Sound Rays Research Articles

Revision of Sabine's and Eyring's reverberation theories

Sabine's and Eyring's reverberation theories are still the most important theoretical frameworks for room acoustics. The important physical quantities derived from these theories are the average sound pressure level (sound energy density) and the reverberation time (sound energy decay). Eyring revised Sabine's theory to become the reverberation time zero in the perfect absorption condition. However, Eyring's theory has contradictions regarding the sound energy density in a steady state and the energy decay from the steady state. In this study, in order to resolve these contradictions, the theoretical framework for the consistent system is presented introducing the new concept of the average impulse response in a room, and the contradictions in the current room acoustic theory are clarified. Based on the theoretical framework, Sabine's reverberation theory is revised by a different way of Eyring's theory. The reverberation time of the revised theory is shorter than that of Sabine's theory and longer than that of Eyring's theory. Finally, ray-tracing computer simulations were performed to verify the revised theory. Results of sound ray tracing simulations were in better agreement with the values calculated using the revised theory rather than those calculated using Sabine's and Eyring's theories.

Research on Sound velocity model construction method in GNSS-A underwater positioning

Abstract GNSS-A technology is a submarine positioning technique used to establish ocean control networks, and its positioning results are primarily affected by errors in ocean sound velocity. To address this issue, this paper analyzes the spatial representativeness error of the weighted average sound velocity based on the GNSS-A positioning principle. It also explores the construction method of a sound velocity model in the time domain using the average sound velocity. A sinusoidal diurnal variation model for sound velocity is developed through expanded fitting. Finally, actual measured data is used to perform GNSS-A submarine positioning, verifying the effectiveness of the sound velocity model. The results show that when the horizontal distance of the sound ray is less than 1.7 times the water depth, the average sound velocity does not introduce significant systematic errors. The constructed sound velocity model aligns with local solar elevation patterns, improving the unit weight error of GNSS-A positioning results by several decimeters and controlling the mutual difference of positioning results from different tracks to the decimeter level.

Segmented propagation model for the paths and travel times of surface duct leaky signals.

In the deep ocean environment with a surface duct, sound propagating within the duct leaks into the geometric shadow zone below it. However, the propagation paths and time of these leaky parts have not been fully characterized. This paper investigates the mechanism of surface duct leaky (SDL) signals based on normal mode theory. It reveals that SDL signals are caused by specific modes with grazing angles close to zero at the bottom of the surface duct. Combining the theory of diffracted sound rays, the study proposes a Segmented Propagation model (SPM) for SDL signals. The propagation paths of SDL signals are divided into three segments: S1, which extends from the source to the surface duct; S2, the segment propagating within the surface duct; and S3, the segment leading from the surface duct to the receiver. The proposed SPM describes the propagation mechanism of SDL signals and allows for precise calculation of their propagation time. Experimental data from the western Pacific are used to verify the SPM.

A high-precision localization method for underwater targets incorporating direct path recognition and sound rays bending compensation

A high-precision localization method for underwater targets incorporating direct path recognition and sound rays bending compensation

Spatiotemporal Analysis of Sonar Detection Range in Luzon Strait

Sonar serves as a critical submarine detection apparatus for naval vessels, with its detection range forming the foundation of its overall performance in underwater surveillance. The Luzon Strait, in the eastern part of the South China Sea, presents a complex hydrographic setting that profoundly influences sonar performance, necessitating mastery of the detection range variation for enhanced anti-submarine operational efficiency. This study employs the Bellhop acoustic propagation model to estimate the transmission loss. Subsequently, a detection probability integration approach is applied to determine the sonar detection range in the Luzon Strait from 2019 to 2023, which is then subjected to statistical analysis. The findings indicate the following. (1) During the summer and autumn, the shallow mixed layer fails to generate a surface duct, resulting in shorter detection ranges that are primarily dependent on the water depth. In the Shallow Water Zone (<150 m), frequent interactions between sound waves and the sea boundaries lead to considerable acoustic energy attenuation, maintaining a short detection range. In the Intermediate Depth Zone (150–2500 m), sound rays retain adequate energy post-seabed reflection, extending the sonar detection to 5–8 km. Beyond 2500 m, the diminishing reflective energy restricts the range to 2–5 km. (2) Conversely, in the winter and spring, the formation of a surface duct becomes the predominant determinant of the detection range, capable of exceeding 10 km, overshadowing the influence of the water depth.

A Method for Full-Depth Sound Speed Profile Reconstruction Based on Average Sound Speed Extrapolation

The speed of sound in seawater plays a crucial role in determining the accuracy of multibeam bathymetric measurements. In deep-sea multibeam measurements, the challenge of inadequate longitudinal coverage of sound speed profiles arises from variations in seafloor topography, meteorological conditions, measurement equipment, and operational efficiency, resulting in diminished measurement precision. Building upon the EOF (Empirical Orthogonal Function), a method employed to analyze spatiotemporal data such as sound speeds, this paper addresses the limitations of the EOF method caused by the shallowest sampling depth of the sound speed profile samples. It proposes two methods for EOF reconstruction of measured sound speed profiles extended to full water depth by splicing measured sound speed profiles at non-full water depths with historical average sound speed profiles of the surveyed sea area. Specially, Method 2 introduces the latest metaheuristic optimization algorithm, CPO (Crested Porcupine Optimizer), which exhibited superior performance on multiple standard test functions in 2024. The study reconstructs randomly sampled measured sound speed profiles using the two proposed methods and commonly employed substitution and splicing methods, followed by a comparative analysis of the experimental outcomes. At a sampling depth of 200 m, Method 2 demonstrates performance superior to other methods, with RMSE, MAE, MAPE, and R2 values of 0.9511 m/s, 0.8492 m/s, 0.0566%, and 0.9963, respectively. Method 1 yields corresponding values of 0.9594 m/s, 0.8492 m/s, 0.0568%, and 0.9962, respectively. Despite its slightly inferior performance compared with Method 2, it offers substantial advantages over the substitution and splicing methods. Varying the sampling depth of measured sound speed profiles reveals that Methods 1 and 2 exhibit inferior reconstruction performance in shallow water compared with the substitution and splicing methods. Nevertheless, when the sampling depth surpasses the depth range of initial spatial modes with abrupt variations, both methods achieve notably higher reconstruction accuracy compared with the substitution and splicing methods, reaching a stabilized state. Sound ray tracing reveals that the reconstructed sound speed profiles from both methods meet the stringent accuracy standards for bathymetric measurements, achieving an effective beam ratio of 100%. The proposed methods not only provide rapid reconstruction of sound speed profiles, thereby improving the efficiency of multibeam bathymetric surveys, but also provide references for the reasonable determination of sampling depths of sound speed profiles to ensure reconstruction accuracy, demonstrating practical application value.

Enhanced Multi-Beam Echo Sounder Simulation through Distance-Aided and Height-Aided Sound Ray Marching Algorithms

The study proposes two innovative algorithms in the field of multi-beam echo sounder (MBES) simulation: distance-aided sound ray marching (DASRM) and height-aided sound ray marching (HASRM). These algorithms aim to enhance the efficiency and accuracy of MBES simulations, particularly when dealing with long-distance propagation and real-time processing limitations. DASRM addresses issues related to simulation accuracy by efficiently utilizing the KD-tree for spatial indexing and intersection detection instead of the signed distance field (SDF). Building upon the further analysis of DASRM, HASRM is proposed, which improves the search strategy for ray intersections and utilizes a height field pyramid for sampling and retrieval, thereby reducing memory usage while enhancing indexing efficiency. The experimental results demonstrate that both algorithms significantly outperform traditional methods in terms of simulation time, with HASRM exhibiting particular advantages in parallel computing due to its data structure and improved strategies. Additionally, DASRM is well suited for applications requiring complex scene construction, while HASRM proves especially effective in simulating MBES with a focus on underwater terrain due to its effectiveness in handling large incident angles and long-distance propagation.

A differential-based method for correcting ultra-short baseline positioning results

The primary factors influencing the positional accuracy of an ultra-short baseline (USBL) system are errors in sound speed, delay, installation deviation, and the bending of sound rays. Premised on the USBL positioning model, an error contribution model including ranging error, delay error, sound speed error and array element installation deviation was constructed. In parallel, an indirect difference correction method with additional coefficients was proposed based on the geometric correlation of the error function model. Specifically, a reference beacon was deployed on the seabed, and differential correction was achieved by directly computing target coordinates, integrating them with the positional data from the reference beacon. The proposed method demonstrated efficacy in mitigating errors associated with gradual variations or pronounced geometric correlations, including discrepancies in sound speed, bending of sound rays, and deviations in the installation of array elements. The correction method was applied to the USBL positioning, and the simulation results show that the proposed method notably enhanced both accuracy and consistency in positioning, particularly in shallow water environments characterised by significant sound speed errors. The sea trial data from the R/V Dayang Yihao in the Western Pacific demonstrate that the proposed method can effectively mitigate the errors induced by sound ray bending in deep-sea environments. The mean absolute error (MAE) and standard deviation (STD) were reduced by 51.3% and 55.3%, respectively, compared with the results of the USBL direct solution.

FPGA-Based Real-Time Synchronous Parallel System for Underwater Acoustic Positioning and Navigation

With the development of autonomous underwater vehicles, the research of underwater acoustic positioning and navigation technology is becoming increasingly important. However, most underwater positioning systems use the traditional acoustic response synchronization method, which leads to insufficient positioning real-time performance and refresh rate. To solve this problem, this paper proposes a real-time global synchronization mechanism with high-precision atomic clocks, which can realize one positioning through one-way propagation, so that the positioning efficiency is at least doubled. To further improve the positioning accuracy, an M-sequence-based phase offset modulation method is proposed to facilitate beacon identification. Consequently, a normalized signal matching capture algorithm against Doppler effect is designed, and the positioning solution is fused with the real-time sound ray bending compensation mechanism. Based on the above content, we developed an FPGA-based real-time synchronous parallel underwater positioning and navigation (RSPUPN) system, which uses FPGA+MCU architecture to accelerate signal processing operations in a low-power and parallel way. The test results in the South China Sea show that the operating range of the system can reach 8 km, the positioning refresh rate can reach 0.2 Hz, and the relative average position error is 0.25%, confirming the effectiveness of the designed system in industrial applications.

Sound Speed Inversion Based on Multi-Source Ocean Remote Sensing Observations and Machine Learning

Ocean sound speed is important for underwater acoustic applications, such as communications, navigation and localization, where the assumption of uniformly distributed sound speed profiles (SSPs) is generally used and greatly degrades the performance of underwater acoustic systems. The acquisition of SSPs is necessary for the corrections of the sound ray propagation paths. However, the inversion of SSPs is challenging due to the intricate relations of interrelated physical ocean elements and suffers from the high costs of calculations and hardware deployments. This paper proposes a novel sound speed inversion method based on multi-source ocean remote sensing observations and machine learning, which adapts to large-scale sea regions. Firstly, the datasets of SSPs are generated utilizing the Argo thermohaline profiles and the empirical formulas of the sound speed. Then, the SSPs are analyzed utilizing the empirical orthogonal functions (EOFs) to reduce the dimensions of the feature space as well as the computational load. Considering the nonlinear regression relations of SSPs and the observed datasets, a general framework for sound speed inversion is formulated, which combines the designed machine learning models with the reduced-dimensional feature representations, multi-source ocean remote sensing observations and water temperature data. After being well trained, the proposed machine learning models realize the accurate inversion of the targeted ocean region by inputting the real-time ocean environmental data. The experiments verify the advantages of the proposed method in terms of the accuracy and effectiveness compared with conventional methods.

Low frequency inversion method based on multi-layer holizontal variation shallow seafloor model

Sound propagation in shallow water is significantly influenced by geoacoustic properties. Estimating these geoacoustic parameters is essential for sound field analysis and sonar performance assessment. As a common practice, the seafloor is often treated as a single-layer or two-layer range-independent geoacoustic model to reduce the number of involved parameters. However, acoustic parameters inverted through these two geoacoustic models are typically limited in their applicability to a specific frequency range, thus posing challenges when applied across a broader frequency range. A range-dependent multi-layer geoacoustic model based on experimental measurements obtained with a sub-bottom profiler is proposed in this study. The inversion scheme combines three inversion methods to estimate geoacoustic parameters, considering the different sensitivities of geoacoustic parameters to different physical parameters within the acoustic field. Firstly, modal dispersion is used to invert the geoacoustic parameters of each layer, with the dispersion curve obtained through warping transform and the Wigner-Ville distribution. After that, both the localization using matched field processing and the dispersion curve fitting demonstrate the effectiveness of the inversion results for each layer, although the peak of the probability distribution of sound speed in the first layer is broader than in others. Secondly, matched field processing is employed to invert the geoacoustic parameters of the first layer. This method is based on the theory that as frequency increases, the depth of sound rays penetrating the seabed decreases, revealing changes in the first layer's sound speed with the seabed depth. Lastly, bottom attenuation coefficients at different frequencies are inverted by the transmission loss (TL), and a fitting relationship between the attenuation coefficient and the frequency is derived. The inversion results obtained by using the range-dependent multi-layer geoacoustic model are compared with results estimated by the single-layer geoacoustic model. The findings indicate that the transmission loss (TL) error from the range-dependent multi-layer geoacoustic model in this study is smaller than that from the single-layer geoacoustic model, especially in the lower frequency band. The range-dependent multi-layer geoacoustic model proves to be suitable for a broader frequency range, providing better precision in explaining various acoustic phenomena.

Fundamental study on directivity of acoustic radiation from tire by using ray tracing method

Ray tracing method is classified as a geometric acoustic theory and is a commonly used method for analysing sound field in buildings. It traces the reflection and propagation paths of a number of sound rays radiated from a sound source. Originally, ray tracing method does not take frequency response into account, but in this study, ray tracing method is modified so that frequency response can be calculated in order to apply ray tracing method to general sound field analysis other than buildings. For this purpose, the propagation distance of each sound ray due to reflection are considered, and the interference of each sound ray at the receiver is calculated. To verify the effectiveness of the proposed method, it is applied to the acoustic radiation of tire noise as an example. In addition, the directivity of the tire noise acoustic radiation is investigated on the basis of ray tracing method.

Theatres from roman age to renaissance: a short survey on the meaning of reverberation time measurements

In the mind of C.W. Sabine, reverberation time was thought as a numerical index of what was happening in a closed hall when a sound source acting within was suddenly stopped: the original idea was that sound rays where travelling in any direction reinforcing residual sound energy, but at the same time overlapping audible messages that these rays where carrying to the listener's brain. As well known, he stated a formula linking the R.T. value to the hall volume and to the capacity of the impinged surfaces to keep a fraction of the sound energy: from one hundred years to now, many authors researched in the field and stated the best R.T. values for the listener of different kinds of sound. Surely Greeks and Romans did not know the possible existence of such a parameter, as they acted in open spaces, neither Vitruvius and, successively Alberti, Milizia, Poletti and so on, even if the tile cover utilized by the Romans to preserve from sun light and rain was avoiding that some sound energy dispersed in the sky. Surely the modern computer assisted measurement techniques are able to keep some kind of sound decay even in an ancient theatre, but we are aware, as Greeks were, that they are derived only from reflections travelling quite horizontally, between vertical structures, or inclined between actors and spectators via orchestra floor, when not occupied from public. This paper will present a specific and synthetic survey on the subject.

Feature extraction and classification of deep-sea mobile underwater acoustic channels

The reliable acoustic path (RAP) is one of the crucial channels for deep-sea sound propagation, which is affected weakly by the interface and has lower transmission loss, enabling long-distance communication. However, RAP-based deep-sea acoustic communication may face channel model mismatch issues. In order to analyze the dynamic characteristics of spatial-temporalvariability channels, deep-sea mobile underwater acoustic channel measurement experiments were conducted. This work proposes a deep learning method based on multi-dimensional properties to classify deep-sea channels. Specifically, the sound ray convergence zone leads to a complex multipath structure and severe delay spread in the RAP channel. The fuzzy c-means (FCM) algorithm is used for multipath clustering to extract accurate channel features, and then the Markov chain (MC) is introduced to track the evolution characteristics of multipath clusters. Finally, the coupling features of channel time-variant impulse response (TVIR) and multi-dimensionalstatistical properties are used as the input of convolutional neural networks (CNNs) to obtain the quantitative evaluation index as the channel classification to build a channel feature dataset for underwater mobile platforms. This dataset can effectively assist in identifying deep-sea mobile channels and promote the development of adaptive underwater acoustic communication systems on mobile platforms.

Characterization and modeling of high-speed underwater acoustic communication channels

High-speed mobile underwater acoustic communication (HSM-UAC) is a relatively unexplored terrain, but its importance is expected to increase with the widespread application of flexible underwater mobile platforms such as AUVs and UUVs. Knowledge of HSM-UAC channels is a prerequisite to achieving reliable communication. This work conducted two HSM-UAC channel measurement experiments with a maximum speed of 20knots. The analysis of channel time-varying characteristics demonstrates the shortcomings of traditional consistent Doppler frequency offset channel model. The experimental findings reveal the presence of two non-stationary modes in the HSM-UAC channel. For short moving distances, the changes in channel geometry result in each path experiencing a different Doppler scale, thus observing the multiscale-multilag (MSML) channels. For long moving distances, the alteration in sound ray propagation tracks entirely reshapes the channel impulse response (CIR) structure, leading to a rapid decline in channel time correlation. In further analysis, the correlation coefficient of the power delay profile (PDP) is used to measure channel stationarity. Subsequently, the stationary time and corresponding stationary distance are calculated as characterization parameters for the time-varying channel model. The quantitative evaluation results are helpful for the communication signal design and determining the update frequency of channel state information.

Assessing the feasibility of conducting coastal acoustic tomography using BELLHOP modeling

In order to apply coastal acoustic tomography (CAT) efficiently to a specific coastal area, it is necessary to design a measurement system in consideration of various variables related to the marine environment of the area. In particular, to consider seasonal variations in the water temperature structure quantitatively is important regarding the formation of sound rays. In this study, the feasibility of performing CAT according to the seasonal variations in the water temperature structure of Yeosu and Gwangyang Port was studied through simulation using BELLHOP model. First, BELLHOP model simulations were performed using the precise chart data and seasonal water temperature structure data of Yeosu and Gwangyang Port as input data. As a result, signal received during transmitting and receiving between candidate locations of stations could be calculated for each season. And, by estimating the minimum sound source level required to obtain an identifiable peak from the SNR value of the signal, the feasibility of tomography measurement could be assessed. It is expected that some important information, in constructing a tomography system with specifications appropriate for any coastal area of interest, can be provided in advance utilizing the method used in this study.

Effects of internal solitary waves on three-dimensional sound propagation and DOA estimation in the South China Sea

Internal solitary waves (ISWs) in the South China Sea, characterized by their large amplitude and strong nonlinearity, have attracted a lot of attention. In this paper, we use the Massachusetts Institute of Technology general circulation model (MITgcm) to construct the processes of generating and propagating ISWs in the South China Sea from the Luzon Strait to the continental shelf. The simulated east–west flow velocity is compared with remote sensing images, and the results demonstrate the accuracy of the ISW model in the South China Sea. Inserting the simulated three-dimensional (3D) sound speed from the ISW model into the Bellhop3D model, key findings emerge that ISWs cause depressions in the iso-sonic surface, which lead to drastic fluctuations in sound rays and the horizontal refraction effect in the progress of sound propagation. ISWs disturb the convergence zone of sound rays, but the position of the internal wave crest line is consistent with that of the collective deflection of rays. In addition, the results of direction of arrival (DOA) estimation under ISWs demonstrate that the internal wave increases the DOA estimation error. Together, ISWs induce fluctuations in sound propagation and degrade sonar performance. This study creatively combines ISWs with the underwater sound field and DOA estimation, which provides support for the 3D sound propagation mode and the arrangement of the sonar array in the internal wave environment.

Analysis of the influence of the continental shelf slope in the South China Sea on sound propagation

Continental shelf slopes are widely found in transitional sea areas, which are the connecting part between shallow and deep seas. The sound propagation in this part has special effects. This paper takes the continental shelf slope sea area of the South China Sea (SCS) as the research object to analyze the influence of the shelf slope on sound propagation at different seasons. The seasonal difference in the three-dimensional sound ray trajectory and its corresponding transmission loss (TL) are mainly reflected in the case of a shallow sound source, which is caused by the difference in the sound speed field environment. Due to the presence of a strong surface sound channel in winter, the sound source at shallow depths can achieve long-distance propagation. As the strength of the surface sound channel becomes weaker, sound rays with large grazing angles can deflect across the surface sound channel towards the seabed, and sound energy leaks out of the surface sound channel. This part of the sound energy complements the area that the original sound energy can not reach, so the TL in this area is less than 90 dB. As for the slope enhancement effect, we verify it from the perspective of sound ray propagation, calculate the maximum distance between the sound ray and the shelf slope, and the mean absolute percentage error (MAPE) between the theoretical value and the actual value is 7.6%. The above results will have important implications for target detection and hydroacoustic communication in the sea area of continental shelf slopes.

Water Temperature Reconstruction via Station Position Correction Method Based on Coastal Acoustic Tomography Systems

Underwater acoustic tomography is an advanced technology in water environment observation. Sound propagation duration between transceivers is used for underwater parameter distribution profile reconstruction in the inverse problem. The key points of acoustic tomography are accurate station distance and time synchronization. Two methods are introduced in this study for sound station position correction. The direct signal transmission correction (DSC) method corrects the multi-peak (expect direct ray) travel time via the travel time difference between different sound rays and reference direct ray. The ray-model position correction (RMC) method calculates exact station position by the station drift distance obtained from transceiver depth variations to correct direct ray travel time; the other multi-peak travel time is revised by the corrected direct ray travel time. A water temperature observation experiment was carried out in a reservoir using coastal acoustic tomography (CAT) systems to verify the flexibility of these two methods. Multi-ray arrival peaks are corrected using DSC and RMC methods; water temperature inversion results in a 2D vertical profile are obtained. The reliability of the method is proved by comparison with temperature depth sensor (TD) data. The methods improve the quality of initial data and can be attempted for further water environment observation in acoustic tomography observation studies.

Investigation on Vertical Position and Sound Velocity Variation for GNSS/Acoustic Seafloor Geodetic Calibration Based on Moving Survey Data

The accuracy of GNSS/Acoustic seafloor geodetic calibration is greatly influenced by the temporal variation of sound velocity, especially in the vertical direction. Aiming at correcting of the unknown parameters related to both the positions and the sound velocity, this paper proposes a step-by-step inversion scheme based on moving survey data. The proposed method firstly estimates the horizontal normalized travel time delay with sound ray tracing strategy and then computes the horizontal position with circle line observations. We reconstructed an inversion scheme for extracting the surface sound velocity disturbance (SSVD) and corrected the vertical position from cross line data. The SSVD is decomposed into a sum of different period disturbances, and a new SSVD is reconstructed by combining the long period disturbance and short period disturbance. The proposed algorithm is verified by the South China Sea experiment for GNSS/Acoustic seafloor geodetic calibration. The results demonstrate that the new method can take the effects of sound velocity variation into consideration and improve the precision of the vertical position, which is superior to the least squares (LS), the single-difference LS for seafloor geodetic calibration.