Sound Rays Research Articles

Sound propagation in shallow water with periodic rough bottom

The rough sea bottom has a large effect on underwater acoustic propagation and underwater acoustic detection applications. By using the typical shallow water environment from the Yellow Sea, the acoustic propagation characteristics under the condition of both periodic rough sea bottom and strong negative thermocline layer are systematically analyzed by using the parabolic equation model RAM (where RAM stands for range-dependent acoustic model) and ray theory. For a low-frequency and short-range acoustic source, the transmission loss (TL) increases up to about 5–30 dB due to the existence of the periodic rough bottom. Abnormal TLs and pulse arrival structures with different source depths, different periods and heights of the rough bottom are analyzed and summarized. Specifically, when the period of the rough bottom is constant, TL increases with the height of the rough bottom increasing. When the height of the rough bottom is constant, the effect of the rough bottom on the sound propagation becomes smaller with the increase of the period. The mechanism of the TL difference caused by rough bottom is explained by using the ray theory. The incidence and reflection angle of the sound ray on the sea bottom are changed due to the periodic rough bottom, which makes small grazing angles of some of the rays incident at sea bottom become large grazing angles, and the bottom loss increases. On the other hand, the change of the reflection angle increases the number of ray interaction with the sea bottom, causing the reversion propagation. Therefore, the energy of the sound field will attenuate with range increasing. The influence of the periodic rough bottom on the sound pulse propagation is mainly reflected in the energy conversion between sound rays (or normal modes) with different angles, the increasing of energy attenuation of some sound rays with large angles, and the decreasing of multipath structure. The change of the arrival time and relative amplitude of the multipath structure affect the frequency spectrum of the sound field, which will affect the performance of the method based on matching field localization. Most of existing studies focus on the influence of the change in large scale sea bottom topography on the sound field, but there are few studies on small scale periodic sea bottom fluctuations, and the relevant summary of the law of sound propagation is lacking. When sonar is used in the actual shallow water environment, more attention should be paid to the influence of the periodic rough bottom. In addition, the present research results also have important reference significance for the spatial accuracy of surveying and mapping of sea bottom topography.

Influence of Mesoscale Vortex on Underwater Low-Frequency Sound Propagation

To discuss the effect of an ocean mesoscale vortex on underwater low-frequency sound propagation, a theoretical model of a sound field under the action of an ocean mesoscale vortex was established based on acoustic wave theory and ray theory, using the finite element method. The influences of vortex properties and vortex intensity on the characteristics of sound propagation are discussed. The simulation results indicate that, in a cold vortex, the acoustic convergence zone moves toward the sound source, the span of the convergence zone decreases, and the convergence gain increases. Alternatively, for a warm vortex, the convergence zone moves away from the sound source, the span of the convergence zone increases, the sound rays diffuse, and the convergence gain decreases; the greater the vortex intensity, the greater is the effect on the motion and gain of the convergence region.

Depth estimation of deep water moving source based on ray separation

Source localization based on reliable acoustic path is an important scheme for ocean monitoring in the deep sea. The fluctuating sound pressure propagated from a submerged moving source to deep receivers provides information for source localization. The grazing angle difference between the multipath eigenrays can be estimated using the interference fringes, thereby inferring the source depth. This paper describes a ray separation method and introduces a solution to using broadband and long-term observation information. A method of frequency focusing and grazing angle normalization is proposed to integrate the multi-frequency sound pressure that has been received for a long time, thus reducing the difficulty of extracting the interference fringe interval. Additionally, the analysis on the environmental robustness of source localization using back-propagating sound rays is presented. The simulation results of ray separation and source depth estimation are also given. The grazing angle separation method can be used as a supplementary method for vertical direction estimation. Integrating multi-frequency and grazing angle information with sound pressure field can also be used as an idea of feature engineering in intelligent matching field processing.

Geometry outside of acoustic black holes in ( 2+1 )-dimensional spacetime

Analogue black holes, which can mimic the kinetic aspects of real black holes, have been proposed for many years. The growth of the radial momentum of test particles toward the acoustic horizon is calculated for acoustic black holes in flat and curved spacetimes. Surprisingly, for a freely infalling vortex approaching the acoustic black hole, the Lyapunov exponent of the growth of the momentum at the horizon saturates the chaos bound $\Lambda_{\rm Lyapunov}\leq 2 \pi T$. We investigate the orbits of test vortices and sound wave rays in the $2+1$-dimensional "curved" spacetime of an acoustic black hole. We show that the vortices orbit, the sound wave orbit, and the time delay of sound are similar to those famous effects of general relativity. These effects can be verified experimentally in future experiments.

3D matching positioning method for landslide using infrasound signal received by triangular pyramid vector array, based on ray theory

Several hours before landslides occur, part of the rock and soil body begin to burst, rub, and fracture, generating infrasound signals propagate outward. 3D advanced positioning of the landslide has remained unsolved, which is important for disaster prevention. Using the infrasound signal send from location of the landslide, this work aimed at proposing an advanced 3D matching positioning method, based on ray theory. We first proved vectority of the instantaneous sound pressure field from the perspective of air dynamics, and used ray theory to deduce a point’s instantaneous sound pressure in the air as the sum of all characteristic sound ray vectors. Based on this, the 3D vector acoustic field model was established through simulation. We also found that the triangular pyramid array has vertical and horizontal sampling capabilities, which can collect the vector signals due to the directional anisotropy between the elements. Consequently, the 4-element triangular pyramid vector array was designed to be placed in the acoustic field to receive infrasound signals. Since the infrasound signal is issued before the landslide, we then proposed the 3D matching positioning method: by calculating the cost function of the measurement signal of the triangular pyramid vector array and the copy signals calculated by the propagation model in the predetermined space, point by point, the maximum value was predicted as the infrasound source position, also as the predicted location of landslide. We performed simulations in complex mountainous terrain and applied the method to localization of infrasound sources before the occurrence of the landslide. As a result, by searching and matching in massive space points, we obtained the accurate infrasound source coordinates. This study shows the application prospects of this method for predicting geohazards position several hours in advance.

Sound Velocity Estimation of Seabed Sediment Based on Parametric Array Sonar

Backscattered sound waves of seabed sediments are important information carriers in seafloor detection and acoustic characteristic parameters inversion. Most of the existing methods for estimating geoacoustic parameters are based on multiangle seabed backscattered signal processing and suitable for flat seafloor conditions with uniform sediment thickness. This usually deviates from the real field conditions and affects the accuracy of parameter estimation. In this paper, the sound ray propagation theory is studied and analysed under the condition of sloping seabed and uneven sediment thickness. Based on the phased parameter array sonar system, a method of acoustic parameters estimation of the sediment under inclined seabed conditions is proposed. The simulation results show that the new method shows good adaptability to different inclination angles of the seabed and solves the problem of accuracy of acoustic parameter estimation of the inclined seabed sediments. The model will greatly reduce the seafloor topography requirements in the sediment acoustic parameter inversion, such as velocity, layer thickness, and acoustic impedance.

Analysis of sound field distribution of angle dimension in deep ocean bottom bounce area and its application to active sonar vertical beam pitch

In the deep ocean environment, the sound energy from the direct path is very hard to illuminate a target located in the shadow zone. To solve the problem, the bottom bouncing technique, in which the vertical transmitting beamforming and the bottom bouncing are used to illuminate the target in the shadow zone, provides a potential way. However, due to the sound field interference in the bottom bouncing area in the deep ocean environment, the sound energy in the bottom bouncing area is fluctuant, which produces several discrete detectable areas. In order to detect underwater targets in these areas when using an active sonar with a transmitting vertical linear array, the selecting of reasonable vertical transmitting beam angles is necessary. Therefore, the relationship between the discrete detectable area and the transmitting vertical angle in deep ocean is very important for the active sonar using a transmitting vertical linear array. In this paper, it is shown that the sound field fluctuation in the bottom bouncing area is due to the energy fluctuation of the rays having different grazing angles. And the active sonar can achieve high noise gain in a detectable area when the vertical transmitting angle is equal to the grazing angle of the sound ray with the peak energy. To obtain a high noise gain of the active sonar using the vertical transmitting array, an efficient method to estimate the grazing angle of sound rays with peak energy according to the sound field distribution of angle dimension is proposed, which is helpful for selecting a group of best vertical transmitting angles. Meanwhile, a transmitting signal which contains a group of subpulses is designed. Furthermore, each subpulse is applied to the whole transmitting array by using the vertical steering to illuminate a certain detectable area in the bottom bouncing area. By doing so, a subpulse steered to the previously selected vertical angle will ensure a high transmitting array gain in a detectable area, and all of pulses will illuminate the whole detectable areas with high array gains almost simultaneously. Numerical simulations show that the proposed method is stable and efficient, and has good noise gain in the shadow zone (where almost no direct path exists) in the deep ocean environment.

Levin's collocation method for predicting sound fields in the presence of sound speed gradients

Sound propagation in a stratified medium has been studied for decades. The Ray tracing method, which is one of the most popular methods, calculates the ray path and propagating angle of a sound ray. However, the ray method is not accurate under many circumstances compared with the wave-based numerical schemes. The Fast field program (FFP), an efficient method for numerical evaluation of the Fourier integral, is accurate but requires significant computational resources for high frequency sound fields because of the highly oscillatory functions found in the integrand. In this paper, a Levin’s collocation method is introduced and used in the evaluation of the sound fields above a locally reacting ground with the presence of the sound speed gradient. The method is far more efficient than most other available numerical techniques such as the FFP and Parabolic Equation method.

Integração de simulador acústico em ferramenta de modelagem BIM

Este artigo apresenta os resultados obtidos na primeira fase de desenvolvimento de uma aplicação que integra a interface de um ambiente de projeto BIM (Building Information Modeling) ao simulador acústico BRASS (Brazilian Room Acoustic Simulator). O objetivo do projeto é obter um ambiente de auralização integrado à ferramenta de concepção do projeto, buscando facilitar o trabalho de simulação acústica. Uma interface de auralização unificada evita que arquitetos e engenheiros tenham que comutar entre diversas aplicações gráficas para ouvir o resultado da simulação, facilitando a tomada de decisão projetual. Para efetuar a auralização de salas, os procedimentos de cálculo utilizados pelo simulador acústico BRASS foram implementados no aplicativo de modelagem BIM Revit, testando duas implementações: scripts programados no ambiente de programação visual Dynamo e funções programadas em C# no ambiente .NET. Como resultado da integração, são obtidos arquivos de áudio biauriculares que consideram a espacialidade do som através das funções de transferência relativas à cabeça e a visualização da posição da fonte sonora e do campo acústico, definido pelo conjunto de raios sonoros que se propagam dentro do ambiente simulado. São apontados problemas referentes ao desempenho necessário para realizar este tipo de simulações e relacionados à classificação dos parâmetros utilizados.

An analytical model for reverberation energy decays in rooms with specular and diffuse reflections.

This research is focused on rooms with a pair of parallel surfaces in which non-exponential reverberation energy decays are expected. An analytical model developed in a previous paper is first simplified and completed. It is based on the assumptions of geometrical room acoustics and the formalism of sound particles. The energy of the flux of sound particles emitted by the source in the room is evaluated by introducing some approximations. As a result, a simplified and intuitive model of the reverberation decay is obtained. This model is then extensively compared with reverberation decays computed by a sound ray program, for several kinds of rectangular rooms. A good agreement is obtained between corresponding decays and reverberation times T30.

Accurate Multiple Ocean Bottom Seismometer Positioning in Shallow Water Using GNSS/Acoustic Technique.

The Global Navigation Satellite System combined with acoustic technique has achieved great economic benefits in positioning of ocean bottom seismometers, with hundreds of underwater transponders attached to seismometers typically being deployed during oil exploration. The previous single transponder positioning method ignored the similar underwater environments between the transponders. Due to the refraction effect of sound, the technique usually showed poor positioning accuracy in shallow water when the incidence angles are large. In this paper, the effect of sound ray bending is analyzed based on the sound ray tracing method in shallow water, and a new piecewise incidence angle model is proposed to improve the positioning accuracy of multiple objects in order to estimate the sound ray bending correction. The parameters of the new model are divided into groups and estimated by sequential least squares method, together with all of the transponders. The observability analysis is discussed in simulation and testing experiments in the South China Sea. The results show that the newly proposed method is able to make full use of the acoustic observation data of hundreds of transponders to accurately estimate the SRB correction, which could also significantly improve the positioning accuracy of multiple transponders.

Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise

This paper determines the three-dimensional structure of certain single-frequency canonical sound fields occurring in the theory of blade–vortex interaction when the flow velocity relative to the blade is supersonic. A relative velocity of this magnitude occurs at the outer part of the fan blades in an aeroengine, at which the incoming vorticity has either been ingested from the atmosphere or created in the aeroengine itself. The sound fields analysed are those produced by the leading edge of a flat-plate blade at zero angle of attack on being struck by a gust which is either (i) localized along the span, or (ii) non-localized but discontinuous. The canonical gusts of type (i) have either a delta-function or Gaussian shape, and those of type (ii) are either anti-symmetric or described by a Heaviside function; these gusts give rise to the four basic canonical sound fields. The paper also analyses a fifth sound field, produced by a single-frequency top-hat gust. This sound field has a complex structure involving aspects of both (i) and (ii), but can nevertheless be analysed in terms of the canonical sound fields. The main results of the paper are exact and approximate analytical formulae giving the dependence of the acoustic field on gust-shape and flow parameters, and also a simple formula which is ideal for numerical work. The last of these is used to assess in detail the numerical accuracy of all the approximate formulae, which are of either Fresnel or Keller type. A key result is that Keller-type formulae, representing sound rays produced in accord with the geometrical theory of diffraction, have a very wide range of validity. A companion paper (Chapman & Powles 2019) determines the canonical sound fields in the corresponding time-domain theory.

Characteristics of convergence zone formed by bottom reflection in deep water

There appears a convergence effect on the sound filed under the condition of sound channel in the deep sea due to the refraction effect of the sea water. For the deep water environment with an incomplete channel, sea bottom has an important influence on sound propagation. A long-range sound propagation experiment was conducted in the South China Sea in April 2018. Hyperbolic frequency modulated (HFM) signals with a frequency band of 250-350 Hz are transmitted by an acoustic source which is towed at a speed of 4 knots away from a vertical line array (VLA). The VLA consists of 20 hydrophones which are arranged from 85 m to 3400 m with an unequal depth space. Using the data collected in the experiment, the effects of bathymetry variation on sound propagation are studied. The physical causes of the seafloor reflection convergence phenomenon are explained by using the parabolic equation combined with ray theory. The observed phenomenon is different from the convergence phenomenon in the typical deep water environment, the spatial variation of bathymetry contributes to the formation of the seafloor reflection convergence zone in advance, and the sound intensity in part of shadow zone is significantly increased. Due to the reflection from the seabed, two obvious seafloor reflection convergence zones are observed near the range of 20 km and 40 km respectively, in which both gains increase up to 10 dB, and a high sound intensity area is formed in the shadow zone near the range of 11 km, where the gain is less than the gains in the two convergence zones. In addition, the grazing angle of the sound ray reaching the second convergence zone is smaller than that reaching the first convergence zone when the receiving depth is the same as the source depth, and the rays with smaller glancing angle have less reflection loss, which leads to a higher gain in the second convergence zone. As the water depth becomes gradually shallower with range increasing, the convergence zone near the range of 51 km under the SOFAR channel is destroyed, and the sound field energy in the corresponding range is much smaller since the number of arriving refracted sound rays is reduced. In the first convergence zone, the path of arriving rays is gradually increased as the receiver becomes deeper. Therefore, the arrival structure tends to be complicated, and the multi-path effect is more obvious. The study result is meaningful for the performance analysis of sonar in complex deep water environment.

A fast algorithm to compute shadow areas for Kirchhoff approximation-based underwater acoustic scattering simulation

Kirchhoff approximation method is a fast underwater acoustic scattering numerical method which adaptive to engineering application. Shadow areas calculation is one of the most important factors for computational efficiency. In this paper, several existing shadow domain calculation methods for underwater acoustic numerical simulation based on Kirchhoff approximation are introduced. On this basis, a fast sheltering method based on the linked-list search algorithm is proposed. Linked-list search algorithm uses element geometric center to express the element space position and projects the geometric center on incident wave plane along the incident sound ray. And linked-list relationship of elements is established by dividing background mesh cell on the screen. The algorithm achieves fast calculation by using linked-list relationship and optimizing the calculation path. Linked-list search algorithm and all-pair search algorithm are compared and analyzed by an example of numerical simulation. The computational efficiency of the fast shadow domain algorithm is verified by comparing the results of the two algorithms. And the suggestions for further improving the computational efficiency of the algorithm are proposed.

Node Selection Algorithm for Underwater Acoustic Sensor Network Based on Particle Swarm Optimization

Underwater target positioning technology is the most important part of UnderWater Acoustic Sensor Network(called UWASN), and it is one of the most important research directions in this field with broad application prospects in commercial and military fields. Due to the complex and variability of underwater acoustic environment, the underwater acoustic sensor network has the characteristics of fluidity, sparse deployment and energy limitation, which brings certain challenges to underwater positioning technology. Aiming at the scenario that the node redundancy in the underwater acoustic sensor network leads to low positioning efficiency, this paper considers the sound velocity correction factor based on the traditional anchor node selection algorithm in this paper. Under the premise of ensuring certain positioning accuracy, considering the communication overhead, node residual energy, position suspiciousness, sound ray propagation bending characteristics and other factors, the anchor node optimization mechanism which uses the particle swarm algorithm to iterate out the optimal sensor combination for improving the accuracy of positioning is designed. The simulation results show that the proposed algorithm shows small calculation, fast convergence and high positioning accuracy. It can effectively improve the energy utilization of nodes, balance positioning performance as well as energy use efficiency, and optimize the positioning result of UWASN, which is well suited for underwater acoustic positioning scenarios.

Ray-tracing-based time-domain wideband fractional delay beamforming for underwater acoustic positioning

Underwater acoustic positioning systems are essential for underwater vehicles positioning and navigation. In this paper, a time-domain wideband fractional delay beamforming (WFDB) technique is proposed to improve underwater localization capability of planar arrays. In our method, digital delay lines are combined with adaptive-finite-impulse-response filters to achieve high accuracy beamforming results and reduce the design burden of the WFDB systems. Further, the beamforming results are used in the ray-tracing method to eliminate curvature effect of sound rays caused by the inhomogeneity of water, and therefore improving the computation accuracy of target position. We further develop a hexagonal planar array of 30 elements to verify the WFDB method in an indoor experimental pool. The experimental results demonstrate that the proposed method could successfully mitigate the ray bending problem and accurately estimate the position of targets in low SNR condition.

The influence of the nature of sound reflection from enclosures on the reverberation processes in the rooms

The article considers the questions of assessment of reverberation processes in rooms with various character of a sound reflection from the enclosures. An efficient technique for calculating of the reverberation sound energy in the rooms with mirror-diffuse reflection of sound is offered. The technique is based on the representation of mirror reflected sound rays in the form of separate groups with parameters corresponding oblique, axial and tangential rays. The article includes the comparison of the calculation of reverberation time results on the basis of the division of all the rays into groups with the results of direct reverberation modeling by tracing rays. A good convergence of the results was obtained.

A Combined Ray Tracing Method for Improving the Precision of the USBL Positioning System in Smart Ocean.

The ultra-short baseline positioning system (USBL) has the advantages of flexible application and easy installation, and it plays an extremely important role in the underwater positioning and communication. The error of the USBL in underwater positioning is mainly caused by a ranging error due to ray tracing, a phase difference error of the USBL, and acoustic noise in the underwater communication. Most of these errors are related to the changes in the sound speed during its propagation through the ocean. Therefore, when using the USBL for underwater detection, it is necessary to correct the sound speed profile in the detection area and optimize the ray tracing. Taking into account the actual conditions, this paper aims at correcting the model of underwater sound speed propagation and improving the tracking method of sound lines when the marine environment in the shallow sea area changes. This paper proposes a combined ray tracing method that can adaptively determine whether to use the constant sound speed ray tracing method or the equal gradient ray tracing method. The theoretical analysis and simulation results show that the proposed method can effectively reduce the error of slant distance in USBL compared with the traditional acoustic tracking method and the constant sound speed ray tracing method. The proposed sound ray correction algorithm solves the contradiction between the number of iterations and the reduction of positioning error and has engineering application value.

Using a regional ocean model to understand the structure and sampling variability of acoustic tomography arrivals in Fram Strait

A regional ocean model for Fram Strait allows to understand the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical layers and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modelling on the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic model gives insights into acoustic propagation during winter and spring. Overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of sound channel rays and bottom-reflected rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of bottom-reflected rays is valuable information for choosing appropriate observation kernels for the data assimilation of acoustic tomography data in Fram Strait.

An improved numerical scheme for predicting sound propagation in a vertically stratified medium

Propagation of sound in a stratified medium has been studied for many decades. The ray tracing method, which is one of the most popular ways to solve this kind of problems, involves identifying the sound rays connecting the source with the receiver. However, the ray method does not yield accurate solutions when either the source or the receiver is placed near a turning point. Under these circumstances, it is found necessary to use a wave-based approach leading to a more accurate solution for predicting the sound fields. Typically, the solution is written in a form of a highly oscillatory integral that can be evaluated numerically. High computational times are required to obtain accurate solutions. There have been significant developments in the numerical approximation of highly oscillatory integrals. An improved scheme, which is known as Levin’s collocation method, has low computational costs but it gives accurate numerical solutions for high-frequency sound fields. In this paper, the propagation of sound in a stratified and unbounded medium is considered where there is only one turning point. The Levin collocation method is explored for calculating the sound fields efficiently. In addition, an asymptotic solution is also derived for comparison with the Levin collocation method.Propagation of sound in a stratified medium has been studied for many decades. The ray tracing method, which is one of the most popular ways to solve this kind of problems, involves identifying the sound rays connecting the source with the receiver. However, the ray method does not yield accurate solutions when either the source or the receiver is placed near a turning point. Under these circumstances, it is found necessary to use a wave-based approach leading to a more accurate solution for predicting the sound fields. Typically, the solution is written in a form of a highly oscillatory integral that can be evaluated numerically. High computational times are required to obtain accurate solutions. There have been significant developments in the numerical approximation of highly oscillatory integrals. An improved scheme, which is known as Levin’s collocation method, has low computational costs but it gives accurate numerical solutions for high-frequency sound fields. In this paper, the propagation of sound...