sound speeds in human tissue (e.g., 1540 m/s). However, phase distortions occur due to variations of sound speeds in soft tissues, resulting in degradation of image quality. Thus, an optimal estimation of sound speed is required in order to improve image quality. Implementation of real-time sound speed estimation is challenging due to high computational and hardware complexities. In this paper, an optimal sound speed estimation method with a low-cost hardware resource is presented. In the proposed method, the optimal mean sound speed is determined by measuring the amplitude variance of pre-beamformed radio-frequency (RF) data. The proposed method was evaluated with phantom and in vivo experiments, and implemented on Virtex-4 with Xilinx ISE 12.4 using VHDL. Experiment results indicate that the proposed method could estimate the mean optimal sound speed and enhance spatial resolution with a negligible increase in the hardware resource usage.

In situ measurements of compressional and shear wave properties during gravity coring operations

Sediment cores provide valuable insight about the physical properties of the seabed, and laboratory measurements of sediment wave speed from cores are often considered “ground truth.” However, sound-speed estimates obtained from cores can be inaccurate due to changes in pressure, temperature, and mechanical properties of the sediment caused by the removal of the core from the seabed and its subsequent transport to the laboratory. To address these issues, the Acoustic Coring System (ACS) was developed. The system uses sets of transducers mounted below the penetrating tip of a sediment corer to make in situ measurements of geoacoustic properties as the corer penetrates the seabed. Compressional wave measurements are obtained with rod-mounted piezoelectric cylinders, and shear wave measurements are obtained with bender elements mounted in flat blades. The ACS was deployed during the environmental survey for ONR Seabed Characterization Experiment (SBCEX) in 2016 and in support of the ONR Canada Basin Acoustic Propagation Experiment (CANAPE) in 2017. In both cases, the system provided measurements of the sediment sound-speed profile as a function of depth within the seabed. On-going work focused on the measurement of shear wave speed profiles and compressional and shear wave attenuation will also be presented. [Work supported by ONR.]Sediment cores provide valuable insight about the physical properties of the seabed, and laboratory measurements of sediment wave speed from cores are often considered “ground truth.” However, sound-speed estimates obtained from cores can be inaccurate due to changes in pressure, temperature, and mechanical properties of the sediment caused by the removal of the core from the seabed and its subsequent transport to the laboratory. To address these issues, the Acoustic Coring System (ACS) was developed. The system uses sets of transducers mounted below the penetrating tip of a sediment corer to make in situ measurements of geoacoustic properties as the corer penetrates the seabed. Compressional wave measurements are obtained with rod-mounted piezoelectric cylinders, and shear wave measurements are obtained with bender elements mounted in flat blades. The ACS was deployed during the environmental survey for ONR Seabed Characterization Experiment (SBCEX) in 2016 and in support of the ONR Canada Basin Acoustic...

Geoacoustic Inversion for a New England Mud Patch Sediment Using the Silt-Suspension Theory of Marine Mud

This article provides an application of the silt-suspension theory to a Bayesian-inference inversion for the geo-acoustic parameters in marine mud. The theory, with consequences that have been developed recently, postulates a suspension of water and clay mineral card-houses that supports moderately dilute concentrations of silt particles. The approach is an example of a physically based model inversion, in which parameters representing physical mud-layer properties are obtained by inversion and used to produce estimates of geoacoustic properties, including their frequency dependence. The acoustic data are from a combustive source signal propagated along a track, located over several meters of fine-grained mud in the New England Mud Patch, to a single hydrophone on a receiver array during the 2017 Seabed Characterization Experiment. Data extracted from a nearby piston core inform the physical modeling, with selections of inversion parameters guided by both sensitivity analyses and bounds from archival and core measurements. Results show the feasibility of this inversion approach. The estimates of mud density and sound speed are close to values obtained independently. The frequency dependence of attenuation is estimated over the full low-frequency source band and has an approximate power exponent of 1.72.

Normal mode dispersion and time warping in the coastal ocean.

Simple, analytically solvable models of normal mode propagation in the coastal ocean are developed and applied to study the effect of the seafloor bathymetry on modal travel times. Within the adiabatic approximation, horizontal inhomogeneity of the waveguide is found to change the modal dispersion curves in a way that helps separation of the modal components of the acoustic field using the time-warping transform. It is shown that moderate seafloor slopes can lead to surprisingly large errors in retrieved geoacoustic parameters and cause a positive bias in bottom sound speed estimates if horizontal refraction is ignored.

Maximum Entropy Derived Statistics of Sound-Speed Structure in a Fine-Grained Sediment Inferred From Sparse Broadband Acoustic Measurements on the New England Continental Shelf

Marginal probability distributions for parameters representing an effective sound-speed structure of a fine-grained sediment are inferred from a data ensemble maximum entropy method that utilizes a sparse spatially distributed set of received pressure time series resulting from multiple explosive sources in a shallow-water ocean environment possessing significant spatial variability of the seabed. A remote sensing seabed acoustics experiment undertaken in March 2017 off the New England Shelf was designed so that multiple independent analyses could infer the statistical properties of the seabed. The current analysis incorporates the measured horizontal variability from interpretations of a subbottom profiling survey of the experimental area. An idealized range- and azimuth-dependent parameterization of the seabed is derived from identification of horizons within the seabed that define multiple sediment layers. A sparse set of explosive charges were deployed on circular tracks with radii of about 2, 4, and 6.5 km with an acoustic array at the center to correlate a set of random measurements to physical acoustic processes that characterize the seabed. The mean values of a surface sound speed ratio and a linear sound speed gradient for the fine-grained sediment layer derived from 12 data samples processed in the 25-275-Hz band provide an estimate of the effective sound-speed structure in a 130-km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area. The inferred sediment sound speed values are evaluated by predicting measured time series data not used in the statistical inference, and are also compared to historical measurements. Finally, the low-frequency maximum entropy estimate of the sediment sound speed along with physical measurements derived from piston core measurements are utilized to estimate the sediment grain bulk modulus.

Estimates of Low-Frequency Sound Speed and Attenuation in a Surface Mud Layer Using Low-Order Modes

Whereas there have been numerous theoretical and experimental studies on the properties of marine granular sands, there are significantly fewer studies on sediments classified as muds. The validity of geoacoustic models for muddy sediments has not been successfully tested due to the lack of inverted low-frequency sound speed and attenuation values. The geoacoustic properties of a surface fine-grained mud layer, overlaying three sand transition layers, and a half-space basement within the New England Mud Patch, were studied using explosive signals from long-range along-shelf sound propagation tracks. The sound-speed profile of the mud layer in the low-frequency band (100-500 Hz) was estimated using acoustic normal mode characteristics including the mode shapes and the modal dispersion curves of low-order modes, which mainly propagated in the water column and the surface mud layer. The ambiguity of sound speed at the top of the mud layer and sound-speed gradient was approximately removed. It was found that the resultant sound-speed ratio at the water-sediment interface was close to unity and the sound-speed gradient was 1.8 1/s with a standard deviation of 1.0 1/s. The attenuation in the mud layer was inverted using the attenuation coefficient of the first mode extracted from explosive signals at three source locations. The estimated attenuation at 150 Hz had a mean of 0.006 dB/m and a standard deviation of 0.003 dB/m.

PRELIMINARY EVALUATION OF ATMOSPHERIC TEMPERATURE AND WIND PROFILES OBTAINED USING UNMANNED AERIAL VEHICLE BASED ACOUSTIC TOMOGRAPHY

Abstract. An acoustic signature generated by an unmanned aerial vehicle is used in conjunction with tomography to remotely sense temperature and wind profiles within a volume of atmosphere up to an altitude of 120 m and over an area of 300 m × 300 m. Sound fields recorded onboard the aircraft and by an array of microphones on the ground are compared and converted to sound speed estimates for the ray paths intersecting the intervening medium. Tomographic inversion is then used to transform these sound speed values into three-dimensional profiles of virtual temperature and wind velocity, which enables the atmosphere to be visualised and monitored over time. The wind and temperature estimates obtained using this method are compared to independent measurements taken by a co-located mid-range ZephIR LIDAR and sensors onboard the aircraft. These comparisons show correspondences to better than 0.5 °C and 0.3 m/s for temperature and wind velocity, respectively.

Multipath Broadband Localization, Bathymetry, and Sediment Inversion

Transmission of linearly frequency modulated pulses generates receptions at a vertical line array that can be cross correlated with the source signal to provide estimates of the oceanic waveguide impulse response. For short ranges, distinct path arrivals can be identified including the direct, surface reflection, bottom reflection, and sediment reflection. Accurate estimation of arrival times of such paths is tightly related to successful inversion for source location and water column depth and sound speed and, subsequently, estimation of sediment sound speed and thickness. To achieve accurate estimation, particle filtering is applied to the received time series at 16 phones combined with a simple cross-correlation method. Using linearization, arrival time probability density functions are connected to the geometry and water column sound-speed parameters, providing point estimates as well as probability densities. These are then employed in sediment sound speed and thickness estimation. The results, obtained from the application of the method to data collected during the Seabed Characterization Experiment, are consistent with prior information on the site.

Robust estimation of sediment sound speed from the group speed of the critical mode.

In the ocean waveguide, the sediment sound speed has a simple relationship with the group speed of the highest order mode that propagates close to the critical angle. The paper shows that robust estimates of the sound speed are obtained from estimates of the "critical" mode group speed determined from analysis of the energy distribution of the time-warped spectrum of a broadband signal. The method is applied to experimental data collected in the Yellow Sea of China. Estimated sound speeds agreed closely with expected values for clayey slit (1531 m/s) and sandy silt (1593 m/s) sediment at the sites.

Time warping and acoustic characterization of the seafloor in horizontally inhomogeneous ocean

Time-warping transform is increasingly employed in shallow water acoustics to separate the field due to a compact, broadband sound source or the two-point cross-correlation function of diffuse noise into their normal mode components, and to measure mode travel times as a function of frequency. The time-warping transform was developed for range-independent waveguides, while physical parameters of the ocean are never quite constant in the horizontal plane. Bathymetry variations are typically responsible for the bulk of the waveguide’s range dependence as well as horizontal refraction of sound in the coastal ocean. Simple, exactly solvable models of shallow-water waveguides are used in this paper to illustrate the effects that the range dependence and horizontal refraction have on the performance of the warping transform and on the inferred geoacoustic parameters. Horizontal refraction due to generic bathymetric variations is addressed in the adiabatic approximation using perturbation techniques. Theoretical predictions are verified using numerical simulations. It is found that moderate bottom slopes can lead to large errors in retrieved geoacoustic parameters and cause positive bias in bottom sound speed estimates if horizontal refraction is ignored. [Work supported, in part, by NSF and BSF.]