Acoustic Ray Research Articles

Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

3D reconstruction of nonuniform and unsteady flow velocity distribution using nonlinear acoustic ray tracing and tomography

The nonuniform and unstable gas flow distribution at the air inlets of the boiler combustion chamber can negatively affect the energy efficiency and safety of the boiler. Accurately reconstructing the flow velocity inside the furnace in three dimensions can help the boiler automatically adjust the air supply to reduce unwanted energy waste and gas emissions.In this study, we propose a novel method for three-dimensional velocity reconstruction based on nonlinear acoustic ray tracing and tomography. The model provides the equation of acoustic ray motion in the flow field, which includes spatial and temporal parameters. During the process of measuring flow velocity, higher precision reconstruction of the three-dimensional velocity distribution was achieved by combining acoustic refractive paths based on derivative-free optimization iteration updates with radial basis functions that use Gaussian kernels.The computational time cost and reconstruction accuracy of the proposed algorithm were analyzed numerically and through simulations. The results indicate that the method incorporating acoustic ray tracing greatly improves the reconstruction accuracy of large gradient nonuniform flow fields. Additionally, we analyzed the impact of different numbers of sound tracing paths on reconstruction quality and computation time, providing a reference for the rational placement of microphones and the selection of the most efficient paths in boilers.Experimental results show that this method has good reconstruction capabilities for nonuniform flow fields and practical applications.

Broad-Learning-Based Localization for Underwater Sensor Networks With Stratification Compensation

Localization is an indispensable service for underwater sensor networks (USNs). Generally, the convex optimization method is adopted to solve the localization problem. However, the acoustic ray in water medium does not propagate along a straight line, which makes it difficult or impossible to transform the non-convex optimization problem into a convex optimization problem. This paper develops a broad learning (BL) based localization solution for USNs with isogradient sound speed profile. We first employ the ray tracing model to compensate the range bias caused by straight-line propagation. On the basis of collected range information from anchor nodes, the localization optimization problem is transformed into supervised, unsupervised and semisupervised learning frameworks. Correspondingly, three BL-based location estimators are developed to seek the position information of sensor nodes, where the incremental learning schemes are conducted for fast parameter tuning and remodeling. In addition, the Cramer-Rao Lower Bound (CRLB) of positioning error and the convergence to global optimality are both analysed. Finally, simulation and experiment results are presented to show the effectiveness of our approach. It is demonstrated that the proposed solution in this paper has the following nice features: 1) relax the dependence of convex relaxation over convex optimization-based location estimators; 2) reduce the training time and improve the localization efficiency over deep learning-based location estimators.

Formation of Scattering Characteristics for Acoustical Ray Tracing Simulation

Ray tracing simulation of sound field in rooms is a common tool in room acoustic design for predicting impulse response. There are numerous commercial engineering tools utilising ray tracing simulation. A specific problem in the simulation is the modelling of diffuse reflections when contribution of individual surface is prevailing. The paper introduces modelling of scattering which is interesting when the whole impulse response of a room is not a goal but contribution of certain surface. The main goal of the project is to shape directivity characteristics of scattered reflection. Also, an innovative approach is suggested for converting the energy histogram information obtained by ray tracing into an “equivalent impulse response”. The proposed algorithm is tested by comparing the results with measurements in a real sound field, realised in a scaled model where a diffusing surface is hardware-implemented.

In Situ Measurement of Acoustic Attenuation for Focused Ultrasound Ablation Surgery Using a Boiling Bubble at the Focus.

Acoustic attenuation in the propagation path of focused ultrasound ablation surgery determines the energy loss toward the focal region and is critical to the consequent treatment outcomes. In situ non-invasive, reliable, and accurate measurement is challenging for multi-layered heterogeneous tissues within the focusing angle. A novel measurement approach is proposed and its performance is evaluated using ex vivo porcine tenderloin and bovine heart. A big boiling bubble (i.e., larger than a few millimeters in size) was produced at the focus as a strong reflector inside the tissue, and the echo amplitudes were used to determine the acoustic attenuation. Two models, acoustic ray and energy loss, were developed to derive the equivalent acoustic attenuation coefficient for a focused beam. The measured acoustic attenuation coefficients of ex vivo porcine tenderloin and bovine heart at 0.97 MHz and a thickness of 3 cm are 0.159 ± 0.002 and 0.250 ± 0.005 Np/cm, respectively, which are all within the scope of measured values in the literature. In addition, the echo amplitude is sensitive to the conditions of the propagation path, and the inverse acoustic attenuation coefficient of the silicone gel pad placed in front of the tissue sample was 0.807 ± 0.002 Np/cm, which is comparable to the measurement using the insertion substitution method, 0.766 ± 0.003 Np/cm. Our proposed approach could determine the tissue acoustic attenuation for focused ultrasound ablation surgery reliably and accurately in situ. The easy operating protocol may allow clinical translation and adoption for improved safety and efficacy.

Developing virtual acoustic terrain for Urban Air Mobility trajectory planning

Urban Air Mobility (UAM) is a transformative concept that must operate harmoniously within the constraints imposed by societal impacts. Noise-aware flight trajectory planning can address UAM’s community noise concerns. However, the traditional trajectory optimization paradigm requires repetitive computations of a flight’s noise footprints in complex urban environments and is computationally expensive. In this work, we propose virtual acoustic terrain, a novel concept to enable an efficient trajectory optimization paradigm. By applying acoustic ray tracing and the principle of reciprocity in a complex urban environment, we convert different noise constraints into 3D exclusion zones which UAM operations should avoid to maintain limited noise impact. It combines with the physical urban terrain to define an acceptable fly zone for non-repetitive noise-aware trajectory optimization. This framework provides a new angle to future urban area airspace management and can also accommodate other forms of societal constraints.

Generation of acoustic vortices and acousto-optic interactions with acoustic vortex beams.

We demonstrate the generation of acoustic vortex beams with the aid of an acoustic spiral phase plate and an acoustic grating having a fork-like bifurcation of its slits. The acoustic vortex beam generated in this manner influences the particles floating on a water surface and rotates them. Our experiments show that the intensity of the acoustic vortex beam increases from zero in its center to a certain maximal value near the shell of the beam. The phase of the beam changes by the angle 2π whenever the azimuthal angle is changed by the same value. We also study acousto-optic diffraction of the optical beam by the acoustic beam bearing a vortex and demonstrate that each of the appropriate diffraction maxima are split into two maxima. The latter correspond to diffraction by the elementary acoustic rays which are close to the opposite edges of the acoustic vortex beam. A dark region between the maxima appears due to destructive interference of the elementary optical rays originated from the diffraction by the opposite sides of the acoustic vortex beam, which are phase-shifted by π.

Seamount Clutter Modeling for Long Range Seabed Reverberation in Deep Sea

Reverberation clutter induced by discrete strong scatterers is an important reason which will increase the false alarm probability of active detection, which seriously affects the performance of active sonar detection. In this paper, taking seamount as an example, the theoretical modeling and simulation of the clutter in the deep-sea induced by seamount are carried out by using the ray-mode theory. Through ray-mode approximation, the acoustic rays in surface and reverse channels are ignored, a theoretical model is proposed to calculate the seabed reverberation clutter induced by seamounts, and the physical mechanism of how the seabed reverberation clutter is induced by seamounts is analyzed. The results show that reverberation intensity will increase in the location of seamount and induce discrete reverberation clutter. The greater the fluctuation of seamount, the greater the reverberation clutter intensity.

Remote Sensing Small Explosives With an Ionospheric Radar

AbstractEarth's ionosphere has long been targeted as a medium for remote sensing of explosive terrestrial events such as earthquakes, volcanic eruptions, and nuclear/conventional weapon detonations. Until now, the only confirmed ionospheric detections have been of very large events that were easily detectable through other traditional global sensor systems (e.g., seismic). We present the first clear, confirmed detections of relatively low yield 1‐ton TNT‐equivalent chemical explosions using pulsed Doppler radar observations of isodensity layers in the ionospheric E region. The shape and spectra of the detected waveforms closely match predictions from the acoustic ray tracing and weakly nonlinear waveform propagation models. The explosions were roughly three orders of magnitude lower yield than any previous confirmed ionospheric detection and represent the first conclusive evidence that explosions of this size can have clear impacts on the ionosphere. This technique could improve the remote detection of both anthropogenic and natural explosive events.

Acoustic reconstruction of the vortex field in the nonuniform temperature field of a simulated furnace

The high-temperature thermal vortex flows generated by the tangential combustion of large-scale coal-fired power plant boilers represent a complex medium that causes acoustic ray bending. In this paper, nonlinear acoustic tomography is combined with particle swarm optimization as a means of reconstructing the two-dimensional thermal vortex field. The nonuniform and large-gradient temperature distribution is the main cause of acoustic ray bending. We establish curved paths of acoustic propagation that are closely related to the temperature distribution. Based on these curved paths, a set of radial basis functions combined with Tikhonov regularization is derived to achieve more accurate reconstruction of the temperature field. The nonuniform temperature field affects the reconstruction of the flow field information. Our model considers a variation in the angle between the direction vector of the acoustic curved paths and the horizontal and vertical components of the flow velocity, and incorporates a priori information and a six-parameter hypersurface into the flow field reconstruction scheme. Particle swarm optimization is applied to minimize the objective function and obtain the vortex velocity field. Numerical experiments show that the proposed mathematical model of acoustic ray bending improves the reconstruction accuracy of the temperature distribution and vortex flow field. The acoustic time-of-flight is experimentally measured through the generalized cross-correlation with different window functions. The temperature and vortex fields reconstructed based on the actual time-of-flight are compared with thermocouple and anemometer measurements to demonstrate the validity and robustness of the proposed reconstruction model.

Parameter inversion and target localization in layered media containing solids based on acoustic ray tracing method

A scheme based on the acoustic ray tracing method is proposed to obtain target location and parameter inversion in layered media containing solids with unknown parameters. The longitudinal wave velocity of the upper medium is acquired by measuring the head wave or direct wave propagation. The wave modes of signals received by a linear array are identified using their travel time and amplitude. The position and shape of the interface and the shear wave velocity of the upper solid medium are obtained by processing interface-reflected waves. The acoustic velocity of the lower medium and the target position are determined by processing the target-scattered waves with the minimum dispersion method in single-transmitter and multiple-receiver configurations. The steel-copper, aluminum-water, and water-plexiglass layered media with different interface shapes are selected for experimental verification. The results show that the inversed media parameters and target localization results agree with the actual values.

Regional and global scale propagation simulations of infrasonic signals

Infrasonic signals are frequently observed at large propagation distances of 100s to 1000s of kilometers from the source and, in extreme cases, signals have been observed to circle the globe. Simulating acoustic propagation at these large scales requires a framework that not only accounts for 3D propagation effects including along- and cross-path winds, but also for the non-Cartesian geometry of the atmospheric layer surrounding the globe. Furthermore, interaction of propagating infrasonic energy with terrain features is known to have a notable impact on signals, particularly when the wavelength of the signals is comparable to the terrain scale. Finally, spatial variations in the atmospheric structure beyond simple stratification can have significant impacts on propagation paths. Numerical tools for acoustic ray tracing that account for these and other complications will be detailed and demonstrated using several recent infrasonic events of interest.

An improved method for computing acoustic ray incident angle based on secant method

Constant gradient acoustic ray tracking is usually used in high-precision underwater acoustic positioning. However, it needs to calculate the incident angle of the acoustic ray, and the traditional incident angle computation method is very inefficient. To resolve this problem, we propose an improved acoustic ray incident angle iterative computation method. It firstly constructs the mathematical model for incident angle by using the function between horizontal propagation distance and incident angle based on secant method. The initial value of the incident angle is then determined by the incident angle calculated from the previous epoch and the last iteration. Meanwhile, the root-containing interval of the incident angle is reduced according to experimental parameters and coordinate correction values. Finally, the incident angle calculated in the last iteration is directly used for acoustic ray tracking and positioning solution until the end, when the coordinate correction values reach a threshold. Experiment conducted on the simulation cases demonstrates that the positioning calculation time of the proposed method is 77.7%, 77.1% and 88.1% lower than traditional methods in order of the dichotomy, secant method, and Newton method, respectively. As for the real experiment of the South China Sea, the computation efficiency improvement of the proposed method is about 62.9%, 67.6% and 66.1% compared with the dichotomy, secant method, and Newton method respectively. These results suggest that the proposed method can significantly improve the positioning calculation efficiency without loss of positioning accuracy compared with conventional methods.

Determination of the shadow zone area in the ocean computationally by simulating the propagation of acoustic rays

Simulation of acoustic wave propagation to determine the shadow zone area using computational methods has been carried out using negative value gradients. The study was conducted by varying the angle of incidence and variations in the length of the beam used. This research was conducted by comparing analytical results with computational results. The results of this study indicate that at a depth of 500 meters with a sound speed of 1493.1 m/s, a beam length of 1 meter, and a gradient pattern of -0.1, a maximum angle of 0.255 radians is obtained with the shadow zone area being at a depth of 0 to 800 meters and a distance of 5000 meters of wave source. The value of the difference or error in analytical data and computational data is 0.0817%.

An ocean acoustical ray-tracing tool based on Fermat's least time principle in real a environment

Recently the Underwater Acoustics Modelling and Sonar Prediction - SeaRider tool was developed by the Portuguese Naval Academy. Based on Fermat's least-time principle, 2D and 3D models of propagation of acoustic rays in the ocean were developed. These models consist of an algebraic differential system of equations. In this work we considered additionally the possibility of calculating the trajectory, addressing the occurrence of acoustic ray reflections either on the water surface or on the ocean floor. The reflections in the boundaries were assumed specular and were modelled based on Snell's law. We also considered the possibility of calculating the trajectories, taking into account the actual data of the speed of sound in the ocean as well as the bathymetry of the bottom. For this purpose, the 2D and 3D ocean-acoustic ray tracing developed can use existing data bases (GEBCO, NOAA, WOD18 and TEOS-10), extracting information onthe topography and climatology to compute the acoustic ray trajectories in a real environment. This tool allows us, for example, to identify positions of ecosystems subjects to the effects of different sources of noise. The developed algorithms were submitted to several numerical simulations and compared with other ocean-acoustic modelling programs.

Ultrasonic surface acoustic wave-assisted separation of microscale droplets with varying acoustic impedance.

In droplet-based microfluidic platforms, precise separation of microscale droplets of different chemical composition is increasingly necessary for high-throughput combinatorial chemistry in drug discovery and screening assays. A variety of droplet sorting methods have been proposed, in which droplets of the same kind are translocated. However, there has been relatively less effort in developing techniques to separate the uniform-sized droplets of different chemical composition. Most of the previous droplet sorting or separation techniques either rely on the droplet size for the separation marker or adopt on-demand application of a force field for the droplet sorting or separation. The existing droplet microfluidic separation techniques based on the in-droplet chemical composition are still in infancy because of the technical difficulties. In this study, we propose an acoustofluidic method to simultaneously separate microscale droplets of the same volume and dissimilar acoustic impedance using ultrasonic surface acoustic wave (SAW)-induced acoustic radiation force (ARF). For extensive investigation on the SAW-induced ARF acting on both cylindrical and spherical droplets, we first performed a set of the droplet sorting experiments under varying conditions of acoustic impedance of the dispersed phase fluid, droplet velocity, and wave amplitude. Moreover, for elucidation of the underlying physics, a new dimensionless number ARD was introduced, which was defined as the ratio of the ARF to the drag force acting on the droplets. The experimental results were comparatively analyzed by using a ray acoustics approach and found to be in good agreement with the theoretical estimation. Based on the findings, we successfully demonstrated the simultaneous separation of uniform-sized droplets of the different acoustic impedance under continuous application of the acoustic field in a label-free and detection-free manner. Insomuch as on-chip, precise separation of multiple kinds of droplets is critical in many droplet microfluidic applications, the proposed acoustofluidic approach will provide new prospects for microscale droplet separation.

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.

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.

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.

Observation of a mesoscale warm eddy impacts acoustic propagation in the slope of the South China Sea

Acoustic rays are modified while propagating through oceanic eddies. However, due to the lack of field synchronous observation, the impact of mesoscale eddy on the acoustic propagation is less clarified. To address the issue, an eddy-acoustic synchronous observation (EASO) field experiment for a mesoscale warm eddy was carried out in the slope of the South China Sea (SCS) in October, 2021. During the field experiment, a total of 105 conductivity-temperature-depth (CTD) stations, as well as a zonal acoustic survey line through the center of the warm eddy, were obtained. The vertical structures of temperature and salinity indicate that the warm eddy is surface-intensified with temperature and salinity cores confined within depths from 70 m to 200 m and 10 m to 70 m, respectively. The acoustic observation shows two obvious convergency zones (CZs) at about 39 km and 92 km in the eastern half acoustic line, and one convergency zones (CZ) at about 25 km in the western half acoustic line. By comparing with the none eddy circumstance, the respective impacts of the topography and warm eddy are quantitatively analyzed with a ray-tracing model. The results indicate that the topography shortens the horizontal span of the CZ by 11.4 km, while the warm eddy lengthens it by 1.7 km. Additionally, the warm eddy shallows the depth and broadens the width of the CZ by 32 m and 1.4 km, respectively. The anisotropy of 3D sound fields jointly influenced by the warm eddy and the local topography show that the distance differences of the first CZs in different horizontal directions can be as long as 31 km.