Range-dependent Sound Speed Profile Research Articles

Observed transmissions and ocean-ice-acoustic coupled modelling in the Beaufort Sea

An ocean-ice-acoustic coupled model is configured for the Beaufort Sea. The model uses outputs from a data assimilating global scale ice-ocean-atmosphere forecast to drive a bimodal roughness algorithm for generating a realistic ice canopy. The resulting range-dependent ice cover obeys observed roughness, keel number density, depth, and slope, and floe size statistics. The ice is inserted into a parabolic equation acoustic propagation model as a near-zero impedance fluid layer along with a model defined range-dependent sound speed profile. Year-long observations of transmissions at 35 Hz from the Coordinated Arctic Acoustic Thermometry Experiment and 925 Hz from the Arctic Mobile Observing System source were recorded over the winter of 2019–2020 on a free-drifting, eight-element vertical line array designed to vertically span the Beaufort duct. The ocean-ice-acoustic coupled model predicts receive levels that reasonably agree with the measurements over propagation ranges of 30–800 km. At 925 Hz, seasonal and sub-seasonal ocean and ice driven variations of propagation loss are captured in the data and reproduced in the model.

Acoustic field fluctuation caused by source-generated internal waves and its detection method

The development of noise reduction and silencing technology has brought great difficulties to underwater target detection, and more target characteristics need further studying. When a submerged target travels through density-stratified environment, the fluid will oscillate behind the target owing to gravity and buoyancy and generate internal waves, which are often referred to as source-generated internal waves. These internal waves are difficult to eliminate, which can cause the sound speed profiles to fluctuate. Therefore, these internal waves are expected to be effective for detecting underwater target. In this paper, the fluctuations of the received sound passing through the internal waves produced by a moving sphere are investigated. A typical shallow stratified environment is set up, and internal wave fields generated by a sphere moving in many horizontal directions are simulated. According to the simulation results, these internal wave fields have a much wider range than the scenario of the target body. Based on the relationship between the amplitude of the internal wave and the variation of sound speed, range–dependent sound speed profiles are constructed, and model based on ray acoustics is used to analyze the aberration strength of passing sound fields. Results show that the strength aberration is inversely proportional to the target passing angle, and these characteristics can be covered by the background. Focusing on this problem, an extraction method based on principal component analysis with sliding window is then proposed. The uncorrelation between the disturbance of internal wave and background signal is utilized, and interference is suppressed by removing the component in No.1 principal component space, and retaining the No.2–No.<i>k</i> subspace. Detection can be executed based on multi period received data from single hydrophone. A lake experiment is conducted to verify the performance. A detection scenario of single source and single receiver is established, and the AUV target crosses source–receiver line multiple times. The research results show that the detection scheme based on the acoustic aberration of source-generated internal wave has potential for underwater target detection, possessing the advantages of wide coverage and high robustness. Data on multi depths are processed to show that the detection performance is dependent on the depth of system. Since the acoustic strength variations are derived form local disturbance in channel, the proposed method may be affected by severe environment fluctuation, and further research is still needed.

Influence of Range-Dependent Sound Speed Profile on Position of Convergence Zones

Based on the Wentze–Kramers–Brillouin approximation, we derive formulae to calculate the position of convergence zones in a range-dependent environment with sound speed profiles varying in linear and ellipsoidal Gaussian eddy cases. Simulation results are provided for the linear and ellipsoidal Gaussian eddy cases. Experiment data are used for calculations considering linearly varying sound speed, and the findings suitably agree with the simulation results. According to the evaluated environment, the influence of the range-dependent sound speed profile on the position of the upper and lower convergence zones for different source depths is analyzed through simulations. The corresponding results show that the influence of the sound speed profile on the position of the upper convergence zone is greater for a shallower source. In contrast, the position of the lower convergence zone for large-depth reception is less affected.

An Efficient Coupled-Mode Formulation for Acoustic Propagation in Inhomogeneous Waveguides

The direct-global-matrix coupled-mode model (DGMCM) for sound propagation in range-dependent waveguides was recently developed by Luo et al. [A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides, Sci. China G: Phys. Mech. Astron. 55 (2012) 572–588]. A brief review of the formulation and characteristics of this model is given. This paper extends this model to deal with realistic problems involving an inhomogeneous water column and a penetrable sloping bottom. To this end, the normal mode model KRAKEN is adopted to provide local modal solutions and their associated coupling matrices. As a result, the extended DGMCM model is capable of providing full two-way solutions to two-dimensional (2D) realistic problems with a depth- and range-dependent sound speed profile as well as a penetrable sloping bottom. To validate this model, it is first applied to a benchmark problem of sound propagation in a plane-parallel waveguide with a depth- and range-dependent sound speed profile, and then it is applied to a problem involving both an inhomogeneous water column and a sloping bottom. Comparisons with the analytical solution proposed by DeSanto and with the numerical model COUPLE are also provided, which show that the extended DGMCM model is accurate and efficient and hence can serve as a benchmark for realistic problems of sound propagation in an inhomogeneous waveguide.

Three-dimensional inversion technique in ocean and seabed acoustics using the parabolic equation method

A three-dimensional parabolic equation (PE) and perturbation approach is used to invert for the range-dependent geoacoustic characteristics of the seabed. The model assumes that the sound speed profile is the superposition of a known range-independent profile and an unknown depth and range-dependent perturbation. Using a Green’s function approach, the total measured pressure field in the water column is decomposed into a background field, which is due to the range-independent profile, and a scattered field, which is due to the range-dependent perturbation. When the Born approximation is applied to the resulting integral equation, it can be solved for the range-dependent profile using linear inverse theory. For simplicity, the sound speed profile in the water column is assumed to be known, and the range-dependent perturbation is added to the index of refraction n(x,y,z), rather than the sound speed profile c(x,y,z). The method is implemented in both Cartesian (x,y,z) and cylindrical (r,θ,z) coordinates with the forward propagation of the field in x and r, respectively. Synthetic and experimental data are used to demonstrate the validity of the method. Keywords: Three-dimensional parabolic equation method, geoacoustic inversion, range-dependent sound speed profile, linear inversion, Born approximation, and Green’s functions.

A hybrid approach for estimating range-dependent properties of shallow water environments

H hybrid approach based on statistical signal characterization and a linear inversion scheme for the estimation of range dependent sound speed profiles of compact support in shallow water is presented. The approach is appropriate for ocean acoustic tomography when there is a single receiver available, as the first stage of the method is based on the statistical characterization of a single reception using wavelet transform to associate the signal with a set of parameters describing the statistical features of its wavelet sub-band coefficients. A non-linear optimization algorithm is then applied to associate these features with range-dependent sound speed profile in the water column. This inversion method is restricted to cases where the range dependency is of compact support. At the second stage a linear inversion scheme based on modal arrivals identification and a first order perturbation formula to associate sound speed differences with modal travel time perturbations is applied to fine tune the results obtained by the optimization scheme. A second restriction of this stage is that mode identification is necessary. If this assumption is fulfilled the whole scheme may be applied in ocean acoustic tomography for the retrieval of three-dimensional features, combining inversion results at various slices.

Echo statistics of individual and aggregations of scatterers in the water column of a random, oceanic waveguide.

The relative contributions of various physical factors to producing non-Rayleigh distributions of echo magnitudes in a waveguide are examined. Factors that are considered include (1) a stochastic, range-dependent sound-speed profile, (2) a directional acoustic source, (3) a variable scattering response, and (4) an extended scattering volume. A two-way parabolic equation model, coupled with a stochastic internal wave model, produces realistic simulations of acoustic propagation through a complex oceanic sound speed field. Simulations are conducted for a single frequency (3 kHz), monostatic sonar with a narrow beam (5° -3 dB beam width). The randomization of the waveguide, range of propagation, directionality of the sonar, and spatial extent of the scatterers each contribute to the degree to which the echo statistics are non-Rayleigh. Of critical importance are the deterministic and stochastic processes that induce multipath and drive the one-way acoustic pressure field to saturation (i.e., complex-Gaussian statistics). In this limit predictable statistics of echo envelopes are obtained at all ranges. A computationally low-budget phasor summation can successfully predict the probability density functions when the beam pattern and number of scatterers ensonified are known quantities.

Experience with geoacoustic inversion of transmission loss

This presentation will discuss recent experience with geoacoustic inversion of transmission loss (TL) data from 50 to 5000 Hz from both deep and shallow water regions. For shallow water, a multi-layered geoacoustic profile with range dependent layer thicknesses is used. Layer thickness is not an inversion parameter but is known from ancillary data such as seismic profiling and chirp sonar. Issues related to range dependent sound speed profiles (SVPs) will be discussed as will observation of the time spread of multipath arrivals. For deep water, a single layer geoacoustic profile is assumed. Quality of inversion is assessed using comparison of measured and modeled TL and the estimation error. The estimation error is the dependence of the total rms error—summed over range, frequency, and receivers—on the values of a geoacoustic parameter within the bounds used to constrain inversion. The estimation error identifies geoacoustic parameters that are well constrained or poorly constrained by the TL data. Inversion was carried out using a genetic algorithm model [D. Harvey et al., Oceans '02 MTS/IEEE, 1, 358–362 (2002)]. Acoustic and environmental data were provided by the Naval Oceanographic Office. [Work funded by the Ocean Bottom Characterization Initiative through PEO C4I, PWM 120.]

MEASUREMENT AND SIMULATION FOR WIND NOISES IN THE OCEAN ENVIRONMENTS WITH NONLINEAR INTERNAL WAVES

This study obtains wind noise variations by experimental data and simulated results to describe meteorological and oceanic effects. The ambient noise data were measured by a vertical line array in the 2001 ASIAEX South China Sea experiment. An acoustic propagation model is used in noise modeling for calculating the sound pressure of noises at receiving sites, including the effects of ocean environmental changes, bottom interactions, and noise fluctuations at different depths. Both range-independent and range-dependent sound speed profiles are generated with in-situ water temperature data. Results show fluctuating noise levels with variations in ocean environments. But the fluctuations are small such that only weak correlation exists in the acoustic noise data and ocean data. Results also indicate that using range-independent sound speed profiles can simulate noise field in range-dependent ocean environments with nonlinear internal waves for shallow regions with flat bottoms.

Adjoint modeling for acoustic inversion.

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.

MODE AND PE PREDICTIONS OF PROPAGATION IN RANGE-DEPENDENT ENVIRONMENTS: SWAM'99 WORKSHOP RESULTS

Three numerical acoustic models, a coupled normal-mode model (C-SNAP), an adiabatic normal-mode model (PROSIM), and a parabolic equation model (RAM), are applied to test cases defined for the SWAM'99 workshop. The test cases consist of three shallow water (flat bottom) scenarios with range-dependent sound-speed profiles imitating internal wave fields and a shelf-break case, with range-dependent sound-speed profiles and bathymetry. The bottom properties in all the cases are range-independent and modeled as a homogeneous fluid half-space. The results from the modeling are presented as transmission loss for selected acoustic frequencies and source-receiver geometries, and as received time series. The results are compared in order to evaluate the effect of applying different propagation models to the same range-dependent underwater environment. It should be emphasized that the propagation analysis is not an attempt to benchmark the selected propagation models, but to demonstrate the performance of practical, range-dependent models based on different approximations in particular underwater scenarios.

Mode and PE Predictions of Propagation in Range-Dependent Environments SWAM'99 Workshop Results

Three numerical acoustic models, a coupled normal-mode model (C-SNAP), an adiabatic normal-mode model (PROSIM), and a parabolic equation model (RAM), are applied to test cases defined for the SWAM'99 workshop. The test cases consist of three shallow water (flat bottom) scenarios with range-dependent sound-speed profiles imitating internal wave fields and a shelf-break case, with range-dependent sound-speed profiles and bathymetry. The bottom properties in all the cases are range-independent and modeled as a homogeneous fluid half-space. The results from the modeling are presented as transmission loss for selected acoustic frequencies and source-receiver geometries, and as received time series. The results are compared in order to evaluate the effect of applying different propagation models to the same range-dependent underwater environment. It should be emphasized that the propagation analysis is not an attempt to benchmark the selected propagation models, but to demonstrate the performance of practical, range-dependent models based on different approximations in particular underwater scenarios.

Reduction of the performance of a noise screen due to screen-induced wind-speed gradients. Numerical computations and wind-tunnel experiments

Downwind sound propagation over a noise screen is investigated by numerical computations and scale model experiments in a wind tunnel. For the computations, the parabolic equation method is used, with a range-dependent sound-speed profile based on wind-speed profiles measured in the wind tunnel and wind-speed profiles computed with computational fluid dynamics (CFD). It is found that large screen-induced wind-speed gradients in the region behind the screen are responsible for a considerable reduction of the performance of the screen, for receivers near the boundary of the shadow region behind the screen. The screen-induced wind-speed gradients cause a considerable reduction of the size of the shadow region. If the screen-induced wind-speed gradients are taken into account, computed sound-pressure levels near the shadow boundary are in reasonable agreement with levels measured in the wind tunnel. In contrast, computed levels are considerably lower, up to 10 dB, if the screen-induced wind-speed gradients are ignored. This implies that the performance of a screen can be considerably improved if the screen-induced wind-speed gradients can be suppressed, e.g., by the use of “vented” screens.

Acoustic pulse propagation in a fluctuating ocean with range-dependent sound-speed profile

When an acoustic pulse propagates in a randomly fluctuating ocean with a deterministic sound-speed profile, it is distorted since every frequency component experiences different extents of scattering from the random inhomogeneity and echo numbers. Here, the split-step method is used to simulate an acoustic pulse with a 3-kHz carrier propagating through a turbulent ocean with range-independent/-dependent sound-speed profiles. It is found that (1) the ocean is a frequency-selective fading channel; (2) the received pulse profile is dependent on the received depth, sound-speed distribution, fluctuation strength, and scale length of turbulence in oceans; (3) the rms pulsewidth is broadened by several times its initial value as a consequence of pulse echoes and pulse wandering of every pulse realization of the ensemble; (4) the rms pulsewidth is increased when the fluctuation strength increases or the scale length decreases; and (5) the statistical properties of the propagating pulse are similar for both the range-independent and -dependent cases in the mean square sense.

Environmental data assimilation in matched-field processing with a random normal mode model

Numerical acoustic propagation models used in matched-field processing typically assume that ocean environmental parameters, such as the range-dependent sound-speed profile, are either known exactly or are characterized by stationary prior statistics. However, neither of these modeling approaches is well suited for accurately assimilating measurements of the correct ocean realization into the calculation of point-source acoustic wave front statistics. In this paper, environmental data is assimilated into a random adiabatic normal mode propagation model by calculating the conditional correlation matrix of an acoustic wave front given a set of contemporaneous sound-speed profile measurements made at different points in space. First-order perturbation theory is used to map the conditional statistics of Gaussian-distributed excess sound-speed variations into an estimate of the conditional point-source wave front correlation matrix. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)] conditioned on current environmental measurements is demonstrated as a means of exploiting this random wave front model to achieve improved matched-field source localization performance. [Work supported by ONR.]

Modeling issues for predicting sound propagation at moderate frequencies in bottom-limited sound channels

Consider sound propagation in the moderate frequency range (depth to wavelength ratio, H/λ, between 20 and 100) in shallow water environments with bottom roughness. Measurements in the Straits of Florida have shown remarkable phase stability together with rapid (minutes-to-hours) unstable amplitude fluctuations that nevertheless yield stable envelopes when averaged over many hours. What physical effects should be contained in an acoustic model in order to predict the observed behavior? It is suggested that a full-wave model that is capable of multiple rough bottom forward scattering and includes temporally slowly varying range-dependent sound-speed profiles will yield observed results, when used together with coherent signal processing techniques. A broadband PE model will illustrate the assertion, at least qualitatively. Absolute level prediction is quite another matter that requires more extensive environmental inputs.

Modifications to a parabolic equation algorithm for the prediction of atmospheric sound fields which extend its range and improve its accuracy

A two-dimensional algorithm based on Gilbert and White’s method [West etal., Appl. Acoust. 36, 1–19 (1992)] coded for a 486 PC, has served as a test bed for the following modifications: (i) a new second-order ground boundary condition, (ii) a ‘‘tuned’’ upper absorbing layer, (iii) a novel upper boundary condition, which replaces the absorbing layer, and (iv) a new procedure for calculation of the starter field. The algorithm with the above modifications has also been adapted to operate with range-dependent sound-speed profiles obtained from an isoturbulent atmospheric model. [Work supported by MOD and DRA.]

Matched-field minimum variance beamforming in a random ocean channel

Matched-field source localization methods that employ deterministic full-wave acoustic propagation models can be seriously degraded due to the presence of random inhomogeneities in the ocean channel. In this paper, a minimum variance (MV) matched-field beamformer is presented that achieves greater robustness to random inhomogeneities in the sound-speed profile between the source and receiver. The proposed modification of the MV beamformer consists of employing multiple linear constraints derived from predicted pressure fields obtained using a set of perturbed sound-speed profiles. In order to investigate the nature of wave-front variations due to random sound-speed perturbations, a normal mode model based on adiabatic and first-order perturbation approximations is examined. The signal wave-front spatial correlation implied by this model suggests that the coherence among modes can remain high even in a fluctuating ocean environment. This in turn implies that the dimension of the signal perturbation constraint space for the MV beamformer can be small for typical sound-speed variations at moderate source ranges. Given the signal constraint space, design of the MV beamformer with sound-speed perturbation constraints is achieved by selecting its quiescent response to maximize the average signal-to-noise ratio gain against spatially uncorrelated noise. This leads to a computationally efficient realization of the beamformer that avoids the need to repeatedly compute perturbed pressure fields. Simulation experiments using a realistic deep-water Pacific Ocean environment are presented, which suggest that robust unambiguous low-frequency source location estimates can be achieved in the presence of mesoscale inhomogeneities given only knowledge of the second-order statistics of the random range-dependent sound-speed profile plus a single environmental measurement at the receiving array.

A comparison of parabolic equation predictions with reciprocal transmission measurements in the Florida Straits

A parabolic equation model has been developed to study transmission in the Florida Straits and to interpret the results of reciprocal transmission experiments. The model source is both broadband and narrow beam. The bandwidth makes possible prediction of pulse arrival patterns and travel times. The narrow beam shows the path of sound energy between source and receiver. Both arrival times and sound paths are necessary to invert acoustic measurements to give oceanographic measurements of currents and water temperatures. Color graphic displays are used to demonstrate ray-type paths through the medium, using environmental data as inputs; model results are compared with results of pulse reciprocal transmission experiments for several geometries and range-dependent soundspeed profiles and bottoms.