Sound Speed Variations Research Articles

Uncertainty of transmission loss due to small scale fluctuations of sound speed in two environments

Seismic oceanography techniques reveal detection of small scale variations in sound speed not detectable via conventional oceanographic means, i.e., frequent XBT or CTD casts). Due to computational and practical limitations, such small scale spatial and temporal detail that exists in a real ocean environment is not typically included in acoustic ocean models. However, such measurements can provide insight to the small scale variability (uncertainty) that exists in the ocean but is not predicted by mesoscale ocean models. We show acoustic predictions made with the Range Dependent Acoustic Model (RAM) using measured seismic oceanography and CTD data at two locations in significantly different environments. Additionally, the CTD measurements are smoothed to a resolution comparable to that provided by a dynamic ocean model and acoustic predictions are computed. The Uncertainty Band (UBAND) algorithm (UBAND) [Zingarelli,”A mode-based technique for estimating uncertainty in range-averaged transmission loss results from underwater acoustic calculations,” J. Acoust. Soc. Am. 124(4) (2008)] is applied to the smoothed oceanographic data using estimates of sound speed uncertainty calculated from the high resolution measurements. We find reasonable estimates of uncertainty due to the small scale oceanography that is not characterized by mesoscale ocean models.

The effect of random fluctuations in bottom bathymetry on acoustic coherence in shallow water

The loss of temporal coherence after long range propagation in shallow water is often studied as a consequence of sound speed variability from internal waves. Here, we add the complication of small amplitude and very long wavelength random fluctuations of bottom bathymetry. It is shown that the same range dependent sound speed fluctuations result in markedly different coherence times depending on acoustic wavelength and mode number—a first order effect. A range dependent PE code (MMPE) is used to predict temporal coherence for individual surface reflected-bottom-reflected (SRBR) mode arrivals. Here, a mode coherence calculation is developed and compared for varying RMS bathymetry. Temporal coherence is inferred from mode coherence. We find first order and /or low frequency modes are insensitive to the bottom but when the (sine of the mode angle approaches 1/10 of an acoustic wavelength) the modes structure in amplitude and phase is randomized and the signal decorrelate rapidly in time from just the slightest temporal variations in sound speed. It does not take much; just 1 m in 200 m of range will randomize all but the first mode at mid frequencies (0.5 to 1 kHz). Predictions are in close agreement with SW06 mode coherence measurements.

Acoustical tomography in the shallow water ocean: Dream or reality?

Acoustical tomography in shallow waters relies on the identification and tracking of stable ray arrivals. The variation of the arrival time of these rays is used to solve the inverse problem and to estimate the physical properties as sound speed variations associated to internal waves or currents. In practice, however, technical difficulties appear (1) when the number of resolved eigenrays in this multipath environment is too small using a set of point-to-point recordings or (2) when the travel-time fluctuations are dominated by the fast-evolving surface that blur the slower internal-wave driven perturbations around the thermoclyne. Recent experimental studies based on laboratory-scaled demonstrators showed the efficiency of array processing algorithms in combination with source-receiver arrays to tackle issue (1) above. Depending on the waveguide geometry, the acquisition procedure can also be adjusted to provide a separation between the slow and fast travel-time fluctuations. Inversion results based on laboratory experiments are presented that focus on the dynamics of (1) a gravity wave at the air-water interface and (2) a thermal plume in the water column. Finally, these results are discussed in the framework of ocean acoustic research.

Acoustic interface treatment with an adjoint operator for linear range-dependent ocean index of refraction inversions

Hurskey et al. [J. Acoust. Soc. Am. 115(2), 607–619 (2004)] introduced the adjoint method and incorporated local sound-speed measurements into range-dependent ocean sound-speed inversion. They left two practical issues for the implementation of this method unresolved in this paper: the collection of appropriate environmental measurements and the implementation of bottom boundary conditions. The first of these issues was considered in a simulation study that used an oceanographic glider to collect range-dependent sound-speed measurements [Richards, CMRE memorandum (2012)]. A covariance matrix was constructed from the changes observed in the range-dependent sound-speed field. The adjoint inversion was performed in a reduced element subset of the empirical orthogonal functions (EOF) base of the covariance matrix. The second issue is the focus of this paper, which describes a bottom boundary condition with a defined adjoint operator. A horizontal fluid-bottom interface is implemented using the implicit finite difference form of the parabolic equation introduced by McDaniel and Lee [J. Acoust. Soc. Am. 71(4), 855–858 (1982)]. Combined with local range-dependent sound-speed statistics gathered with gliders, this development may provide a method of near real-time acoustic measurement of ocean sound-speed variations between an acoustic source and vertical hydrophone array.

Toward subsurface positioning of gliders using fixed acoustic tomography sources

Acoustic Seagliders can be positioned precisely using GPS at the surface, but are underwater and unable to utilize GPS for up to 9 hours at a time as they dive to depths of up to 1000 m. During this time, a kinematic model estimates the position of the glider. Four acoustic Seagliders were deployed in the Philippine Sea November 2010 - April 2011, and received transmissions from five broadband acoustic tomography sources moored in the region. Over 2000 acoustic receptions were recorded at ranges up to 700 km from the moored sources. Measured acoustic arrival peaks were unambiguously associated with ray arrivals predicted using the model-estimated glider position at the time of reception and a mean sound-speed profile. Estimates of source-receiver range uncertainty were calculated from statistics of travel-time offsets between the measured arrivals and the eigenray dispersion patterns. The uncertainty in range between the source and the modeled glider position during a dive is estimated to be 639 m (426 ms) rms disregarding the effects of ocean sound-speed variability, which are anticipated to be on the order of 70 ms rms. The range uncertainty is attributed primarily to advection of the glider by unobserved ocean currents.

Robustness analysis of nearfield subband beamformers in the presence of microphone gain and phase errors

Subband beamforming has found many applications in microphone array processing field, due to its advantages over the fullband counterpart. In this paper, the performance of nearfield subband beamformers for arbitrary arrays in the presence of microphone gain and phase errors is studied from the perspective of statistical analysis. Through the bias and variance analysis of array response, some insightful properties on the robustness of nearfield subband beamformers have been derived. It is shown that the robustness of nearfield subband beamformers is dependent on the source-to-array distance, i.e., the robustness will deteriorate when the source is close to microphone arrays. Moreover, the variation in sound speed, i.e., the temperature in homogeneous environments, has little effect on the robustness performance of subband beamformers. The theoretical results are further verified by several numerical examples on nearfield subband beamformers.

Underwater localization using stochastic proximity embedding and multi-dimensional scaling

Localization for underwater acoustic sensor networks is an active research topic where a large number of techniques have been proposed recently. This paper addresses one of the open research issues, the impact of underwater sound speed variation on the localization accuracy. In this paper, modified versions of stochastic proximity embedding and multi-dimensional scaling localization algorithms customized for underwater application are proposed. The algorithms are found to provide good performance in underwater scenario as they take into account refractive ray bending of acoustic waves. Detailed study of the algorithm performance has been done and the results are reported. Cramer Rao Lower Bound for the problem is also derived.

Analysis of optimal conditions for recording signals when studying the atmospheric boundary layer with the acoustic method of partial reflection

Equations for the coefficient of partial reflection K from stratified inhomogeneities in the atmospheric boundary layer have been derived on the basis of the Epstein transition and symmetrical layer models as functions of three dimensionless parameters, i.e., the relative layer altitude, its relative thickness, and the relative variations in the effective sound speed in a layer. The equations have been obtained for the relative layer altitude at which the total internal reflection appears; the behavior of the function K is studied at close altitudes. Significant weakening of the dependence of coefficient K on the relative layer thickness in these conditions is shown, which makes it possible to record partially reflected signals in a wide range of wave-lengths or frequencies of the sounding signal. In other cases, the coefficient of partial reflection K strongly depends on the layer thickness. According to experimental data on variations in the amplitude of received acoustic signals with an increase in the source-detector distance, a technique for the parameterization of the additional impedance attenuation of sound that propagates over the earth’s surface has been developed, and these parameters have been experimentally estimated for different stratification conditions and sounding signal frequencies. Many records of background acoustic noises typical for one or another measurement sites have been distinguished and classified, a technique for estimating the minimum signal amplitude distinguishable against noises has been developed, and the corresponding estimates have been made. Based on these data and the specifications of three different industrial acoustic sources, the parameter limits provided by these sources have been estimated for the method of partial reflection.

Algorithms for Shape and Trajectory Reconstruction of Obstacles in Domains with Variable Speed of Sound

We present new parallel algorithms for shape and trajectory reconstruction of moving obstacles using reflected rays. In contrast to tomography where the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle. The rays are curves determined by the variable speed of sound and initial conditions and we develop ultrasonic ray models based on a system of differential equations. The method can achieve high-resolution and computational efficiency.

Multi-wave imaging in attenuating media

We consider a mathematical model of thermoacoustic tomography andother multi-wave imaging techniques with variable sound speed andattenuation. We find that a Neumann series reconstruction algorithm,previously studied under the assumption of zero attenuation, stillconverges if attenuation is sufficiently small. With completeboundary data, we show the inverse problem has a unique solution, andmodified time reversal provides a stable reconstruction. We alsoconsider partial boundary data, and in this case study thosesingularities that can be stably recovered.

Constraints on primordial gravitational waves with variable sound speed from current CMB data

We make a comprehensive investigation of the observational effect of the inflation consistency relation. We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAP observations. We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When taking smaller values of $c_s$, the positive correlation between $r$ and $n_s$ also leads to slightly tighter constraint on the upper bound of $n_s$, while the running of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For the sound speed $c_s$, it is not well constrained if only the CMB power spectrum data is used, while the constraints are obtainable by taking $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ priors into account. With the constraining data of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$, we find that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$ case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL. In addition, the inclusion of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ into the analysis can improve the constraints on $r$ and $n_s$. We further discuss the implications of our constraints on the test of inflation models.

Acoustic glitches in solar‐type stars from Kepler

AbstractWe report the measurement of the acoustic locations of layers of sharp variation in sound speed in the interiors of 19 solar‐type stars observed by the Kepler mission. The oscillatory signal in the frequencies arising due to the acoustic glitches at the base of the convection zone and the second helium ionisation zone was utilised to determine their location by four independent methods. Despite the significantly different methods of analysis, remarkable agreement was found between the results of these four methods. Further, the extracted locations of these layers were found to be consistent with representative models of the stars (© 2012 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Tissue Classification Using Ultrasound-Induced Variations in Acoustic Backscattering Features

Ultrasound (US) radio-frequency (RF) time series is an effective tissue classification method that enables accurate cancer diagnosis, but the mechanisms underlying this method are not completely understood. This paper presents a model to describe the variations in tissue temperature and sound speed that take place during the RF time series scanning procedures and relate these variations to US backscattering. The model was used to derive four novel characterization features. These features were used to classify three animal tissues, and they obtained accuracies as high as 88.01%. The performance of the proposed features was compared with RF time series features proposed in a previous study. The results indicated that the US-induced variations in tissue temperature and sound speed, which were used to derive the proposed features, were important contributors to the tissue typing capabilities of the RF time series. Simulations carried out to estimate the heating induced during the scanning procedure employed in this study showed temperature rises lower than 2 °C. The model and results presented in this paper can be used to improve the RF time series.

On the significance of density‐induced speed of sound variations on US‐guided radiotherapy

To show the effect of speed of sound (SOS) aberration on ultrasound guided radiotherapy (US-gRT) as a function of implemented workflow. US systems assume that SOS is constant in human soft tissues (at a value of 1540 m∕s), while its actual nonuniform distribution produces small but systematic errors of up to a few millimeters in the positions of scanned structures. When a coregistered computerized tomography (CT) scan is available, the US image can be corrected for SOS aberration. Typically, image guided radiotherapy workflows implementing US systems only provide a CT scan at the simulation (SIM) stage. If changes occur in geometry or density distribution between SIM and treatment (TX) stage, SOS aberration can change accordingly, with a final impact on the measured position of structures which is dependent on the workflow adopted. Four basic scenarios were considered of possible changes between SIM and TX: (1) No changes, (2) only patient position changes (rigid rotation-translation), (3) only US transducer position changes (constrained on patient's surface), and (4) patient tissues thickness changes. Different SOS aberrations may arise from the different scenarios, according to the specific US-gRT workflow used: intermodality (INTER) where TX US scans are compared to SIM CT scans; intramodality (INTRA) where TX US scans are compared to SIM US scans; and INTERc and INTRAc where all US images are corrected for SOS aberration (using density information provided by SIM CT). For an experimental proof of principle, the effect of tissues thickness change was simulated in the different workflows: a dual layered phantom was filled with layers of sunflower oil (SOS 1478 m∕s), water (SOS 1482 m∕s), and 20% saline solution (SOS 1700 m∕s). The phantom was US scanned, the layer thicknesses were increased and the US scans were repeated. The errors resulting from the different workflows were compared. Theoretical considerations show that workflows implementing SOS correction based on SIM-CT scan (INTERc, INTRAc) give null errors in all scenarios except when tissues thickness changes, where an error proportional to the degree of change in SOS maps between SIM and TX (ΔSOS) occurs. An uncorrected workflow such as INTER produces in all scenarios a pure SOS error, while uncorrected INTRA produces a null error for rotation-translation of the patient, a ΔSOS error for changing tissues thickness and an error proportional to the degree of SOS distribution change along the different lines of view when shifting the transducer. The dual layered phantom demonstrated experimentally that the effect of SOS change between SIM and TX is clinically nonrelevant, being less than the intrinsic resolution of imaging systems, even when a substantial change in thicknesses is applied, provided that a SIM-CT-based SOS aberration correction is applied. Noncorrected workflows produce errors up to 4 mm for INTER and to 3 mm for INTRA in the phantom test. A SOS correction is advantageous for all US-gRT workflows and clinical cases, where the effect of SOS change can be considered a second order effect.

Long-term acoustic monitoring off Central California

The use of moored ocean arrays for environmental acoustic measurements off Central California is discussed. A cabled array off Point Sur, CA, which was designed for long-range, low-frequency listening was used by NPS and collaborators from late 1997 through mid-2000 and provides examples of a wide range of activities including use for student laboratories, faculty and student research, as well as monitoring, e.g. ambient acoustic noise, test ban treaty activities. From mid-2006 to present, passive acoustic data have continued to be collected off Pt. Sur using single hydrophone moored autonomous listening stations which record data intermittently at sampling rates of 200 kHz. We have recently considered re-establishment of cabled passive acoustic measurements using MARS, an example of an observatory which was designed and located for more traditional oceanographic studies. The utility of MARS for acoustic measurements depends both on how well it can characterize the regional acoustic environment as well as local oceanographic processes that can be resolved acoustically (canyon effects, geography, sound speed variability, sediments and local vessel traffic). These can be contrasted with existing cabled and autonomous data from Point Sur.

The effects of mode structure on coherence in shallow water propagation

In an ideal shallow water propagation channel the sound field is accurately described by normal modes and the mode structure is predictable with clean separated modes. However the real ocean environment is rarely ideal, and variations in bottom bathymetry and water column sound speed are usually present. When fluctuations are small and on the order of a fraction of an acoustic wavelength the sound field propagation is deterministic and any mode pattern deviations are small and slow and the phase response is linear. Here the propagation is considered phase coherent and spatial and/or temporal averaging will produce gain. When the fluctuations increase to the order of ½ to 1 acoustic wavelength the mode patterns becomes distorted such that slow linear fluctuations in phase can no longer describe the propagation. Here coherence is reduced and in some cases completely lost. A unifying theory will be presented linking mode pattern deviations and coherence. PE models will be used to predict mode structure and individual mode correlation will be computed with the ideal case. These mode correlations will be used to estimate temporal and spatial coherence and the results will be compared with data from three shallow water experiments.

Effects of tropical cyclones on underwater sound propagation

Environmental data collected near the continental shelf and the shelfbreak in the Southern East China Sea around Taiwan are utilized to study sound propagation effects of tropical cyclones (typhoons). These data were from the Conductivity-Temperature-Depth (CTD) profiling casts conducted during the Quantifying, Predicting, Exploiting (QPE) Uncertainty experiments in both 2008 and 2009. These CTD surveys provided observations for the normal physical oceanographic conditions in the area and, most importantly, the extreme conditions induced by a tropical cyclone Typhoon Morakot in the summer of 2009. Strong upwelling currents near the shelfbreak in the experiment area were observed after the typhoon past by, and the water-column stratification was changed. A sound speed variation of 10 m/s over 50 km in distance was measured in the upwelling area, and this can produce significant effects on sound propagation. Numerical models using parabolic-equation and ray tracing methods will be presented to demonstrate the underlying physics of the sound field variability. [Work supported by the Office of Naval Research.]

Ultrasonic Study of Binary Mixture of Acetone with Bromobenzene and Chlorobenzene at Different Frequencies

This paper aims to portray the nature and extent of interaction in the binary mixture of acetone with bromobenzene and chlorobenzene by computing the various acoustic parameters such as acoustic impedance (Z), isentropic compressibility ( �), intermolecular free length (L f) and their excess values at different frequencies (1 MHz, 3 MHz and 5 MHz) using a multi frequency ultrasonic interferometer over the entire range of mole fraction at temperature 303.16 K. The experimental data for sound velocity (C) and density ( �) of the mixture have been used to compute these parameters. The variations of sound speed with frequency plays the key role to execute the variation in these parameters which is explained in terms of different intermolecular interactions present in the binary mixture. The extent of interactions existing between component molecules has been found out. In acetone-bromobenzene system the more negative values of different excess parameter suggest that the interaction between acetone-bromobenzene is more as compare to acetone-chlorobenzene system. Further a comparative study for the above acoustical parameters between two mono substituted benzene in presence of acetone at different frequencies were discussed in terms of molecular interactions.

Acoustic-gravity waves in atmospheric and oceanic waveguides

A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.

Gas Void Fraction Estimation in Gas-Bubble-Contained Sands with Difference Frequency Waves

A nonlinearity parameter can be used for the estimation of the gas void fraction in gassy sediment. If two primary acoustic waves of different frequencies are incident on gassy sediment, nonlinear acoustic waves can be generated at the difference frequency. In the present study, the parametric acoustic array theory for the difference frequency wave was employed to estimate the nonlinearity parameters of gas-bubble-contained sands under laboratory conditions. The nonlinearity parameters of the sands were estimated between 103 and 104. Then, the estimated gas void fractions in the sands were between 10-6 and 10-4. They were similar to those estimated through the sound speed variation method. However, this linear acoustic method could not be applied to gas-bubble-contained sand with a low gas void fraction, because the sound speed variation was not observed in the sand. This study suggests that the nonlinear acoustic method seems very feasible to estimate the gas void fraction in gassy sediment with a low gas content.