Acoustic Propagation Model Research Articles

Development of a three-dimensional semi-coherent energy flux propagation model

The classic energy flux propagation model integrates an averaged intensity distribution over elevation angle for an azimuthally symmetric waveguide, and the method has also been extended to reincorporate some of the coherence in the mode-sum cross product, producing caustic features and convergence zones. Some ocean environments with asymmetric range-dependent bathymetry and acoustic medium properties can refract the acoustic wave horizontally which N-by-2D models cannot capture due to their assumed symmetry. Fully three-dimensional models can capture horizontal refraction but are typically computationally expensive to execute. Further development and study of the energy flux method is worthwhile since it avoids root-finding, is not a marching solution, and it invokes mode number invariance under the adiabatic modes assumption to map propagation angles and directly integrate the intensity distribution at the receiver location. A first-pass at analytically deriving a generalizable three-dimensional energy flux model was presented previously, and this current study focuses on further analytical development, numerical implementation, and efforts to verify the model using other three-dimensional acoustic propagation models.

Machine learning of acoustic propagation models for sound aware autonomous systems

Opportunities exist for autonomous underwater vehicles to optimize acoustic communications with knowledge of the sound channel, but implementation has traditionally been hindered by computationally expensive propagation models. This work addresses computational complexity by enabling machine learning to interpret environmental inputs to predict transmission loss (TL) outputs from a physics-based ray tracing model (BELLHOP). Feature representations to reduce bathymetric and sound speed profile (SSP) information through wavelet decomposition and empirical orthogonal analysis are explored, respectively. A decision tree machine learning algorithm is trained to learn the paths (depths and ranges) of acceptable transmission loss for a pair of acoustic modems within a given environment. Our test case is off the coast of Southern California, and SSPs are collected from a 3 year record sampled from an ocean mooring. Bathymetry data is based on high resolution multibeam data. TL field realizations are calculated as training and testing data for environments of varying bathymetry with frequency of 25kHz and range of 1km through the BELLHOP model. Results are shown with stationary and non-stationary emitters to demonstrate the effectiveness of this approach.

Atmospheric acoustic propagation modeling using heterogeneous wind profiles along the acoustic path

This work presents atmospheric sound propagation predictions using a parabolic equation solver that accounts for heterogeneous wind profile distribution along the acoustic path. Transmission loss predictions using both homogeneous and heterogeneous wind speeds information are compared with data. A three-dimensional scanning Doppler LIDAR wind profiler captures real-time wind speed gradients at many locations along the acoustic propagation path providing the heterogeneous wind speed profiles. The wind measurements are concurrent with a pitch catch transmission loss measurements. A long-range acoustic device on an anchored pontoon sends known chirp sequences to a seven-channel receiver array at the water’s edge at ranges up to approximately one kilometer. Additional synchronized meteorological observations include temperature, humidity, and wind measured with anemometers. Key differences in model results are highlighted and an assessment of the value of the computational cost is presented.

Acoustic wave propagation model in the surface layer area based on the Runge-Kutta method

Simulation of acoustic wave propagation in the surface layer area is carried out by taking a positive value acoustic velocity gradient so that in this simulation there will be a wave phenomenon trapped in the surface layer area. In this study, acoustic beam emission was conducted by varying the angle of incidence and length of the beam used, and the determination of the acoustic velocity gradient was carried out using the Runge-Kutta order of order 2. The results showed that at depths of 0 to 40 meters with an acoustic velocity of 1405 m/s, for a length of 1 meter and a gradient pattern of +2.5 obtained a minimum angle of incidence of 0.09 radians with a wave propagation of 250 meters. Comparison between analytical and computational results on wave propagation in the surface layer area is a 4.51% error.

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

Computational Fluid Dynamic Simulation of Leakage Acoustic Waves Propagation Model for Gas Pipelines

When leakage occurs for natural gas pipelines, acoustic waves generated at the leakage point will propagate to both ends of the pipe, which will be measured and processed to detect and locate the leakage. When acoustic waves propagate in the gas, the amplitude will attenuate and the waveform will spread, which decides the installation distance of acoustic sensors. Therefore, computational fluid dynamic (CFD) simulation research on the acoustic wave propagation model is accomplished and verified by experiments to provide the foundation for the acoustic leak location method. The propagation model includes two parts: amplitude attenuation model and waveform spreading model. Both can be obtained by the established CFD simulation model. Additionally, the amplitude attenuation model can be verified by the experiments. Then, the simulation method is applied to conclude the propagation model under variable conditions, including different flow directions, Reynolds numbers, and diameters. Finally, the experimental demonstration of the leak location based on the propagation model is given. The results indicate that not only the gas viscosity but also the gas flow can influence the propagation model, and the leak location method based on the propagation model is effective. Conclusions can be drawn that CFD simulation on the propagation model for natural gas pipelines is an efficient way to carry out research and provide the theoretical basis for acoustic leak location method application.

Supervised Classification of Sound Speed Profiles via Dictionary Learning

Abstract The presence of internal waves (IWs) in the ocean alters the isotropic properties of sound speed profiles (SSPs) in the water column. Changes in the SSPs affect underwater acoustics since most of the energy is dissipated into the seabed due to the downward refraction of sound waves. In consequence, variations in the SSP must be considered when modeling acoustic propagation in the ocean. Empirical orthogonal functions (EOFs) are regularly employed to model and represent SSPs using a linear combination of basis functions that capture the sound speed variability. A different approach is to use dictionary learning to obtain a learned dictionary (LD) that generates a nonorthogonal set of basis functions (atoms) that generate a better sparse representation. In this paper, the performance of EOFs and LDs are evaluated for sparse representation of SSPs affected by the passing of IWs. In addition, an LD-based supervised framework is presented for SSP classification and is compared with classical learning models. The algorithms presented in this work are trained and tested on data collected from the Shallow Water Experiment 2006. Results show that LDs yield lower reconstruction error than EOFs when using the same number of bases. In addition, overcomplete LDs are demonstrated to be a robust method to classify SSPs during low, medium, and high IW activity, reporting accuracy that is comparable to and sometimes higher than that of standard supervised classification methods.

Mathematical modeling of acoustic wave propagation in elastic materials with multi-periodic hierarchical structure of heterogeneities

An asymptotic homogenization procedure is applied for acoustic waves' propagation in heterogeneous elastic medium with multi-periodic hierarchical structure of heterogeneities. We assume the existence of two periodic cells with characteristic sizes l_2 and l_1 respectfully. The ratio ε=l_2/l_1 is considered to be small and of the same order of magnitude as the ratio l_1/L, where L is the macroscopic characteristic size of a system. The solution of the problem will be largely determined by the relation between the wavelength λ and the characteristic sizes of the system. For the case when λ/l_1 ~1 we derive homogenized macroscopic equation for the displacement and obtain approximations to the displacement and frequency. Several illustrative examples are considered to show the effect of peculiarities of the structure on two different spacial scales on energy distribution in propagating wave.

Riemannian geometric modeling of underwater acoustic ray propagation ·application——Riemannian geometric model of convergence zone in deep ocean remote sound propagation

Convergence-zone (CZ) sound propagation is one of the most important hydro-acoustic phenomena in the deep ocean, which allows the acoustic signals with high intensity and low distortion to realize the long-range transmission. Accurate prediction and identification of CZ is of great significance in implementing remote detection or communication, but there is still no standard definition in the sense of mathematical physics for convergence zone. Especially for the issue of systematic error of computation introduced by the earth curvature, there is no exact propagation model. The curvature-correction methods always lead to the imprecision of the ray phase. In previous research work, we realized that the Riemannian geometric meaning of the caustics phenomena caused by ray convergence is that the caustic points are equivalent to the conjugate points, which form on geodesics with positive section curvature. In this work, we present a spherical layered acoustic ray propagation model for CZ based on the Riemannian geometric theory. With direct computation in the curved manifolds of the earth , a Riemannian geometric description of CZ is provided for the first time, on the basis of comprehensive analysis about its characteristics. And it shows that the mathematical expression of section curvature adds an additional item <inline-formula><tex-math id="M1">\begin{document}${{\hat c(l){{\hat c}^\prime }(l)}}/{l}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221495_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221495_M1.png"/></alternatives></inline-formula> after considering the earth curvature, which reflects the influence of the earth curvature on the ray topology and CZ. By means of Jacobi field theory of Riemannian geometry, computational rule and method of the location and distance of CZ in deep water are proposed. Taking the typical Munk sound velocity profile for example, the new Riemannian geometric model of CZ is compared with the normal mode and curvature-correction method. Simulation and analysis show that the Riemannian geometric model of CZ given in this paper is a mathematical form naturally considering the earth curvature with theoretical accuracy, which lays more solid scientific foundations for the study of convergence zone. Moreover, we find that the location of CZ moves towards sound source when the earth curvature is considered, and the width of CZ near the sea surface first increases and then decreases with sound propagation proceeding. The maximum width is about 20 km and the minimum is about 4 km.

Riemannian geometric modeling of underwater acoustic ray propagation—Basic theory

Underwater sound propagation models are generally established from the extrinsic perspective, that is, embedding acoustic channels in Euclidean space with a fixed coordinate system. Riemannian geometry is intrinsic for curved space, which can describe the essential properties of background manifolds. The underwater acoustic Gaussian beam is originally adopted from seismology. Till now it has been the most important method used in acoustic ray based modeling and applications. Owing to the advantages of Gaussian beam method over the traditional ray counterpart, it is the mainstream technology of ray propagation computational software such as the famous Bellhop. With the assumption of Euclidean space, it is hard to grasp the naturally curved characteristics of the Gaussian beam. In this work, we propose the Riemannian geometry theory of underwater acoustic ray propagation, and obtain the following results. 1) The Riemannian geometric intrinsic forms of the eikonal equation, paraxial ray equation and the Gaussian beam under radially symmetric acoustic propagation environments are established, which provide a Riemannian geometric interpretation of the Gaussian beam. In fact, the underwater acoustic eikonal equation is equivalent to the geodesic equation in Riemannian manifolds, and the intrinsic geometric spreading of the Gaussian beam corresponds to the lateral deviation of geodesic curve along the Jacobian field. 2) Some geometric and topological properties of acoustic ray about conjugate points and section curvature are acquired by the Jacobi field theory, indicating that the convergence of ray beam corresponds to the intersection of geodesics at the conjugate point with positive section curvature. 3) The specific modeling method under horizontal stratified and distance-related environment is presented by using the above theory. And we point out that the method proposed here is also applicable to other radially symmetric acoustic propagation environments. 4) Simulations and comparative analyses of three typical underwater acoustic propagation examples, confirm the feasibility of the Riemannian geometric model for underwater acoustic propagation, and show that the Riemannian geometric model has exact mathematical physics meaning over the Euclidean space method adopted by the Bellhop model. The basic theory given in this paper can be extended to the curved surface, three-dimensional and other complex propagation cases. And especially it lays a theoretical foundation for the further research of long-range acoustic propagation considering curvature of the earth.

An Ocean Acoustic Modeling Based on the Physical Parameters Clustering of the Arctic Ice Floes: Applied to the Study of Acoustic Field Response as Ice Floes Thickness Varies

AbstractThe varies of ice floe thickness (IFH) is a very influential research content in the Earth system academic research, it is closely related to the distribution of underwater acoustic fields. However, the discontinuous physical parameters of ice floes make it difficult to clear this relationship with conventional acoustic propagation models or measured data. Unlike the conventional acoustic models that treat ice floes as one or more physical simplified acoustic reflection layers, this study employs machine learning and FEM (finite element method) modeling to incorporate ice floes' physical parameters into the acoustic field model. The physical parameters of ice floes associated with acoustic field modeling are screened by using the principal component analysis method. On this basis, these ice floes were spatially divided into three highly differentiated and interpretable typical ice clusters using the K‐Means method. We treated ice as a multi‐layer elastic medium, and then the FEM acoustic model was built under the fluid‐structure coupling condition. Measured data (UNDER‐ICE) and MIT acoustic models (OASES) were used to validate our FEM results. We demonstrated that the modeling improves the distribution characteristics of surface channel arrival amplitude under ice floes cover. From the perspective of the model application, the acoustic field response as IFH varies is closely related to the category and region of ice floes.

Three-dimensional anthropogenic underwater noise modeling in an Arctic fjord for acoustic risk assessment

Sea-ice covering is drastically declining in the Arctic, opening new maritime routes and thus introducing underwater noise pollution in nearly pristine acoustic environments. Evaluating underwater noise pollution requires good acoustic propagation modeling to predict sound exposure levels. However, underwater noise modeling for acoustic risk assessments has often been carried out using simplistic propagation models, which approximate a 3D propagation in several planes (Nx2D), instead of using full 3D propagation models. However, Nx2D propagation models are impractical for winding geography and steep bathymetry as found in Arctic fjords. The purpose of this study is to estimate disturbance and masking effects on Arctic animal species from shipping noises, modeled through a traditional Nx2D BELLHOP model and a full 3D BELLHOP model. Classical Nx2D propagation modeling largely underestimates the anthropogenic noise footprint in Arctic fjords compared to using a full 3D propagation model.

A position-dependent acoustic model relevant for some active noise control applications

This paper focuses on acoustic modeling for active noise control applications. The desired model must be finite dimensional and efficient numerically to meet implementation requirements. It must also be parameterized by the position considered inside the cavity. This additional characteristic is desirable for addressing specific active noise control applications such as optimizing microphone placement, estimating acoustic pressure at different positions of the considered cavity, and finally attenuating noise level in a subarea of the cavity. The main contribution of this paper is to propose a finite-dimensional, low-order, and parameterized acoustic model of a cavity, suitable for active noise control applications. The resulting model is defined as a gray box that combines a one-dimensional analytical model of acoustic propagation, which handles the physical parameterization, and a black-box model that copes with actuator and sensor dynamics as well as modeling errors. The parameters of the proposed model are optimized in order to reproduce the frequency behavior of the real system (LS2N active noise control platform) in a frequency range. This model allows one to accurately reproduce the dynamics at any position in the considered cavity. The prediction performance of the proposed model was compared to a classical black-box model (usually used for active noise control applications) and validated experimentally using the LS2N active noise control platform. The analysis highlighted that the proposed gray-box model can predict the acoustic behavior in a great range of positions.

A computational model of acoustic ray propagation in the deep-sound channel axis ocean region based on the Euler-Cromer method

Research on the model of sound wave propagation in the ocean on the axis of the deep sound channel has been carried out using discrete acoustic ray propagation with varying beam lengths. This study aims to obtain parameter values in the form of maximum angle of incidence and effective beam length to simulate acoustic wave propagation around the axis of the deep sound channel. The research was conducted by simulating the acoustic beam at a depth with the minimum acoustic velocity value by varying the angle of incidence and the length of the applied beam. In this study, constant acoustic velocity gradient and gradient data were used. Calculation of the velocity gradient from discrete data using the Euler-Crommer formula. From this research, it can be seen that at a depth of 854 m the minimum acoustic velocity is 1487.53 m/s. For a constant gradient with a value of 0.054 and variations in beam length from 1 m to 4 m, the maximum angle of incidence is 0.4 radians. Analytically, the radius of curvature of the rays is 28107.12 m. Comparing the analysis and computation results, there is a very small error of 0.02%, so this model can be used to simulate acoustic wave propagation based on real data gradients. The gradient pattern based on real data and variations in beam length from 1 m to 4 m, obtained a maximum angle of incidence of 0.4 radians.

High resolution mapping of sound speed and density with broadband echo sounders

Advances in acoustic propagation and physical oceanographic modeling necessitate improved spatiotemporal resolution of water column properties (temperature, salinity, sound speed, and density) to inform and validate models. Shipboard profiling provides adequate vertical resolution, but high-resolution horizontal sampling is expensive and time consuming. Stationary arrays generate critical long-term data sets and high vertical resolution, however, there is a trade-off between dense horizontal sampling and total spatial coverage. Towed systems provide dense coverage horizontally but lack vertical resolution in a single location. During the ONR funded New England Shelf Break Acoustics experiments in 2021, sparse shipboard CTD and expendable bathythermograph (XBT) casts were combined with backscatter measurements by shipboard broadband echo sounders to map water column physical properties of the New England Shelf Break front with high resolution vertically and horizontally. The shipboard echo sounders detected backscatter from the strong gradients of the shelf break front, physical microstructure, and internal waves present at the frontal boundary. Acoustically tracking the front between CTD casts resulted in high resolution profiles of water column properties. Acoustic propagation modeling at 500 Hz and 4 kHz was compared when using the acoustically determined water column profile and when using profiles from CTD and XBT casts alone.

Improved acoustic situation awareness using reduced order models of ocean circulation

Acoustic situation awareness consists of knowing how far own sensors can detect other platforms and how detectable your platform is to their sensors. Since acoustic propagation is reciprocal, differences are down to source levels produced by each platform, transmission loss between them (reciprocal), the relative sensitivity of sensors, and the different directional noise observed at each platform. Noise fields are due to sources present both in the neighborhood (nearby ships) and in distant hubs (harbor shipping). Acoustic propagation models are used to predict transmission loss and received levels at all locations. Such models use sound speed for inputs. Platforms with limited communications can only be updated with the best available sound speed forecasts and measurements on a sporadic basis. We have developed reduced order models for sound speed, which consist of pre-loaded basis sets that capture anticipated ocean state fluctuations, for which very small (easily communicated) sets of coefficients can be used to reconstruct 3D and 4D ocean fields (sound speed and currents) on remote or edge platforms. We will present examples in the simulation of how our reduced order models contribute to improved acoustic situational awareness on such platforms.

A numerical and experimental study of micrometeorological effects on urban sound propagation

In this work, the influence of micrometeorological effects on sound propagation in an urban street canyon is investigated numerically and experimentally. Numerical simulations of acoustic propagation are based on sound particle propagation simulation method. Numerical data are generated for urban street canyons of various widths and height ratios. Experimental data are obtained from longitudinal measurements of urban street canyons in the United States. Temperature and wind profiles are obtained from ultrasonic anemometers and thermocouples. Measurements within and outside the street canyon are of particular interest. The experimental data are useful in integrating micrometeorological effects into the acoustic propagation model. Preliminary numerical results and measurements are presented and discussed.

Dictionary learning for classification of sound speed profile in the ocean

Internal waves (IWs) are waves that propagate along density gradients within the water column and alter the isotropic properties of sound speed profiles (SSPs). Changes in the SSPs modify the acoustic channel ducts and affect underwater acoustic propagation, causing most of the energy to be dissipated into the seabed due to the downward refraction of sound waves. Therefore, variations in the SSP must be considered when modeling acoustic propagation in the ocean. It has been proved that Dictionary learning (DL), an unsupervised machine learning method, succeeds in sparsely representing signals by employing a few non-orthogonal basis functions (atoms) learned from data. In this work, we use the ability of learned dictionaries (LDs) for data representation and thus train class-specific dictionaries to capture relevant features from labeled data within a supervised learning setting. We developed an LD-based supervised framework for SSP classification and compared it with state-of-the-art models. The algorithms presented in this work are trained and tested on data collected from the shallow water experiment 2006. Results show that overcomplete DL is a robust method to classify SSPs during IW activity, reporting comparable and higher accuracy than standard supervised classification methods. [Work supported by ONR, Grants No. N00014-21-1-2424 and N00014-21-1-2760.]

Acoustic scattering from dynamic rough ocean surfaces using finite-difference time-domain modeling techniques

Established models for underwater acoustic propagation and scattering typically assume the sea-surface to be either perfectly smooth or rough but static in time. When the sea-surface is rough and moving, received signals show anomalies such as additional transmission losses (due to scattering) and Doppler effects (due to surface motion). Understanding the mechanisms behind these anomalies leads to better sonar system designs without having to perform expensive at-sea experiments. The Finite-Difference Time-Domain (FDTD) method is ideal to predict these physical phenomena. This work presents a FDTD method implemented to model the impact of both sea-surface roughness and motion on underwater acoustic propagation. The FDTD method allows an arbitrary function to define the rough sea-surface and its time evolution. The surface characteristics are modeled using a Pierson-Moskowitz (PM) frequency spectrum. The PM surface model is simple to implement and fully defined by wind speed and direction. Time-domain results from FDTD simulations of static rough sea-surfaces are compared to an established Helmholtz integral equation (HIE) method to establish the validity of the approach. Broadband signals are used as the source waveform. Results demonstrate the anomalous transmission loss and Doppler in received signals. [Work supported by the Office of Naval Research.]

Scanning Doppler LIDAR wind profiles to inform near shore atmospheric acoustic propagation modeling

This work presents a comprehensive experimental system to measure concurrent atmospheric acoustic transmission loss and meteorological conditions. A three-dimensional scanning Doppler lidar wind profiler captures real-time wind speed gradients at many locations along the acoustic propagation path of a simple pitch catch style study. A long-range acoustic device on an anchored pontoon sends known chirp sequences to a seven-channel receiver array at the water’s edge at ranges up to approximately one kilometer. Additional synchronized meteorological observations include temperature, humidity, and wind measured with anemometers. The meteorological data stream is used to inform the sound speed gradient implemented in a parabolic equation based numerical model of atmospheric acoustic propagation. The model can account for sea surface roughness and accommodate a sound speed profile that changes along the propagation range. Model predictions are compared to measured transmission losses. An assessment of the value of the computational cost of incorporating the varying sound speed profiles in the model is presented.