Sound Speed Variations Research Articles

A wave equation model for retrograde media with a bubble structure

A nonlinear wave equation is obtained for liquid-vapor mixtures with regard to arbitrary change of equilibrium sound speed in a mixture with growth and condensation of vapor bubbles, which has a limit transition to a wave equation for pure liquid at full collapse of vapor cavities. A particular case of a collapsing wave equation (CWE) of retrograde media is considered, e.g., liquid-vapor media with low vaporization heat and low dissipation, observed near the critical liquid-vapor point, where the main effect is variable sound speed. Based on the CWE numerical solutions it is shown that in such liquid-vapor media, one can observe previously unknown nonlinear wave structures with depression waves.

The time‐domain Lippmann–Schwinger equation and convolution quadrature

We consider time‐domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solve a time‐domain volume Lippmann–Schwinger integral equation. Using convolution quadrature in time and trigonometric collocation in space, we can compute an approximate solution. We prove that the time‐domain Lippmann–Schwinger equation has a unique solution and prove conditional convergence and error estimates for the fully discrete solution for globally smooth sound speeds. Preliminary numerical results show that the method behaves well even for discontinuous sound speeds. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 517–540, 2015

Variational Iterative Algorithms in Photoacoustic Tomography with Variable Sound Speed

In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively. We present numerical examples and show the well performance of these variational iterative algorithms.

Estimates of the temporal and spatial variability of ocean sound speed on the New Jersey shelf

Estimates of the spatial and temporal variability of ocean sound speed on the New Jersey shelf were obtained using acoustic signals measured by a set of freely drifting buoys. The range- and time-dependent inversion problem is computationally intensive and a linearized perturbative algorithm was applied to obtain results in an efficient manner. The inversion algorithm uses estimates of modal travel time to determine sound speed as a function of range and depth. In order to handle the high volume of data associated with the acoustic sensing network, the modal travel time estimation process was automated using an adaptive time-frequency signal processing method known as time-warping. Time-warping is a model-based transform that converts the frequency-dependent modal arrivals to monotones in the warped domain where they can be easily filtered. The data analyzed in this paper were collected on 16 March 2011 on the New Jersey shelf when the ocean was relatively well-mixed. While the observed sound-speed variations are small, both spatial and temporal trends are observed in the results. Furthermore, the estimated sound-speed profiles show good agreement with temporally and spatially collocated measurements.

Travel-time approximation of acoustic ranging in GPS/Acoustic seafloor geodesy

Previous studies have proposed methods to reduce the effect of sound-speed variation in the water column on the precision of GPS/Acoustic positioning. However, the fit of temporal travel-time variation makes reference to sound-speed profiles without considering depth-dependent variation. Accordingly, the goal of this study is to provide a simple and precise approximation for a given sound-speed profile considering its depth-dependent variation. We propose two synthetic models for sound-speed profiles, one linear and the other bilinear, for better travel-time approximations of acoustic ranging in GPS/Acoustic seafloor geodesy. The linear and bilinear models are tested on three types of sound-speed profiles derived from conductivity–temperature–depth (CTD) casts made at water depths of 300, 1000, and 2000m, respectively. The change in error of the best acoustic travel-time approximation resulting from the change in break depth of the bilinear model is investigated for the three types of sound-speed profiles. Furthermore, the performance of the linear and bilinear models is evaluated using the data collected from a GPS/Acoustic survey. The evaluation results demonstrate that both the linear and bilinear models can effectively reduce the effect of sound-speed variation on the precision of GPS/Acoustic positioning.

Distributions and vertical variation patterns of sound speed of surface sediments in South China Sea

The distributions of sound speed show different characteristics in continental shelf, continental slope and Nansha Trough. The differences have closely related to the distributions of sediment physical properties in the southern South China Sea. According to the analysis of sound speeds and physical properties variation characteristics with buried depth, the vertical variations of sound speed are closely related to sediment texture, sedimentary environment, transport, erosion, compaction, consolidation, etc. The comparison results indicate 3 vertical variation patterns of sound speed: increasing model, invariant model and complicate variation model. The above 3 variation models represent the vertical distribution characteristics of sound speed in different depositional environments. Different variation patterns have different key factors which generally contain porosity or grain size. The calculated sound speeds with Buckingham’s theory of compressional waves in fluid-like marine sediments follows the trend of measured speeds accurately.

Acoustic propagation in surface channel formed by low salinity water in the East China Sea and the tropical Atlantic Ocean

Salinity is usually neglected in underwater acoustics because of its minimal contribution on sound speed variation. However, it is required to consider in calculation of sound speed and acoustic propagation for low salinity water freshened by continental run-off. Furthermore, the acoustic characteristics of low salinity environment are not fully investigated yet. Therefore, regional difference of acoustic propagation in low salinity water was studied by comparing the acoustic characteristics of the East China Sea with those of the tropical Atlantic Ocean in this paper. Frequency dependency of sound propagation in the haline channel was analyzed with transmission losses and low frequency cut-off using oceanic data from NODC (National Oceanographic Data Center). The tropical Atlantic Ocean showed larger channel depth, critical angles and less transmission loss in the haline channel than the East China Sea. The cut-off frequency in the haline channel was computed as around 1 kHz and 5 kHz in the tropical Atlantic Ocean and the East China Sea, respectively. The effects of low salinity water on sound propagation showed regional characteristics, and need to be considered in sonar operation near sea surface. [This work was supported by Defense Acquisition Program Administration and Agency for Defense Development under the contract UD130007DD.]

Approximation of a physics-based model of surface reflection loss

A model of coherent acoustic reflection loss at the ocean surface had been prepared by the authors by combining a model of surface roughness loss with a description of surface incidence angle which accounted for the refractive effects of a uniformly stratified distribution of wind-driven bubbles. Here, surface roughness loss was based on a second-order small-slope approximation, and the surface incidence angle was obtained using a formulation for stratified media from Brekhovskikh applied to the sound speed variation resulting from the bubble distribution used by Ainslie [JASA 118, (2005)]. More recent work by the authors has shown that the analyses for each of surface roughness loss, and surface incidence angle, may be approximated adequately by relatively simple expressions, and that the complete model of surface reflection loss inclusive of the refractive effects of bubbles may be approximated in expressions suitable for hand calculations. Results from the use of this approximated model with a Gaussian-beam acoustic propagation code are compared with results obtained from the authors' more complete model for several surface ducted transmission scenarios. Both sets of results are also compared with predictions based on Monte Carlo parabolic equation (PE) transmission calculations.

The effect of large- and small-scale sound velocity field structure on shallow water sound propagation in the East China Sea

During the Transverse Acoustic Variability Experiment (TAVEX) in 2008, towed CTD measurements were used to record the sound speed field over an area of the East China Sea surrounding 34- and 20-km acoustic paths. The data revealed several propagating internal wave packets along with sound speed variability due to density-compensated thermohaline variations (spice). Concurrent acoustic data were also recorded from 300- and 500-Hz sources. Parabolic equation modeling is used to examine the effects of the measured internal waves and spice on acoustic propagation and to make comparisons with the recorded acoustic data.

VERIFICATION OF THE HELIOSEISMOLOGY TRAVEL-TIME MEASUREMENT TECHNIQUE AND THE INVERSION PROCEDURE FOR SOUND SPEED USING ARTIFICIAL DATA

We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.

SIMULATION OF UNDERWATER ACOUSTICAL FIELD FLUCTUATIONS IN RANGE-DEPENDENT RANDOM ENVIRONMENT OF SHALLOW SEA

To investigate statistical problem of moderate to low-frequency sound scattering on the two-dimensional (2D) random inhomogeneities of a shallow sea with horizontal boundaries (bottom and surface) and loss local-mode approach has been utilized. An explicit-form solution by quadrature for modal amplitudes as a function of distance is represented. In adiabatic approximation asymptotical estimations have been performed, which demonstrate how medium weak fluctuations influence the local eigenvalues and statistical characteristics of a field. It is shown that general effects previously established while studying the random layered problem keep the force. Spatial scales of statistical influence and laws of dependences are determined. Also it follows from the analysis of the explicit-form solution for modal amplitudes that in this shallow-sea model with horizontal boundaries and in the absence of regular variations of sound speed the coupling of modes is insignificant. General statistical effects are described well within the framework of adiabatic approximation.

Future shallow water low frequency (100–1000 Hz) acoustic signal propagation physics studies

The measurement and prediction of the phase and amplitude properties of acoustic signals (1 to 1000 Hz) propagating in the dynamic shallow water (30 to 500 m water depths) environment has been a focus of the underwater acoustic research community for nearly 20 years. The majority of the ocean studies have occurred during late spring to summertime oceanic conditions when the sound speed variability was influenced by nonlinear mode 1 internal wavefields. Sound speed variability during the summer-to-winter and winter-to-summer water column transition periods will cause variability in the phase coherent properties of acoustic signals. Few experimental studies explicitly focused on quantifying the variability of phase coherent properties of acoustic signals during these periods have been performed. Illustration of the types of fluid processes that will perturb the sound speed structure during the fall-to-winter transition periods will be presented. Included will be mode 1 and mode 2 internal wave perturbation of the sound speed field as well as the locations and spatial scales of sound speed variability caused by interleaving water masses of varying temperature and salinity (Spice). Fall-to-winter transition sound speed fields will be contrasted with summer time sound speed conditions. [Work supported by the Office of Naval Research.]

Modeling sound propagation through internal waves using a spectral element method

Considered here is the problem of low-frequency sound propagation over shallow, shoaling bathymetry in the presence of perturbations to the background sound velocity profile due to internal waves (IW). The question we attempt to answer is: to what degree can heuristic models of IWs coupled to numerical sound propagation models capture the variability in sound propagation observed in the environment? A high-order finite element model is employed to compute the acoustic field as it propagates through these IWs. The generality of the finite element method allows for spatial and temporal sound speed variations, and its convergence properties yield arbitrarily small error as the grid is rened. Simulations in the presence and absence of IWs will demonstrate the degree to which IWs influence sound propagation. Different models of IWs will demonstrate the sensitivity of the sound propagation to the choice of heuristic used for the IWs. Results will be shown for shoaling waveguides of O(100 m) depth and O(10 km) range, and frequencies of O(50 Hz). [Work supported by the NDSEG Fellowship.]

Millimeter‐level precision in a seafloor geodesy experiment at the Discovery transform fault, East Pacific Rise

Direct‐path acoustic ranging is a promising seafloor geodetic technique for continuous high‐resolution monitoring of geodynamical process such as fault slip and magma intrusion. Here we report on a yearlong acoustic ranging experiment conducted across the discovery transform fault at ∼4°S on the East Pacific Rise. The ranging instruments utilized a novel acoustic signal designed to enhance precision. We find that, after correcting for variations in sound speed at the path end‐points, the ranging measurements have a precision of ∼1 mm over baselines approaching 1 km in length. The primary difficulty in this particular experiment was with the physical stability of the benchmarks, which were deployed free fall from a ship. Despite the stability issues, it appears that the portion of the transform fault that the array covered was locked during the year of our survey. The primary obstacle to continuous, high sample rate, high‐precision geodetic monitoring of oceanic ridges and transform faults is now limited to the construction of geodetic monuments that are well anchored into bedrock.

Structure and stability of wave-theoretic kernels in the ocean

Wave-theoretic modeling can be applied to obtain travel-time sensitivity kernels (TSKs) representing the amount ray travel times are affected by sound-speed variations anywhere in the medium. This work explores the spatial frequency content of the TSK compared to expected ocean variability. It also examines the stability of the TSK in environments that produce strong sensitivity of ray paths to initial conditions. The conclusion is that the linear TSK model is an effective predictor of travel-time changes and that the rays perform nearly as well as the full-wave kernel. The TSK is examined in physical space and in wavenumber space, and it is found that this is the key to understanding how the travel time reacts to ocean perturbations. There are minimum vertical and horizontal length scales of ocean perturbations that are required for the travel time to be affected. The result is that the correspondence between true travel times and those calculated from the kernel is high for large-scale perturbations and somewhat less for the small scales. This demonstrates the validity of ray-based inversion of travel time observations for the cases under study.

Observations of sound-speed fluctuations in the western Philippine Sea in the spring of 2009

As an aid to understanding long-range acoustic propagation in the Philippine Sea, statistical and phenomenological descriptions of sound-speed variations were developed. Two moorings of oceanographic sensors located in the western Philippine Sea in the spring of 2009 were used to track constant potential-density surfaces (isopycnals) and constant potential-temperature surfaces (isotherms) in the depth range 120-2000 m. The vertical displacements of these surfaces are used to estimate sound-speed fluctuations from internal waves, while temperature/salinity variability along isopycnals are used to estimate sound-speed fluctuations from intrusive structure often termed spice. Frequency spectra and vertical covariance functions are used to describe the space-time scales of the displacements and spiciness. Internal-wave contributions from diurnal and semi-diurnal internal tides and the diffuse internal-wave field [related to the Garrett-Munk (GM) spectrum] are found to dominate the sound-speed variability. Spice fluctuations are weak in comparison. The internal wave and spice frequency spectra have similar form in the upper ocean but are markedly different below 170-m depth. Diffuse internal-wave mode spectra show a form similar to the GM model, while internal-tide mode spectra scale as mode number to the minus two power. Spice decorrelates rapidly with depth, with a typical correlation scale of tens of meters.

Estimating uncertainty in subsurface glider position using transmissions from fixed acoustic tomography sources

Four acoustic Seagliders were deployed in the Philippine Sea November 2010 to April 2011 in the vicinity of an acoustic tomography array. The gliders recorded over 2000 broadband transmissions at ranges up to 700 km from moored acoustic sources as they transited between mooring sites. The precision of glider positioning at the time of acoustic reception is important to resolve the fundamental ambiguity between position and sound speed. The Seagliders utilized GPS at the surface and a kinematic model below for positioning. The gliders were typically underwater for about 6.4 h, diving to depths of 1000 m and traveling on average 3.6 km during a dive. Measured acoustic arrival peaks were unambiguously associated with predicted ray arrivals. Statistics of travel-time offsets between received arrivals and acoustic predictions were used to estimate range uncertainty. Range (travel time) uncertainty between the source and the glider position from the kinematic model is estimated to be 639 m (426 ms) rms. Least-squares solutions for glider position estimated from acoustically derived ranges from 5 sources differed by 914 m rms from modeled positions, with estimated uncertainty of 106 m rms in horizontal position. Error analysis included 70 ms rms of uncertainty due to oceanic sound-speed variability.

Radial Anatomic Variation of Ultrasonic Velocity in Human Cortical Bone

Quantitative ultrasound techniques can be used to retrieve cortical bone quality. The aim of this study was to investigate the anatomic variations in speed of sound (SOS) in the radial direction of cortical bone tissue. SOS measurements were realized in 17 human cortical bone samples with a 3.5-MHz transverse transmission device. The radial dependence of SOS was investigated in a direction perpendicular to the periosteum. For each sample, bone porosity was measured using an X-ray micro-computed tomography device. The mean SOS was 3586±255m/s. For 16 of 17 specimens, similar radial variations in SOS were observed. In the periosteal region, SOS first decreased in the direction of the endosteum and reached a minimum value approximately in the middle of the cortical bone. SOS then increased, moving to the endosteal region. A significant negative correlation was obtained between SOS and porosity (R=-0.54, p=0.02).

Enhancement of photoacoustic tomography by ultrasonic computed tomography based on optical excitation of elements of a full-ring transducer array

Photoacoustic computed tomography (PACT) is a hybrid technique that combines optical excitation and ultrasonic detection to provide high-resolution images in deep tissues. In the image reconstruction, a constant speed of sound (SOS) is normally assumed. This assumption, however, is often not strictly satisfied in deep tissue imaging, due to acoustic heterogeneities within the object and between the object and the coupling medium. If these heterogeneities are not accounted for, they will cause distortions and artifacts in the reconstructed images. In this Letter, we incorporated ultrasonic computed tomography (USCT), which measures the SOS distribution within the object, into our full-ring array PACT system. Without the need for ultrasonic transmitting electronics, USCT was performed using the same laser beam as for PACT measurement. By scanning the laser beam on the array surface, we can sequentially fire different elements. As a first demonstration of the system, we studied the effect of acoustic heterogeneities on photoacoustic vascular imaging. We verified that constant SOS is a reasonable approximation when the SOS variation is small. When the variation is large, distortion will be observed in the periphery of the object, especially in the tangential direction.

Simulation of Wave-Flow-Cavitation Interaction Using a Compressible Homogenous Flow Method

AbstractA numerical method based on a homogeneous single-phase flow model is presented to simulate the interaction between pressure wave and flow cavitation. To account for compressibility effects of liquid water, cavitating flow is assumed to be compressible and governed by time-dependent Euler equations with proper equation of state (EOS). The isentropic one-fluid formulation is employed to model the cavitation inception and evolution, while pure liquid phase is modeled by Tait equation of state. Because of large stiffness of Tait EOS and great variation of sound speed in flow field, some of conventional compressible gasdynamics solvers are unstable and even not applicable when extended to calculation of flow cavitation. To overcome the difficulties, a Godunov-type, cell-centered finite volume method is generalized to numerically integrate the governing equations on triangular mesh. The boundary is treated specially to ensure stability of the approach. The method proves to be stable, robust, accurate, time-efficient and oscillation-free.Novel numerical experiments are designed to investigate unsteady dynamics of the cavitating flow impacted by pressure wave, which is of great interest in engineering applications but has not been studied systematically so far. Numerical simulation indicates that cavity over cylinder can be induced to collapse if the object is accelerated suddenly and extremely high pressure pulse results almost instantaneously. This, however, may be avoided by changing the traveling speed smoothly. The accompanying huge pressure increase may damage underwater devices. However, cavity formed at relatively high upstream speed may be less distorted or affected by shock wave and can recover fully from the initial deformation. It is observed that the cavitating flow starting from a higher freestream velocity is more stable and more resilient with respect to perturbation than the flow with lower background speed. These findings may shed some light on how to control cavitation development to avoid possible damage to operating devices.