Sound Speed Fluctuations Research Articles

Effects of non-adiabaticity in modal propagation through random sound speed perturbations.

Modal propagation through sound speed fluctuations in shelf environments can be modeled adiabatically or fully coupled through polynomial chaos (PC) expansions of the modal amplitudes or complex phase. The importance of modal scattering versus adiabatic effects is explored for random sound speed fields in the mid-frequency regime. It is shown that the importance of inter-modal scattering is related to the interference wavelength between the modes in relation to the horizontal wavelengths of the sound speed fluctuations as well as the vertical structure of the sound speed fluctuations with respect to the shape of the interacting modes. Modal scattering is also highly affected by the relative amplitudes between the modes with strong scattering into weaker modes. While these effects are well known, the coupled mode PC equations give unique insight into the detailed physics of these controlling factors.

Anisotropy in internal gravity waves in conditions of a stable nocturnal boundary layer

In July 2005 the Oboukhov Institute of Atmospheric Physics (OIAP) and the Leipzig Institute for Meteorology (LIM) conducted a joint experiment at Zvenigorod (Russia) using the OIAP's acoustic pulse sounding method and the acoustic travel time tomography of the LIM group. These were deployed simultaneously with SODAR and temperature profiler measurements of wind speed and temperature profiles used for monitoring the state of the lower atmosphere. Internal gravity waves (IGWs) in the stably stratified atmosphere were detected by means of cross-coherence analysis of the acoustic travel times. The acoustic receivers were placed in groups of three at several locations distributed within the measurement field. Two methods were employed for detecting coherent structures: first in the vertical direction along refracting ray paths with turning points in the atmosphere between 50 m to 300 m and second the pulse propagation along almost horizontal ray paths that connect pairs of source and receivers. In this way both horizontal and vertical information of the state of the atmosphere was monitored continuously during the experiment; this allowed both the detection of wave-like structures and the spatial and temporal characteristics of the effective sound speed fluctuations. From these fluctuations the anisotropy of the IGW's is deduced. Two measurement days are analysed in this study which revealed several anisotropic frequency domains caused by wave-like structures.

The vertical structure of shadow-zone arrivals at long range in the ocean

Multimegameter-range acoustic data obtained by bottom-mounted receivers show significant acoustic energy penetrating several hundred meters into geometric shadow zones below cusps (caustics) of timefronts computed using climatological databases [B. D. Dushaw et al., IEEE J. Ocean. Eng. 24, 202-214 (1999)]. This penetration is much larger than predicted by diffraction theory. Because these receivers are horizontal arrays, they do not provide information on the vertical structure of the shadow-zone arrivals. Acoustic data from two vertical line array receivers deployed in close proximity in the North Pacific Ocean, together virtually spanning the water column, show the vertical structure of the shadow-zone arrivals for transmissions from broadband 250-Hz sources moored at the sound-channel axis (750 m) and slightly above the surface conjugate depth (3000 m) at ranges of 500 and 1000 km. Comparisons to parabolic equation simulations for sound-speed fields that do not include significant internal-wave variability show that early branches of the measured timefronts consistently penetrate as much as 500-800 m deeper into the water column than predicted. Subsequent parabolic equation simulations incorporating sound-speed fluctuations consistent with the Garrett-Munk internal-wave spectrum at full strength accurately predict the observed energy level to within 3-4-dB rms over the depth range of the shadow-zone arrivals.

Probability density functions of modal amplitudes and complex acoustic pressure in fluctuating shallow water waveguides.

The polynomial chaos method is applied to the problem of predicting the probability density functions of complex modal amplitudes and acoustic pressure in the presence of water column sound speed fluctuations in shallow water waveguides. Results for both the intrusive implementation of the polynomial chaos technique, where the governing coupled mode differential equations for the complex modal amplitudes are augmented with the random states of the chaos expansion, and the non-intrusive method, where legacy codes can be run over an ensemble of ocean realizations and the results fitted by a truncated chaos expansion, are shown. Both methods give good agreement with Monte Carlo histograms of the modal amplitudes and the pressure field for slight water column variability, but the non-intrusive formulation shows more robustness for larger variability. The relative merits of PC expansions for the complex modal amplitudes vs the log amplitudes for the complex pressure amplitudes are also discussed.

Ray-based description of normal modes in a deep ocean acoustic waveguide

Modal structure of the wave field in a deep ocean environment with sound speed fluctuations induced by random internal waves is considered. An approximate analytical description of the modal structure at megameter ranges is derived by combining two known results: (i) relations expressing mode amplitudes through parameters of ray paths and (ii) stochastic ray theory. For a monochromatic wave field, a simple analytical estimate has been obtained for a coarse-grained distribution of acoustic energy between normal modes. Significant attention has been paid to the investigation of the mode pulses, that is, sound pulses carried by individual modes. Analytical estimates for the spread of mode pulse and bias of its mean travel time in the presence of internal waves are derived.

Mesoscale variations in acoustic signals induced by atmospheric gravity waves

The results of acoustic tomographic monitoring of the coherent structures in the lower atmosphere and the effects of these structures on acoustic signal parameters are analyzed in the present study. From the measurements of acoustic travel time fluctuations (periods 1 min-1 h) with distant receivers, the temporal fluctuations of the effective sound speed and wind speed are retrieved along different ray paths connecting an acoustic pulse source and several receivers. By using a coherence analysis of the fluctuations near spatially distanced ray turning points, the internal wave-associated fluctuations are filtered and their spatial characteristics (coherences, horizontal phase velocities, and spatial scales) are estimated. The capability of acoustic tomography in estimating wind shear near ground is shown. A possible mechanism describing the temporal modulation of the near-ground wind field by ducted internal waves in the troposphere is proposed.

Broadband high frequency matched-field processing.

Adaptive matched-field processing (MFP) is extremely sensitive to environmental uncertainties. While conventional and adaptive techniques may work for low-frequency signals in well-studied environments, the localization performance usually degrades rapidly as frequency increases, such that MFP in the 3.5 kHz regime, in shallow water environments, is typically problematic. A broadband coherent method [IEEE J. Ocean. Eng. 21, 384–392], combined with white noise constraint and principal component techniques, is implemented to construct robust replicas from experimental data. Matched-field tomography is then used to better understand the origin of the frequency dependent MFP mismatch (uncertain bottom structure, sound speed fluctuations, or both), and the results are compared with simulations. Ultimately, we want to gain some insights into how to implement a robust matched-field processor for high-frequency scenarios without using experimental data to create replica vectors. In particular, we are seeking to understand the thresholds for adaptive processors as function of signal to noise ratio and frequency dependent environmental mismatch. [Work supported by ONR.]

RAY CHAOS IN UNDERWATER ACOUSTIC WAVEGUIDES

The chaotic motion of a ray path in a deep water acoustic waveguide with internal-wave-induced fluctuations of the sound speed is investigated. A statistical approach for the description of chaotic rays is discussed. The behavior of ray trajectories is studied using Hamiltonian formalism expressed in terms of action-angle variables. It is shown that the range dependence of the action variable of chaotic ray can be approximated by a random Wiener process. On the basis of this result, analytical expressions for probability density functions of ray parameters are derived. Distributions of coordinates, momenta (grazing angles), and actions of sound rays are evaluated. Numerical simulation shows that statistical characteristics of ray parameters weakly depend on a particular realization of random perturbation giving rise to ray chaos.

Application of the matrix Rytov method to the calculation of the coherence function of a sound field in an oceanic waveguide

Closed equations for the coherence function of a monochromatic sound field propagating in a statistically inhomogeneous 3D oceanic waveguide have high dimensions and are difficult to solve even with the use of modern computers. Significant reduction of the dimension of the problem was achieved by assuming that sound speed fluctuations are statistically isotropic in a horizontal plane. However, even in this case calculation of the coherence function for a megameter range takes about a day. In this paper, we develop an approximate solution of the closed equations for the coherence function which is similar to a matrix version of the Rytov method. An explicit expression for the coherence function is obtained which contains exponent of an "interaction" matrix. This matrix is determined in terms of the acoustic and internal wave modes and spatial spectrum of the sound speed fluctuations. It is shown that the matrix Rytov method provides an accurate solution for the coherence function which coincides with the solution of the closed equations within a few percent. Calculation of the coherence function now takes only about an hour. This allows us to study in detail the dependence of the coherence function on parameters of the problem.

Ocean acoustic tomography using a double-beamforming algorithm

Since Munk and Wunsch proposed the basis for ocean acoustic tomography, many experiments have been performed to estimate sound speed fluctuations in the ocean, using ray identification and measurement of their travel times. However, technical limitations appeared such as the precision of the arrival time measurements or the number of ray arrivals that can be extracted from the signal. Recently, technical improvements allowed more complete experiments using two vertical arrays of sensors (source array and hydrophone array). In this configuration, the signals between each source and receiver are recorded which greatly improve the available information to identify the acoustic rays. One way to increase the number of rays in the tomography algorithm is to perform double-beamforming on the source and receive arrays. With double-beamforming, ray arrivals are separated by emission angle, reception angle and arrival time. Thus, we solve more ray arrivals than with a single beamforming or with a point-to-point approach. In order to avoid previous limitations and to explore acoustical limitations, we study two simple cases through the double-beamforming algorithm: with simulated data and with ultrasonic small-scale experimental data.

An optimized source transmission scheme based on pressure sensitivity kernels

A first‐order Born approximation is used to obtain the pressure sensitivity of the received signal to small changes in medium sound speed. The pressure perturbation to the received signal caused by medium sound speed changes is expressed as a linear combination of single‐frequency sensitivity kernels weighted by the source signal in the frequency domain. This formulation is used to optimize the pressure sensitivity kernel to give a new source transmission that can produce a focal spot and at the same time, to have less sensitivity to sound speed fluctuations than time‐reversal. The formulation allows for a trade‐off between quality of focal spot and sensitivity to environmental fluctuations. The optimized new source transmission uses knowledge of the medium statistics and is related to the regularized inverse filter.

Acoustic tomography of the internal wave‐ssociated fluctuations in the lower atmosphere

The two different schemes of acoustic tomography of the atmospheric boundary layer (ABL) were used in the field experiments conducted near Melpitz (Germany) and Zvenigorod (Russia). The mesoscale effective sound speed fluctuations (periods 1min‐1h) averaged over different acoustic ray paths were retrieved from the fluctuations of sound travel time between sources and receivers. It was found that a major contribution to the retrieved fluctuations comes from the wind speed fluctuations. By using a coherence analysis of the retrieved and measured wind speed fluctuations in the spatially distanced points the wave like fluctuations with periods of 16‐20min, 8‐10min, 4‐5min, 1‐2min have been filtered, and their horizontal translation velocities and scales have been estimated. Similar periods were also found in the variations of the vertical turbulent fluxes of momentum and heat near ground. The mechanism of origination of these periods in the observed fluctuations is proposed. The effect of the wind shear varia...

The possibility of reconstruction of two-dimensional random inhomogeneities in a shallow sea by frequency shifts of the spatial interference structure of the sound field

Fluctuations of frequency shifts of the spatial interference structure of the sound field in the oceanic waveguide, caused by a two-dimensional field of a random perturbation, are described. Various schemes of observation point spacing are considered. The possibility is shown to reconstruct the spatial spectrum of waveguide perturbations by measuring the spatial spectrum of the frequency shift of the interference pattern. The results of the theoretical treatment are illustrated by the examples of background internal waves and bottom roughness. The sensitivity of monitoring based on measurements of frequency shifts of the interference structure of the sound field is estimated. For medium perturbations by background internal waves, the fluctuations of liquid layer vibrations, sound speed, and temperature, which are minimum detectable by frequency shifts of the interference pattern, were estimated.

Study of sound speed in near-critical carbon dioxide

Based on the condensing vapor model, the expression of sound speed close to critical point is deduced,which shows the relationship between the sound speed and the density fluctuating index and thermal capacity at constant volume. Close to critical point, the sound speed of liquid carbon dioxide is inversely proportional to the density fluctuation index. The bigger the density fluctuation index, the smaller the sound speed. The sound speed is maximal at minimal density fluctuation index, where small fluctuations of density induces large fluctuations of sound speed. When the pressure increases and approaches to critical point, the rapid increase of thermal capacity induces decrease of sound speed. When the pressure increases and departs from critical point, the rapid decrease of thermal capacity at constant volume induces increase of sound speed. The calculated values of sound speed from the expression are in good agreement with the reference values from NIST.

Acoustic tomographic study of the mesoscale coherent structures in the lower atmosphere

The results of acoustic tomographic monitoring of the coherent structures in the lower atmosphere and the effects of these structures on the acoustic signal parameters (travel time, duration and direction of propagation) are studied. From the measurements of acoustic travel time fluctuations (periods 1 min-1h) by a net of distanced receivers the temporal fluctuations of the effective sound speed are retrieved along different ray paths connecting a pulse source and the receivers. By using a coherence analysis of the fluctuations near spatially distanced ray turning points, the internal wave-associated fluctuations are filtered and their spatial characteristics (coherences, horizontal translation velocities, and spatial scales) are obtained. A possible explanation of the presence of the dominant periods in the observed mesoscale variations of the acoustic parameters, wind shears and turbulent fluxes of momentum near ground is done.

Applying data nullspace projection method on matched-field source localization in a random internal wave field

In a random internal wave field where temporal varying water-column soundspeed profiles are very difficult to measure, matched-field source localization methods can be greatly degraded due to water-column model mismatch. In this paper, the data nullspace projection is applied to this source localization technique to reduce the effect of unknown water-column soundspeed variations. The basis of this method is to project the acoustic signal onto a data nullspace that is insensitive to water-column soundspeed fluctuations. This method only requires the mean and the second-order statistics of temporal varying water-column soundspeed profiles to calculate soundspeed empirical-orthogonal-functions. It does not require measurements of the exact soundspeed field, i.e., each snapshot, for the matched-field processing. In a simulation test case, a linear wave model is used to generate a random internal wave field, an acoustic source continuously transmits a single frequency tone, and the matched-field processing is implemented with the signal received on both a VLA and a HLA, respectively, for localizing the source position. The simulation results show that applying the data nullspace projection method can dramatically improve the robustness and accuracy of the matched-field source localization, resulting in a random internal wave field.

Statistical description of chaotic rays in a deep water acoustic waveguide

This paper analyzes the chaotic ray dynamics at multimegater ranges in a deep water environment with internal-wave-induced fluctuations of the sound speed. The behavior of acoustic ray paths is investigated using the Hamiltonian formalism expressed in terms of action-angle variables. It is shown that the range dependence of the action variable of chaotic ray can be approximated by a random Wiener process. On the basis of this result an approximate statistical description of the chaotic ray structure is derived. Distributions of coordinates, momenta (grazing angles), and actions of sound rays are evaluated. This statistical approach is used for studying ray travel times, that is, arrival times of sound pulses coming to the receiver through different ray paths. The spread of travel times for a bundle of rays with close starting parameters and the influence of sound speed fluctuations on the timefront representing ray arrivals in the time-depth plane are examined. Estimates for the widening and bias of the timefront segment caused by the fluctuations are obtained.

Sound fluctuation in a non-Gaussian random field: A wavelet-based Wiener chaos expansion approach

Recently Wiener chaos derived stochastic expansion methods, especially polynomial chaos (PC), have caught great attention in the underwater acoustics community for its success in modeling random properties of underwater acoustic field. However, most research until now concern a Gaussian random field, while fluctuations in ocean medium are not always Gaussian. For non‐Gaussian probability density function (PDF) with a finite support, it is reported that a Wiener chaos decomposition, which use wavelets as basis functions instead of orthogonal polynomials, is more suitable than PC. This paper concentrates on non‐Gaussian high frequency internal waves [T. Wang and T. Gao, Chin. J. Ocean. Limnol. 20, 16–21 (2002)] and presents a multi‐resolution stochastic expansion approach to handle acoustic field fluctuation in a non‐Gaussian internal wave field. The depth dependent PDF of sound speed fluctuation is determined empirically from experiment results. Spatial coherence function and scintillation index of acoustic field were calculated for Gaussian and non‐Gaussian cases. In addition, a comparison between both situations was made, which shows that in the non‐Gaussian case, the acoustic field has a more complex coherence structure. [Work partially supported by NSFC.]

Effects of offshore mesoscale eddies and fronts on inshore shallow water acoustic propagation

Shallow water shelf areas inside of western boundary currents have two distinctly different ocean acoustic environments determined by the type of front that separates deep offshore from shallow inshore. Prograde fronts allow for the ducting of offshore internal waves up onto the shelf as the main source the sound speed fluctuations over the internal wave band. Retrograde fronts block the propagation of offshore internal waves setting up stability conditions that allow for propagation of locally generated, large amplitude non‐linear solitary waves as the major source of sound speed variability. Here, acoustic propagation is examined for both environments with data from two similar fixed system propagation experiments, one for the prograde environment off the coast of south Florida near the site off the Acoustic Observatory, and the second for the retrograde front environment of the Mid‐Atlantic Bight the SWO6 site. Offshore mesoscale features of fronts and eddies are shown to determine mean sound speed profiles and the energy of the internal wave fields. In turn, intensity fluctuations and temporal coherencies of broadband acoustic signals over several octaves are observed to vary with variations of the sound speed. For some locations, observations of mesoscale features alone can predict sonar performance.

Concerning the sediment volume contribution to scattering in SAX04 (Sediment Acoustics Experiment 2004) sediment: Sound speed and bulk density fluctuations

Sound speed and bulk density profiles measured from SAX04 sediment cores are used to estimate correlation lengths of fluctuations in the sound speed and the bulk density. Sound speed is measured from 5.9-cm-diameter cores at 1-cm intervals and bulk density is measured at 2-cm intervals from the same cores. Previous estimates of these parameters from experimental data involved fewer realizations (cores), limited sampling areas, and samples without mud flasers within the sand sediment. Values of correlation length may vary according to location within the SAX04 site. Correlation length values estimated with Burg’s algorithm from sediment sound-speed fluctuations averaged 2.24 cm, from sediment bulk density fluctuations averaged 2.53 cm. Ranges of values of correlation length estimated from bulk density fluctuations from locations inside the experiment site are used to present a range of volume scattering strength predictions, given the other parameters of sediment sound speed, sound attenuation, density ratio variance, and ratio of sound speed to density fluctuations used by the perturbation approximation to the composite roughness model for each location. At the SAX04 site, interface scattering dominated over volume scattering, despite the presence of mud inclusions with strong sound speed and bulk density contrasts. [Work sponsored by ONR.]