Sound Speed Fluctuations Research Articles

Polynomial chaos expansions for modelling the statistics of acoustic propagation in random waveguides

The use of Polynomial Chaos expansions to model the transfer of the statistical properties of the sound speed in ocean waveguides to those of acoustic waves passing through them is described. A perturbational framework approximating the interaction of acoustic normal modes with fluctuations around a background sound speed is used, with the fluctuations being represented vertically by empirical orthogonal functions and horizontally by correlation functions. The Polynomial Chaos expansions are derived to second order in the uncorrelated random variable representing the sound speed fluctuations for the generalized phase of the complex modal amplitudes, and to third order for the modal amplitudes themselves. The ability of the second order polynomial chaos expansion for the generalized model phase to accurately model acoustic propagation statistics is closely coupled to the accuracy of the adiabatic approximation in light scattering regimes. The weights of the Polynomial Chaos expansions are obtained using both direct (theoretical) and indirect (least-squares fit) methods. Divergence between these two sets of weights increases with combinations of increasing strength of sound speed fluctuations, increasing frequency, or increasing range, indicating where a higher order expansion may be necessary. Modelling results for the first and second moments of the acoustic intensity and the Scintillation Index in random waveguides are presented and compared to Monte Carlo results.

The Acoustic Laboratory for Marine Applications (ALMA) applied to fluctuating environment analysis

The Acoustic Laboratory for Marine Applications (ALMA) has been used to address problems in underwater acoustics, such as sound propagation in fluctuating environments. In this work, data from the ALMA-2016 at-sea campaign are used to analyze the ocean fluctuation's influence on sound propagation in a shallow-water waveguide. The experiment took place in November 2016 on the continental shelf of the eastern coast of the island of Corsica. A source and a receiver array were 9.3 km apart in a nearly constant water depth of 100 m. A thermistor chain was moored near the source to monitor sound speed fluctuations. The source emitted a variety of signals from which the chirp (1–13 kHz) is used to extract the waveguide eigenrays. To do so, a time-domain beamforming is performed on the match-filtered received signals with an automatic detection of local maxima in the time of arrival/direction of arrival (TOA/DOA) domain. A 2 min acquisition period of more than 13 h duration shows significant fluctuations in eigenray TOAs/DOAs. Qualitative comparisons with synthetic signals obtained from simulations permit reproduction of the observed eigenray fluctuations without including range dependence of the sound-speed profile. In addition, the joint analysis of the probability density function of the normalized acoustic intensity and of the thermistor chain data highlights the time dependence of the received signal characteristics.

The statistical characteristics of the atmospheric anisotropic inhomogeneities and their effect on the intensity fluctuations of infrasound field

The influence of anisotropic wind velocity and temperature inhomogeneities on the attenuation of infrasound field intensity with increasing distance from a point source and on its altitude distribution is studied. The field is calculated as a function of receiver height and horizontal distance from the source using method of the pseudo-differential parabolic equation for the atmosphere with model realizations of anisotropic effective sound speed fluctuations. These realizations are obtained from the nonlinear shaping model for the gravity wave perturbations which produces the fluctuations with both the vertical and horizontal spectra consistent with the observed spectra. When propagating in the stratospheric and thermospheric wave guides the multiple scattering of infrasound field from the anisotropic fluctuations results in certain vertical wave number spectra and probability density functions of infrasound intensity fluctuations in the stratospheric (altitudes 30–40 km) and mesospheric layers (50–70 km). The statistical characteristics of the intensity fluctuations as a function of distance from the source (up to 2200 km) were studied. The same characteristics were obtained for the infrasound field scattered from the inhomogeneities whose vertical profile was retrieved from the infrasound signals from surface explosions detected in the shadow zone.

Estimating the Location of Acoustic Sources with Oceanic Internal Gravity Waves via Frequency-Difference Source Localization

Frequency-difference source localization (FDSL) is a relatively new method for locating sources emitting acoustic or electromagnetic waves from recorded data. Estimates of location are produced by matching a nonlinear function of the received data with the same nonlinear function of modeled data. This so-called matched-field approach depends on the accuracy of the modeled field. FDSL exhibits less sensitivity to model errors in some cases of interest. Fluctuations of the speed of sound in the ocean are affected by a wide variety of phenomena and internal gravity waves is one where their spectrum is usually well known. There is no analytical theory for predicting how these fluctuations of sound speed affect the accuracy of FDSL, leaving a numerical evaluation as the alternative for the focus of this paper. Experimental application of FDSL was previously made for an acoustic source of 100 Hz bandwidth surrounding 250 Hz for a 129 km section in the Philippine Sea with data recorded on a long vertical array [Geroski and Dowling, Long-range frequency-difference source localization in the Philippine Sea, J. Acoust. Soc. Am. 146 (2019) 4727–4739.]. The role of internal waves is quantified with a realistic FDSL simulation using models based on the parabolic and ray approximations of the linear acoustic wave equation. The modeled vertical variation of FDSL error is similar to observed while the modeled horizontal error is too small. The complicated software model is automatic but is computationally intensive, with our version needing about 1.5 mo to compute on a PC with 16 cpu cores.

Frequency dependent effects of environmental parameters on the broadband acoustic wave propagation in shallow water waveguides

Acoustic wave intensity plays a crucial role in underwater acoustics, particularly in shallow water regions in which the signal suffers substantial energy fluctuations. The physical properties of the environment significantly impact the intensity of broadband acoustic waves in shallow water waveguides. The accuracy of the intensity is vital for the reliability of any inverse algorithm used to obtain the physical properties of the waveguide boundaries. In this paper, we explore the effects of sound speed fluctuations in the water column on broadband acoustic propagation across different frequencies. Our observations reveal that at higher frequencies the sound intensity is more sensitive to oceanographic variability. This poses challenges for geo-acoustic inversions when parameters in the water column are not well-known, particularly at higher frequencies. To validate our findings, we present simulations using normal modes and parabolic equation with examples from recent experimental observations conducted on the New England Mud Patch Area and the continental shelf region of the United States during 2017, 2021, and 2022. These experiments provide valuable insight into the intricate behavior of acoustic waves in shallow water environments at different frequency bands. [Work supported by ONR (Grant No. N00014-21-1-2760).]

Observations of the space/time scales of Beaufort sea acoustic duct variability and their impact on transmission loss via the mode interaction parameter.

The Beaufort duct (BD) is a subsurface sound channel in the western Arctic Ocean formed by cold Pacific Winter Water (PWW) sandwiched between warmer Pacific Summer Water (PSW) and Atlantic Water (AW). Sound waves can be trapped in this duct and travel long distances without experiencing lossy surface/ice interactions. This study analyzes BD vertical and temporal variability using moored oceanographic measurements from two yearlong acoustic transmission experiments (2016-2017 and 2019-2020). The focus is on BD normal mode propagation through observed ocean features, such as eddies and spicy intrusions, where direct numerical simulations and the mode interaction parameter (MIP) are used to quantify ducted mode coupling strength. The observations show strong PSW sound speed variability, weak variability in the PWW, and moderate variability in the AW, with typical time scales from days to weeks. For several hundreds Hertz propagation, the BD modes are relatively stable, except for rare episodes of strong sound speed perturbations. The MIP identifies a resonance condition such that the likelihood of coupling is greatest when there is significant sound speed variability in the horizontal wave number band 1/11<kh<1/5 km-1. MITgcm ocean model results are used to estimate sound speed fluctuations in this resonance regime.

Sound propagation and scattering in turbulent media

This presentation overviews sound propagation and scattering in turbulent media and pertinent acoustic remote sensing of turbulence. Although sound propagation through a turbulent atmosphere is mainly considered, the presented results apply to other media such as oceanic turbulence. Formulations are provided for various statistical characteristics of acoustic signals such as the scattering cross section, the variances of the phase and log-amplitude fluctuations, the spatial, temporal, and cross-frequency coherences, and the probability density functions. Monte Carlo simulation of sound propagation in a random medium is explained. Specifics of acoustic signals in turbulent media as compared to electromagnetic waves are highlighted. For example, sound waves are scattered by both the sound speed and medium velocity fluctuations, which are scalar and vector random fields, respectively, with different statistical properties. Also, fluctuations in the acoustic refractive index are much stronger than those in electromagnetic propagation, and sound can be scattered by humidity (or salinity) fluctuations. Finally, the Markov approximation, which is widely used for electromagnetic waves, might not be applicable for some statistical characteristics of acoustic signals. It is explained how these specifics of sound propagation are addressed in atmospheric acoustics.

Efficient Mode-Coupling Calculation for Constant Depth Ocean with Range-Dependent Sound–Speed Fluctuation

In this paper, a criterion for efficient coupled-mode matrix calculation in a constant depth ocean with range-dependent sound–speed fluctuation is proposed. The usual stepwise coupled mode requires high computational power to calculate the mode-coupling matrix at each interface of the range segment. To reduce the computational complexity, the criterion for selecting appropriate mode pairs, which strongly affects the mode-coupling matrix, is derived from perturbation theory. This criterion determines the effective range of the modal beat wavenumber. Numerical examples indicate that compared with the full calculation of the mode-coupling matrix, for the calculation using the proposed criterion, the computational complexity is significantly reduced, while the accuracies of the mode-coupling matrix and acoustic field are maintained.

Influence of internal wave induced sound speed variability on acoustic propagation in shallow waters of North West Bay of Bengal

This study focuses on the influence of internal wave induced sound speed variability on acoustic propagation parallel to the coast in shallow waters of North West Bay of Bengal (BoB). An acoustic transmission and reception experiment had been conducted at the site during February 2018 with simultaneous acquisition of oceanographic data, to examine propagation characteristics. The 950 Hz signal from an anchored vessel was received by an array of hydrophones moored 50 km away, with a loss of ∼ 80–95 dB with respect to the source position, receiver depth and sound speed variability. Sound speed variations in the acoustic environment were simulated using a shallow water internal wave model called WAVE to characterize the acoustic environment. Derived internal wave features from oceanographic and acoustic observations from study location during the experiment period were used to simulate the internal wave acoustic environment. Sound propagation using BELLHOP model was carried out with a simulated internal wave sound speed environment for 950 Hz source frequency. Model and observed temporal variability of transmission loss with sound speed at both source depth and thermocline depth has been addressed. Transmission loss features are comparable with field observations and model limitations are reflected in the results thus showing errors between two approaches. Range dependent bathymetry and other ocean acoustic parameters influence transmission loss at the study location. Temperature and salinity are major parameters influencing sound speed fluctuation in shallow waters, and corresponding variations are reflected in transmission loss and propagation. Finally this study provides a quantitative support in transmission loss in both modeling and experimental approaches at the study location.

Infrasound propagation through the atmosphere with mesoscale wind velocity and temperature fluctuations

Some results on modeling and observation of infrasound propagation in the atmosphere in a presence of mesoscale and anisotropic wind velocity and temperature fluctuations are presented. The theoretical model of infrasound scattering from anisotropic wind velocity and temperature inhomogeneities of the atmosphere is developed. With this model, the appearance of the stratospheric, mesospheric, and thermospheric arrivals of the infrasound signals in the acoustic shadow zones is explained. The analytic relation between the wave field of the scattered infrasound signal and the vertical profile of the effective sound speed fluctuations is obtained. Using this relation, the vertical profiles of the fluctuations within the upper stratosphere (25–55 km) and the lower thermosphere (105–140 km) were retrieved from the waveforms and travel times of the signals recorded in the acoustic shadow zones. The theoretical frequency spectrum of the infrasound wavefield reflected from the fine-scale layered structure of the atmosphere is obtained and compared with the spectra of the observed stratospheric arrivals.

Average Intensity of Low-Frequency Sound and Its Fluctuations in a Shallow Sea with a Range-Dependent Random Impedance of the Liquid Bottom

In this study, the problem of the influence of a horizontally inhomogeneous liquid bottom impedance, given by random Gaussian function of the speed of sound and by density, on the propagation of low-frequency sound in a shallow-water waveguide is considered. The model parameters are referenced to the conditions of sound propagation in the regions of the seas of the Russian Arctic shelf. By the example of statistical modeling of the sound field intensity, we show that sound speed fluctuations in the bottom lead to similar effects that were previously established for volumetric fluctuations of the speed of sound in the water layer. With the distance from the source, the decrease in the average intensity slows down in comparison with a deterministic medium in which there are no fluctuations. This deceleration of the decay of the intensity in a random waveguide can be significant already at short distances. Changes in the law of decay of intensity at a fixed frequency are mainly determined by the correlation radius of inhomogeneities and the average penetrability of the bottom, which leads to attenuation of sound propagating in the waveguide.

Data-driven approaches for ray-based ocean acoustic tomography

Ray-based acoustical tomography typically provides estimates of local ocean sound speed fluctuations from precise measurements of acoustic travel times fluctuations (with respect to a reference environment) between multiple sources and receiver arrays along with a model of the ray propagation in the reference (i.e., fluctuation-free) environment. Traditionally, this is achieved using a sensitivity kernel, a Born–Frechet linearization of the non-linear relationship between ray arrival-times and sound speeds fluctuations. However, computing the full sensitivity kernel can be computationally intensive and is restricted to only small sound-speed fluctuations (due to the linearization procedure) and does not inherently leverage any available history of the arrival time or sound speed fluctuations which may have been collected prior to performing the inversion procedure. As an alternative solution for ray-based acoustical tomography, we investigated the use of data-driven methods, such as linear regression, nearest neighbors, neural networks, and kernel (ridge) regression, to directly learn the non-linear relationship between sound speed fluctuations and ray arrival time variations using previously collected measurements. Additionally, the experimental training data set is augmented by generating synthetic SSPs based on empirical orthogonal function analysis of the historical SSP data. This approach is demonstrated for short vertical bottom-mounted arrays deployed in littoral environments.

Observations of sound-speed fluctuations in the Beaufort Sea from summer 2016 to summer 2017.

Due to seasonal ice cover, acoustics can provide a unique means for Arctic undersea communication, navigation, and remote sensing. This study seeks to quantify the annual cycle of the thermohaline structure in the Beaufort Sea and characterize acoustically relevant oceanographic processes such as eddies, internal waves, near-inertial waves (NIWs), and spice. The observations are from a seven-mooring, 150-km radius acoustic transceiver array equipped with oceanographic sensors that collected data in the Beaufort Sea from 2016 to 2017. Depth and time variations of the sound speed are analyzed using isopycnal displacements, allowing a separation of baroclinic processes and spice. Compared to lower latitudes, the overall sound speed variability is small with a maximum root mean square of 0.6 m/s. The largest source of variability is spice, most significant in the upper 100 m, followed by eddies and internal waves. The displacement spectrum in the internal wave band is time dependent and different from the Garret-Munk (GM) spectrum. The internal wave energy varied with time averaging 5% of the GM spectrum. The spice sound-speed frequency spectrum has a form very different from the displacement spectrum, a result not seen at lower latitudes. Because sound speed variations are weak, observations of episodic energetic NIWs with horizontal currents up to 20 cm/s have potential acoustical consequences.

Random matrix theory and underwater sound propagation

Random matrix theory originated as the statistical theory of strongly interacting quantum systems, and has since been applied in an extremely broad range of applications. For example, it has been developed to accurately and efficiently model long range acoustic propagation in the ocean, including the construction of propagating acoustic time fronts. This problem can be viewed as dynamical symmetry breaking, i.e., the breaking of integrability, which has been explored in a variety of quantum mechanical contexts. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. In addition to its efficiency, the theory helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered wave guide contexts where the use of random matrix theory has a multi-decade history.

Atmospheric Boundary Layer as a Laboratory for Modeling Infrasound Propagation and Scattering in the Atmosphere

In this work, we show that large-scale processes of the long-range propagation and scattering of infrasound signals in stratospheric and thermospheric waveguides are to some extent similar to the smaller scale processes of waveguide propagation and scattering of acoustic signals in stably stratified ABL. Moreover, we note a resemblance between the zeroth order tropospheric mode and the Lamb mode that is observed for larger nuclear explosions. The results of physical modeling of the long-range propagation of infrasound signals in the atmosphere by studying the propagation of the acoustic pulses from detonation sources in the stably stratified atmospheric boundary layer (ABL) are presented. Such modeling became possible due to continuous measurement of the wind velocity and temperature profiles in the ABL by Doppler sodar and temperature profiler, respectively. The resemblance between the propagation of the infrasound signals from surface explosions (20–70 t TNT) in the “shallow” tropospheric wave guide and propagation of Lamb mode from nuclear explosions is found. Also, the propagation of infrasound signals in the stratospheric wave guide is modeled by studying the propagation of acoustic pulses in the ABL during morning hours (after sunrise), when an effective sound speed profile in the ABL is similar to that in the stratospheric wave guide. The instantaneous vertical profiles of the effective sound speed and wind velocity fluctuations in the thin layers of the stably stratified ABL located at different heights (up to 700 m) above the ground and at different distances from the source (up to 2.25 km) have been retrieved using the wave forms and travel times of the recorded arrivals of the acoustic pulses from the detonation sources. The effect of scattering of acoustic pulses from the fine-scale layered structure of the stably stratified ABL is studied to model the effect of scattering of infrasound signals from the fine-scale layered structure of the stratosphere.

Effect of mesoscale eddies on the vertical spatial characteristics of wind-generated noise in deep ocean

Mesoscale eddy is a marine phenomenon occurring frequently in deep ocean, and it will disturb the sound speed in the upper water layer. As a result, the mesoscale eddies will influence the propagation of wing-generated noise and cause the noise field to vary. In this paper, we investigate the effects of mesoscale eddies on the vertical spatial characteristics (including the noise vertical directionality and the noise vertical correlation) of wind-generated noise at different depths of its horizontal center of the eddy. In the study, the Gaussian eddy model is used to describe the sound speed fluctuation, and the ray and parabolic equation theories are used to describe the noise propagating in the near field and far field, respectively. Simulations indicate as follows. 1) At the depth of the eddy center, a clod-core eddy causes both the width of the horizontal notch and the noise vertical correlation to decrease, while the effect of a warm-core eddy is contrary to that of the cold-core eddy. 2) At the depth far from the eddy center, the effect of eddies is reduced, a cold-core and a warm-core eddy only lead the peak at the down edge of the horizontal notch in the noise directionality to rise and fall, respectively, and do not influence the noise vertical correlation. 3) The effect of an eddy becomes severe as its absolute strength becomes higher. The ray reversion method based on the principle of reciprocity is used to explain the physical reason behind the above phenomena. By the method the rays are launched from the noise receiving point and the polar angle and the strength of the noise arriving reversely along the ray paths are analyzed. It is shown that the change of the polar angle and the strength of the noise arriving reversely along the surface reflected ray paths in the presence of eddies are the main cause for changing the noise vertical spatial characteristics. Furthermore, simulations show that the analyses and conclusions in the study are still approximately valid when the receiving point deviates from the eddy center but the horizontal distance between them is short.

Regional Variability of Influence of Small-Scale Sound-Speed Fluctuation Levels on the Acoustic Fields Formation in the Ocean

The results presented herein are the research findings about the influence of small-scale inhomogeneity’s in water environment on the structure of acoustic fields for hydrological and acoustical conditions that are typical for the Atlantic and Pacific Oceans. Small-scale sound-speed fluctuations were modeled by adding a stochastic perturbation to the deterministic mean profile. Quantitative experiment was conducted to determine the dynamics of changes in the first three convergence zones at the depths of emission source in relation to the random componentry in the sound-speed field. Analytical dependences of increasing widths of upper convergence zones on the level of the random componentry in the sound-speed field were determined based on the results of quantitative experiment. With increasing stochasticity levels, the width of convergence zones increases in accordance with linear law, and the absolute increments grow with the increase of convergence zone number. When the values of a random componentry in the sound-speed field are fixed, the absolute increment of width of the upper convergence zones in the Atlantic Ocean is higher than in the Pacific Ocean. This said, the gradient of a smooth profile of the sound velocity by depth above the axis of hydroacoustic channel is higher in the Atlantic Ocean. Consequently, the absolute increments of width of the convergence zones depend not only on the levels of stochasticity parameters of water environment, yet, also, on the gradient size of smooth profile of the sound speed at depths above the axis of hydroacoustic channel.

Sensitivity of sound speed fluctuation on acoustic arrival delay of middle range in deep water

For middle range acoustic propagation in deep water, there exists mainly four types of ray arrivals, namely direct path arrival, one time surface-reflected (SR) arrival, one time bottom-reflected (BR) arrival and one time surface-reflected bottom-reflected (SRBR) arrival. With Bellhop ray model, sensitivity of sound speed fluctuation on the arrival delay of middle range in deep water was studied. Argo profiles in Philippine Sea were used to establish the Sound Speed Profile (SSP) fluctuation set with the Empirical Orthogonal Function (EOF) method. Numerical simulation suggests that when the source was closer to the sea surface, the relative delay structure was more sensitive to the SSP fluctuation, and that the SR arrival and the SRBR arrival were more sensitive to the fluctuation than the BR arrival. When receiver range increases from 20 km to 30 km, sensitivities of ray arrivals gradually increase. Acoustic arrival delay data in the Philippine Sea experiment was used to invert the SSP. The inverted result agrees with the measured data well, suggesting the arrival structure was a nice choice for acoustic tomography of middle range in deep water.

On spatial structure of the wave field in a vertical section of a deep water acoustic waveguide

The spatial structure of the wave field excited by a tonal point source in an underwater acoustic waveguide with random sound speed fluctuations is analyzed. This is done using an approach in which the field is approximated by a sum of components formed by contributions of narrow beams of rays. These components fluctuate less than the total field and, therefore, they are called stable. Each ot them can be isolated from the total field recorded by a long vertical antenna, using the coherent state expansion developed in quantum mechanics. An approximate analytical expression is obtained for the correlation matrix of the superposition of several stable components. The applicability of this equation is confirmed by the results of Monte Carlo simulation. The simulation has confirmed the theoretical prediction that nearly the same stable components can correspond to the sound speed fluctuations with completely different correlation functions.

Incoherent source localization in random acoustic waveguides

ABSTRACTWe consider the problem of localizing one or more sources in a two-dimensional waveguide with horizontal flat boundaries and random sound speed fluctuations. Our data are the acoustic pressure field, measured on a vertical array of hydrophones that may span the entire depth of the waveguide or a part of it. We use randomness to model the effect of internal waves on the sound channel. Although the strength of the fluctuations is small, the transmitted signal is significantly affected from the multiple scattering of the waves with the random inhomogeneities, especially since we consider large propagation distances between the sources and the receiver array. Source localization is performed following an incoherent approach relying on a transport system of equations that describes wave propagation in random waveguides and that takes into account modal dispersion and energy transfer between modes.