Geometry of locating sounds from differences in travel time: isodiachrons

Calling animals may be located from measurements of the differences in acoustic travel time at pairs of receivers. For inhomogeneous fields of speed, locations can be made with better accuracy when the location algorithm allows the speed to vary from path to path. A new geometrical shape, called an isodiachron, is described. It is the locus of points corresponding to a constant difference in travel time along straight paths between the animal and two receivers. Its properties allow an interpretation for locations when the speed differs from path to path. An algorithm has been developed for finding the location of calling animals by intersecting isodiachrons from data collected at pairs of receivers. When the sound speed field is spatially homogeneous, isodiachrons become hyperboloids. Unlike a hyperboloid that extends to infinity, an isodiachron is confined to a finite region of space when the speeds differ between the animal and each of two receivers. Its shape is significantly different than a hyperboloid for cases of practical interest. Isodiachrons can be used to better understand locations of calling animals and other sounds in the sea, Earth, and air.     

Probability density functions for hyperbolic and isodiachronic locations

Animal locations are sometimes estimated with hyperbolic techniques by estimating the difference in distances of their sounds between pairs of receivers. Each pair specifies the animal's location to a hyperboloid because the speed of sound is assumed to be spatially homogeneous. Sufficient numbers of intersecting hyperboloids specify the location. A nonlinear method is developed for computing probability density functions for location. The method incorporates a priori probability density functions for the receiver locations, the speed of sound, winds, and the errors in the differences in travel time. The traditional linear approximation method overestimates bounds for probability density functions by one or two orders of magnitude compared with the more accurate nonlinear method. The nonlinear method incorporates a generalization of hyperbolic methods because the average speed of sound is allowed to vary between different receivers and the source. The resulting "isodiachronic" surface is the locus of points on which the difference in travel time is constant. Isodiachronic locations yield correct location errors in situations where hyperbolic methods yield incorrect results, particularly when the speed of propagation varies significantly between a source and different receivers.     

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.     

Relating the performance of time-reversal-based underwater acoustic communications in different shallow water environments

The performance of underwater acoustic communications, such as the output signal-to-noise ratio (OSNR), is generally dependent on the channel specifics, hence a channel model is normally required as the performance of the channel equalizer depends on the number of tap coefficients used (e.g., a sparse equalizer) which are different for different oceans having different multipath arrivals. This letter presents theoretical arguments, and experimental data from different oceans that suggest that the increase of OSNR with the number of diverse receivers (in terms of the effective number of receivers) and the decrease of OSNR with the channel-estimation error follow a universal relationship using the time-reversal or correlation-based equalizer, despite the fact that the channels have very different properties. The reason is due to the fact that the OSNR is a function of the q function, the auto-correlation of the received impulse responses summed over all receiver channels, and the q function is approximately the same for all shallow waters given a sufficient (≥4-6) number of receivers.     

A reflected energy prediction model for long-range hydroacoustic reflection in the oceans

Acoustic energy from underwater earthquakes and explosions can propagate over long distances with very little attenuation in the deep ocean. When this sound encounters a seamount, island, or continental margin, it can scatter and again propagate over long distances. Hydrophones in the deep sound channel can detect these reflections tens of minutes or hours after arrivals from the direct source-to-receiver path. This paper presents the Reflected Energy Prediction (REP) model, a model for predicting these reflected arrivals. For a given source and receiver, the REP model uses a detailed knowledge of the underwater environment and components of the Hydroacoustic Coverage Assessment Model, HydroCAM, to predict the impulse response of the ocean. When this impulse response is convolved with a source function, a waveform envelope prediction is made that can be compared with recorded data. In this paper we present the model and a few applications of the model using data recorded from earthquakes and explosions in the Atlantic and Indian Oceans. These examples illustrate the use of the model and initial steps toward model calibration.     

Impulse propagation in the nocturnal boundary layer: analysis of the geometric component

On clear dry nights over flat land, a temperature inversion and stable nocturnal wind jet lead to an acoustic duct in the lowest few hundred meters of the atmosphere. An impulsive signal propagating in such a duct is received at long ranges from the source as an extended wave train consisting of a series of weakly dispersed distinct arrivals followed by a strongly dispersed low-frequency tail. The leading distinct arrivals have been previously shown to be well modeled by geometric acoustics. In this paper, the geometric acoustics approximation for the leading arrivals is investigated. Using the solutions of the eikonal and transport equations, travel times, amplitudes, and caustic structures of the distinct arrivals have been determined. The time delay between and relative amplitudes of the direct-refracted and single ground reflection arrivals have been investigated as parameters for an inversion scheme. A two parameter quadratic approximation to the effective sound speed profile has been fit and found to be in strong agreement with meteorological measurements from the time of propagation.     

Tomographic inversion of measured cross-correlation functions of ocean noise in shallow water using ray theory

Based on experimental data obtained in 2012 in the Florida Strait, we study the feasibility of employing ray tomography to retrieve sound speed and flow velocity profiles from measured noise cross-correlation functions. We describe the results of numerical experiments that characterize the inversion errors resulting from peculiarities of the ray structure in shallow water, difficulties in unambiguous identification of ray arrivals, and a decrease in accuracy of ray theory at low frequencies. We show that under conditions of low-mode sound propagation, the use of the classical ray tomography scheme can yield only a rough estimate of the sound speed profile, but it allows approximate reconstruction of the current velocity profile. Application of passive ray tomography to the experimental data yields the current velocity profile in the Straits of Florida, which agrees with independent measurements within the inversion error limit.     

Interfering modes and an axial wave in an underwater sound channel

Experiments on long-range propagation of low-frequency sound that were conducted starting from the mid-1980s indicate a complex character of propagation in an underwater sound channel, in which a source and a receiver are located close to the channel axis. A burst of energy propagating along the axis follows early arrivals, which are well described by the formulas of geometrical acoustics, in plots of acoustic intensity as a function of propagation time and hydrophone depth. This energy burst cannot be described using geometrical acoustics because of caustics with caustic beaks located near the channel axis. Very complex interference processes occur near these caustics. As the distance from the source grows, the dimensions of the interference vicinity increase and start to overlap producing a peculiar “axial wave.” For an arbitrary two-dimensional underwater sound channel, the axial wave can be represented as a sum of the first normal modes and a residue. This conclusion is based on the use of two representations for an acoustic field. The first of them includes the sum of ray components and an axial wave. The second representation consists of ray addends, the sum of the first normal modes, and a residue. Numerical results are obtained for a canonical profile of sound velocity at the frequency of 200 Hz for the distances of 1600–1650 km.     

Numerical evaluation of tree canopy shape near noise barriers to improve downwind shielding

The screen-induced refraction of sound by wind results in a reduced noise shielding for downwind receivers. Placing a row of trees behind a highway noise barrier modifies the wind field, and this was proven to be an important curing measure in previous studies. In this paper, the wind field modification by the canopy of trees near noise barriers is numerically predicted by using common quantitative tree properties. A realistic range of pressure resistance coefficients are modeled, for two wind speed profiles. As canopy shape influences vertical gradients in the horizontal component of the wind velocity, three typical shapes are simulated. A triangular crown shape, where the pressure resistance coefficient is at maximum at the bottom of the canopy and decreases linearly toward the top, is the most interesting configuration. A canopy with uniform aerodynamic properties with height behaves similarly at low wind speeds. The third crown shape that was modeled is the ellipse form, which has a worse performance than the first two types, but still gives a significant improvement compared to barriers without trees. With increasing wind speed, the optimum pressure resistance coefficient increases. Coniferous trees are more suited than deciduous trees to increase the downwind noise barrier efficiency.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.     

Annoyance caused by simultaneous impulse, road-traffic, and aircraft sounds: a quantitative model.

In this study, total annoyance caused by different simultaneous environmental sounds is investigated. In spite of a number of puzzling data in the literature, it is fairly well established that in combinations in which the annoyance of one source is considerably higher than that of another source, total annoyance is equal to the maximum annoyance of the separate sources. For combinations in which both sounds are about equally annoying, total annoyance seems to be higher than the maximum source-specific annoyance. The available data, however, are too rough to model total annoyance in these conditions. The present laboratory studies were therefore designed to explore further possible procedures to quantify total annoyance. Subjects rated the (total) annoyance caused by various combinations of impulse, road-traffic, and aircraft sounds. The results support a simple model which predicts the overall or total rating sound level L(t) for combinations of several types of sounds. Here, L(t) is numerically equal to the A-weighted equivalent sound level L(eq) of road-traffic sound with the same annoyance as caused by the combination of sounds. In the model, the sound exposure caused by the impulse and/or aircraft sounds is first expressed in the L(eq) of equally annoying road-traffic sound. With the help of source-specific dose-effect relationships, this is achieved by adding level-dependent penalties to the L(eq) of the respective sources. Weighted summation of the corrected L(eq)'s of the various sources then results in L(t). An optimal overall fit of the data from two separate experiments was obtained when the weighted summation of the corrected L(eq)'s was performed with the parameter k in k log(sigma 10(corrected L(eq) of source j)/k) set to 15. The standard deviation of the differences between the experimental results and the model predictions with k = 15 was equivalent to the small change in annoyance produced by a 1.5-dB shift in the L(eq) of road-traffic sound. Adoption of k = 15 implies that after correction, two equal L(eq)'s yield a total rating sound level which is 4.5 dB higher than each single-source corrected L(eq).     

Detecting pipe changes via acoustic matched field processing

Detecting pipe irregularities such as intrusions can be challenging. However, subtle changes can be identified in the complex acoustic fields measured over a range of frequencies and over a time interval given an “array” of receivers. In particular, for two receivers one can coherently process the signals via matched field processing (MFP) to infer whether or not there have been changes such as new intrusions relative to undisturbed fields measured earlier. There is no acoustic modelling of the fields required, only the simple linear processor is applied, and only test data (five scenarios) are used in this demonstration. A key advantage to using MFP plus two (or more) microphones is that absolute sound levels need not be carefully measured.     

Outdoor sound propagation under the influence of wind and temperature gradients

The situation investigated is sound propagation from a monopole point source located over an impedance surface. The sound propagation is assumed to be influenced by wind and temperature gradients. A very accurate calculation method for taking into account the effect of wind and temperature gradients on sound propagation outdoors is presented and used for verification of a new approximate calculation model. This comparison shows that the approximate model is accurate. A series of loudspeaker measurements has been carried out over a grass-covered ground for distances up to 80 m. The measurements were carried out for a wind speed fo 2–2·5 m/s measured 10 m above the ground. The measured data agree very well with the calculated results. Furthermore the results from the approximate calculation model agree with results from previous investigations [1,2]. Hence, the main conclusion is that a simple and powerful approximate model for sound propagation under the influence of wind and temperature gradients has been developed. However, the influence of turbulence is not taken into account in this paper, and the wind and temperature gradients are assumed to be constant as functions of height.     

涌浪条件下的浅海表面声道脉冲声传播*

在冬季,海水表面受到海面强风的影响,普遍存在表面声道。当声源位于表面声道中并且声源频率高于表面声道的截止频率时,声能量几乎被完全限制其中,不与海底作用,十分有利于声传播。但当表面声道上边界为较大涌浪所形成的粗糙界面时,这种优良性能会被破坏。在南海北部陆坡海区的一次冬季实验中,发现表面声道以下水听器接收到的首个脉冲的幅度明显增加,通过研究表明,其原因是：存在较大涌浪时,部分表面声道内传播的声能量,经粗糙海面反射作用后进入下层水体中,使得位于表面声道以下的水听器的第一个到达的脉冲幅度增强。     

Prediction of underwater sound levels from rain and wind

Wind and rain generated ambient sound from the ocean surface represents the background baseline of ocean noise. Understanding these ambient sounds under different conditions will facilitate other scientific studies. For example, measurement of the processes producing the sound, assessment of sonar performance, and helping to understand the influence of anthropogenic generated noise on marine mammals. About 90 buoy-months of ocean ambient sound data have been collected using Acoustic Rain Gauges in different open-ocean locations in the Tropical Pacific Ocean. Distinct ambient sound spectra for various rainfall rates and wind speeds are identified through a series of discrimination processes. Five divisions of the sound spectra associated with different sound generating mechanisms can be predicted using wind speed and rainfall rate as input variables. The ambient sound data collected from the Intertropical Convergence Zone are used to construct the prediction algorithms, and are tested on the data from the Western Pacific Warm Pool. This physically based semi-empirical model predicts the ambient sound spectra (0.5-50 kHz) at rainfall rates from 2-200 mm/h and wind speeds from 2 to 14 m/s.     

Modeling acoustic propagation of airgun array pulses recorded on tagged sperm whales (Physeter macrocephalus)

In 2002 and 2003, tagged sperm whales (Physeter macrocephalus) were experimentally exposed to airgun pulses in the Gulf of Mexico, with the tags providing acoustic recordings at measured ranges and depths. Ray trace and parabolic equation (PE) models provided information about sound propagation paths and accurately predicted time of arrival differences between multipath arrivals. With adequate environmental information, a broadband acoustic PE model predicted the relative levels of multipath arrivals recorded on the tagged whales. However, lack of array source signature data limited modeling of absolute received levels. Airguns produce energy primarily below 250 Hz, with spectrum levels about 20-40 dB lower at 1 kHz. Some arrivals recorded near the surface in 2002 had energy predominantly above 500 Hz; a surface duct in the 2002 sound speed profile helps explain this effect, and the beampattern of the source array also indicates an increased proportion of high-frequency sound at near-horizontal launch angles. These findings indicate that airguns sometimes expose animals to measurable sound energy above 250 Hz, and demonstrate the influences of source and environmental parameters on characteristics of received airgun pulses. The study also illustrates that on-axis source levels and simple geometric spreading inadequately describe airgun pulse propagation and the extent of exposure zones.     

Comprehensive studies of sound fields in the Kuril-Kamchatka region of the northwestern Pacific

The technique, experimental conditions, and main results of comprehensive studies of sound fields in the northwestern region of the Pacific Ocean are presented. The experiments are carried out on paths up to 2100 km in length. The power-frequency, space-time, and correlation characteristics of the sound fields are studied in sonic and infrasonic frequency bands for long-and extra-long-range propagation with the use of cw and explosion-generated sound signals. Effects of the bottom relief and the spatial distribution of the speed of sound on the frequency characteristics of the sound field are investigated. The role of front zones in the formation of sound fields received at the coastal shelf and in the open ocean is revealed. The loss coefficients are estimated. The space-time stability of the sound field components is studied, and the possibility is shown for the coherent components to be conserved and resolved in frequency at distances up to 2100 km. The phase velocities of these components are determined. The total broadening of the frequency spectra is considered. The correlation characteristics of the total field are obtained for horizontally separated receivers in sonic and infrasonic frequency bands.     

Evaluation of times and arrival angles of surface prereverberation in the ocean

Acoustic prereverberation caused by sound scattering from the rough sea surface is considered. For the case of low-frequency scattering described by the first approximation of the small perturbation method, the arrival times and angles of prereverberation signals in the subsurface sound channel are calculated as functions of the wind speed, sound frequency, and distance.     

Where the ocean influences the impulse response and its effect on synchronous changes of acoustic travel time

In 1983, sounds at 133 Hz, 0.06 s resolution were transmitted in the Pacific for five days at 2 min intervals over 3709 km between bottom-mounted instruments maintained with atomic clocks. In 1989, a technique was developed to measure changes in acoustic travel time with an accuracy of 135 microseconds at 2 min intervals for selected windows of travel time within the impulse response. The data have short-lived 1 to 10 ms oscillations of travel time with periods less than a few days. Excluding tidal effects, different windows exhibited significant synchronized changes in travel time for periods shorter than 10 h. In the 1980s, this phenomenon was not understood because internal waves have correlation lengths of a few kilometers which are smaller than the way sound was thought to sample the ocean along well-separated and distinct rays corresponding to different windows. The paradox's resolution comes from modern theories that replace the ray-picture with finite wavelength representations that predict sound can be influenced in the upper ocean over horizontal scales such as 20 km or more. Thus, different windows are influenced by the same short-scale fluctuations of sound speed. This conclusion is supported by the data and numerical simulations of the impulse response.