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.     

Experimental investigation of the detection and location of a target in layered media by using the TR-RTM mixed method

Targets in layered media can be detected and located using a time reversal(TR)-reversed-time migration(RTM) mixed method.In this study, this single emission-multiple receiving method is tested experimentally by using two types of layered media and three types of targets. The signal reflected at the interface and the signal scattered by the target are measured by each receiver to obtain the travel time for several transmitter-receiver pairs. Thereafter, the amplitude ratio between the two measured signals is compared with the theoretical amplitude. The RTM process involves the convolution of the forward acoustic beam from the source with the backward acoustic beam from the receiver which adds an appropriate delay determined on the measured travel time data. By using this approach, the acoustic field distribution can be obtained, and the position of the target can be determined.Moreover, the measured positions of the target are compared with the actual position to validate the accuracy of this technique.     

Blue and fin whale call source levels and propagation range in the Southern Ocean

Blue (Balaenoptera musculus) and fin whales (B. physalus) produce high-intensity, low-frequency calls, which probably function for communication during mating and feeding. The source levels of blue and fin whale calls off the Western Antarctic Peninsula were calculated using recordings made with calibrated, bottom-moored hydrophones. Blue whales were located up to a range of 200 km using hyperbolic localization and time difference of arrival. The distance to fin whales, estimated using multipath arrivals of their calls, was up to 56 km. The error in range measurements was 3.8 km using hyperbolic localization, and 3.4 km using multipath arrivals. Both species produced high-intensity calls; the average blue whale call source level was 189+/-3 dB re:1 microPa-1 m over 25-29 Hz, and the average fin whale call source level was 189+/-4 dB re:1 microPa-1 m over 15-28 Hz. Blue and fin whale populations in the Southern Ocean have remained at low numbers for decades since they became protected; using source level and detection range from passive acoustic recordings can help in calculating the relative density of calling whales.     

Model-oriented ocean tomography using higher frequency, bottom-mounted hydrophones

A tomographic scheme is presented that ingests ocean acoustic measurements into an ocean model using data from bottom-mounted hydrophones. The short distances between source-receiver pairs (1-10 km) means arrival times at frequencies of 8-11 kHz are readily detectable and often distinguishable. The influence of ocean surface motion causes considerable variability in acoustic travel times. Techniques are presented for measuring travel times and removing the variability due to surface waves. An assimilation technique is investigated that uses differences in measured and modeled acoustic travel times to impose corrections on the oceanographic model. Equations relating travel time differences to oceanographic variables are derived, and techniques are presented for estimating the acoustic and ocean model error covariance matrices. One test case using a single source-receiver pair shows that the tomographic information can have an impact on constraining the solution of the ocean circulation model but can also introduce biases in the predictions. A second test case utilizes knowledge of a bias in a model-predicted variable to limit grid cells that are impacted by the tomographic data. In this case, using the tomographic data results in significant improvements in the model predictions without introducing any biases.     

Time sequences of sonar signals generated by a beluga whale when locating underwater objects

The results of measuring the sonar signals produced by a beluga whale when locating a target presented at a distance of 600 m are discussed. The head of the beluga whale was positioned at a depth of 1.5 m, and the acoustic pulses emitted by the animal were measured by a horizontal chain of four hydrophones, which was placed at a distance of 1.8 m from the head. The analysis of time sequences of acoustic signals generated by the beluga whale demonstrated that the animal, when searching for an underwater object, uses trains of pulses following at intervals of Δt < 5 ms and emitted within a wide sector (up to 36°). It performs scanning by beamed single pulses with Δt up to 200 ms, and, when it detects the target, it irradiates the latter with a group of such signals. To locate a difficult target (at a small depth and a large distance), the beluga whale uses trains of pulses with a duration of up to 0.6 s and a time-pulse modulation.     

Propagation of beluga echolocation signals

The propagation characteristics of high-frequency echolocation signals (peak energies above 100 kHz) of the beluga (Delphinapterus leucas) were measured while the animal performed a target detection task. The whale was trained to station on a bite plate so that its transmission beam could be measured in the vertical and horizontal planes using hydrophone arrays. The transitional region between the acoustic near- and farfields was also located using an array of hydrophones that extended directly in front of the animal in the horizontal plane. Three distinct modes of signals were observed. Mode 1 signals had click intervals greater than the time required for the signals to travel to the target and back (two-way transit time). Mode 2 signals had click intervals shorter than the two-way transit time, and mode 3 signals had high repetition rates with an average click interval of 1.7 ms, approximately 2% of the two-way transit time. The average click intervals for the modes 1 and 2 signals were 193 and 44 ms, respectively. The vertical and horizontal beam patterns of the mode 1 signals had similar 3-dB beamwidths of approximately 6.5 degrees. The major axis of the vertical beam was directed approximately 5 degrees above the plane defined by the animal's teeth. The near- to farfield transition region was approximately 0.64-0.75 m from the tip of the animal's mouth.     

Long distance passive localization of vocalizing sei whales using an acoustic normal mode approach

During a 2 day period in mid-September 2006, more than 200, unconfirmed but identifiable, sei whale (Balaenoptera borealis) calls were collected as incidental data during a multidisciplinary oceanography and acoustics experiment on the shelf off New Jersey. Using a combined vertical and horizontal acoustic receiving array, sei whale movements were tracked over long distances (up to tens of kilometers) using a normal mode back propagation technique. This approach uses low-frequency, broadband passive sei whale call receptions from a single-station, two-dimensional hydrophone array to perform long distance localization and tracking by exploiting the dispersive nature of propagating normal modes in a shallow water environment. The back propagation approach is examined for accuracy and application to tracking the sei whale vocalizations identified in the vertical and horizontal array signals. This passive whale tracking, combined with the intensive oceanography measurements performed during the experiment, was also used to examine sei whale movements in relation to oceanographic features observed in this region.     

有限长号筒中非线性声传播的数值模拟研究

研究了大振幅活塞声源经有限长号筒向外辐射声波的非线性声学问题。采用具有频散保持特性的高精度计算格式求解了适用于变截面管道的一维非线性声场模型,并考虑到声波的非线性畸变及管口处的声反射,加入了宽频时域声阻抗边界条件。宽频阻抗模型的共轭复数系数采用优化拟合方法近似求解,并采用递推卷积算法快速求解出时域声阻抗。在弱非线性条件下模拟指数形号筒中的声传播取得了与已有实验相一致的结果,表明模型能够描述声波非线性畸变带来的宽频特性。进而采用本模型数值模拟了大振幅活塞声源在双曲形、锥形、指数形和正弦形号筒中的非线性声传播问题,结果表明号筒出口声压级受活塞振动速度、频率以及号筒形状的影响,并分析讨论了波形畸变与号筒几何形状之间的关系。      

Analysis and localization of blue whale vocalizations in the Solomon Sea using waveform amplitude data

During the Woodlark Basin seismic experiment in eastern Papua New Guinea (1999-2000), an ocean-bottom seismic array recorded marine mammal vocalizations along with target earthquake signals. The array consisted of 14 instruments, 7 of which were three-component seismometers with a fourth component hydrophone. They were deployed at 2.0-3.2 km water depth and operated from September 1999 through February 2000. While whale vocalizations were recorded throughout the deployment, this study focuses on 3 h from December 21, 1999 during which the signals are particularly clear. The recordings show a blue whale song composed of a three-unit phrase. That song does not match vocalization characteristics of other known Pacific subpopulations and may represent a previously undocumented blue whale song. Animal tracking and source level estimates are obtained with a Bayesian inversion method that generates probabilistic source locations. The Bayesian method is augmented to include travel time estimates from seismometers and hydrophones and acoustic signal amplitude. Tracking results show the whale traveled northeasterly over the course of 3 h, covering approximately 27 km. The path followed the edge of the Woodlark Basin along a shelf that separates the shallow waters of the Trobriand platform from the deep waters of the basin.     

Measuring the off-axis angle and the rotational movements of phonating sperm whales using a single hydrophone

The common use of the bent-horn model of the sperm whale sound generator describes sperm whale clicks as the pulse series {p0, p1, p2, p3,...}. Clicks, however, deviate from this standard when recorded using off-axis hydrophones. The existence of additional pulses within the {p0, p1, p2, p3, ...} series can be explained still using the bent-horn model. Multiple reflections on the whale's frontal and distal sacs of the p0 pulse lead to additional sets of pulses detectable using a farfield, off-axis hydrophone. The travel times of some of these additional pulses depend on the whale's orientation. The authors propose a method to estimate the off-axis angle of sperm whale clicks. They also propose a method to determine the nature of the movement (if it is pitch, yaw, or roll) of phonating sperm whales. The application of both methods requires the measurement of the travel time differences between pulses composing a sperm whale click. They lead, using a simple apparatus consisting of a single hydrophone at an unknown depth, to new measurements of the underwater movements of sperm whales. Using these methods shows that sperm whales would methodically scan seawater while searching for prey, by making periodic pitch and yaw movements in sync with their acoustic activity.     

Male sperm whale acoustic behavior observed from multipaths at a single hydrophone

Sperm whales generate transient sounds (clicks) when foraging. These clicks have been described as echolocation sounds, a result of having measured the source level and the directionality of these signals and having extrapolated results from biosonar tests made on some small odontocetes. The authors propose a passive acoustic technique requiring only one hydrophone to investigate the acoustic behavior of free-ranging sperm whales. They estimate whale pitch angles from the multipath distribution of click energy. They emphasize the close bond between the sperm whale's physical and acoustic activity, leading to the hypothesis that sperm whales might, like some small odontocetes, control click level and rhythm. An echolocation model estimating the range of the sperm whale's targets from the interclick interval is computed and tested during different stages of the whale's dive. Such a hypothesis on the echolocation process would indicate that sperm whales echolocate their prey layer when initiating their dives and follow a methodic technique when foraging.     

Three-dimensional localization of sperm whales using a single hydrophone

A three-dimensional localization method for tracking sperm whales with as few as one sensor is demonstrated. Based on ray-trace acoustic propagation modeling, the technique exploits multipath arrival information from recorded sperm whale clicks and can account for waveguide propagation physics like interaction with range-dependent bathymetry and ray refraction. It also does not require ray identification (i.e., direct, surface reflected) while utilizing individual ray arrival information, simplifying automation efforts. The algorithm compares the arrival pattern from a sperm whale click to range-, depth-, and azimuth-dependent modeled arrival patterns in order to estimate whale location. With sufficient knowledge of azimuthally dependent bathymetry, a three-dimensional track of whale motion can be obtained using data from a single hydrophone. Tracking is demonstrated using data from acoustic recorders attached to fishing anchor lines off southeast Alaska as part of efforts to study sperm whale depredation of fishing operations. Several tracks of whale activity using real data from one or two hydrophones have been created, and three are provided to demonstrate the method, including one simultaneous visual and acoustic localization of a sperm whale actively clicking while surfaced. The tracks also suggest that whales' foraging is shallower in the presence of a longline haul than without.     

Calibration and comparison of the acoustic location methods used during the spring migration of the bowhead whale, Balaena mysticetus, off Pt. Barrow, Alaska, 1984-1993

Between 1984 and 1993, visual and acoustic methods were combined to census the Bering-Chukchi-Beaufort bowhead whale, Balaena mysticetus, population. Passive acoustic location was based on arrival-time differences of transient bowhead sounds detected on sparse arrays of three to five hydrophones distributed over distances of 1.5-4.5 km along the ice edge. Arrival-time differences were calculated from either digital cross correlation of spectrograms (old method), or digital cross correlation of time waveforms (new method). Acoustic calibration was conducted in situ in 1985 at five sites with visual site position determined by triangulation using two theodolites. The discrepancy between visual and acoustic locations was <1%-5% of visual range and less than 0.7 degrees of visual bearing for either method. Comparison of calibration results indicates that the new method yielded slightly more precise and accurate positions than the old method. Comparison of 217 bowhead whale call locations from both acoustic methods showed that the new method was more precise, with location errors 3-4 times smaller than the old method. Overall, low-frequency bowhead transients were reliably located out to ranges of 3-4 times array size. At these ranges in shallow water, signal propagation appears to be dominated by the fundamental mode and is not corrupted by multipath.     

Three-dimensional passive acoustic tracking of sperm whales (Physeter macrocephalus) in ray-refracting environments

A wide-aperture towed passive acoustic array is used to obtain ranges and depths of acoustically active sperm whales in the Gulf of Mexico in June 2004, by extending a technique previously reported [Thode, J. Acoust. Soc. Am. 116, 245-253 (2004)] to explicitly account for ray-refraction effects arising from a depth-dependent sound speed profile. Under this expanded approach, three quantities are measured from an impulsive sound: the time difference between direct-path arrivals on a forward and rear subarray, the time difference between the direct and surface-reflected paths on the rear subarray, and the acoustic bearing measured on the rear subarray. These quantities, combined with independent measurements of hydrophone depths and cable inclination, are converted into range-depth position fixes by implementing an efficient numerical procedure that uses a ray-tracing code to account for ray-refraction effects caused by depth-dependent sound speed profiles. Analytic expressions that assume a constant waterborne sound speed are also derived. Foraging depths of various sperm whales over 10 days in June, 2004 are estimated using the numerical technique.     

深海不平海底对声场水平纵向相关性的影响

海底地形变化对与海底作用的声反射区声场空间相关性有重要影响。利用南中国海某深海海域的一次声学实验数据,对深海海底反射区的声场空间相关性进行了分析。实验观测到,在距离声源约29 km至35 km距离范围处,不平海底环境下的水平纵向相关性出现了一些不同于平坦海底环境下的振荡结构,利用射线声学理论分析并解释了这两种不同海底环境产生水平纵向相关差异的原因。结果表明,在深海平坦海底方向一次海底反射到达区,对声场起主要贡献的经过一次海底反射声线间的到达时间差随着水平距离的增加而逐渐减少,从而干涉叠加后的相位差在[0,2π]内发生周期性变化,导致该区域声场的水平纵向相关性随着间距增加呈周期性振荡现象;而不平海底方向的海底小山丘恰对一次海底反射声线的阻挡影响,不仅使得与平坦海底方向相同区域的声传播损失明显增大,而且由于相对更多的本征声线路径的复杂多途干涉,该区域水平纵向相关性不再呈现明显的振荡周期,相关系数也有所下降。研究结果对于分析在深海复杂海底地形环境下的声呐阵列探测性能具有重要意义。      

Whole-lung resonance in a bottlenose dolphin (Tursiops truncatus) and white whale (Delphinapterus leucas)

An acoustic backscatter technique was used to estimate in vivo whole-lung resonant frequencies in a bottlenose dolphin (Tursiops truncatus) and white whale (Delphinapterus leucas). Subjects were trained to submerge and position themselves near an underwater sound projector and a receiving hydrophone. Acoustic pressure measurements were made near the thorax while the subject was insonified with pure tones at frequencies from 16 to 100 Hz. Whole-lung resonant frequencies were estimated by comparing pressures measured near the subject's thorax to those measured from the same location without the subject present. Experimentally measured resonant frequencies for the white whale and dolphin lungs were 30 and 36 Hz, respectively. These values were significantly higher than those predicted using a free-spherical air bubble model. Experimentally measured damping ratios and quality factors at resonance were 0.20 and 2.5, respectively, for the white whale, and 0.16 and 3.1, respectively, for the dolphin.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

Measurement of the acoustic properties of a sound absorbing material at high temperatures

Measurements have been made of the acoustic properties of a typical mineral wool fibrous material at temperatures up to 500C. In addition to acoustic impedance and propagation constant the flow resistance of the material was measured over the same temperature range. With use of a modified form of the Delany-Bazley empirical formula good agreement was found between predicted and measured values of the acoustic impedance and propagation constant at various temperatures up to 500°C.     

North Pacific right whale up-call source levels and propagation distance on the southeastern Bering Sea shelf

Call source levels, transmission loss, and ambient noise levels were estimated for North Pacific right whale (Eubalaena japonica) up-calls recorded in the southeastern Bering Sea in autumn of 2000 and 2001. Distances to calling animals, needed to estimate source levels, were based on two independent techniques: (1) arrival-time differences on three or more hydrophones and (2) shallow-water dispersion of normal modes on a single receiver. Average root-mean-square (rms) call source levels estimated by the two techniques were 178 and 176 dB re 1 μPa at 1 m, respectively, over the up-call frequency band, which was determined per call and averaged 90 to 170 Hz. Peak-to-peak source levels were 14 to 22 dB greater than rms levels. Transmission loss was approximately 15?log(10)(range), intermediate between cylindrical and spherical spreading. Ambient ocean noise within the up-call band varied from 72 to 91 dB re 1 μPa(2)/Hz. Under average noise conditions, call spectrograms were detectable for whales at distances up to 100 km, but propagation and detection distance may vary depending on environmental parameters and anthropogenic noise. Obtaining distances to animals and acoustic detection range is a step toward using long-term passive acoustic recordings to estimate abundance for this critically endangered whale population.     

Localization of a sound source in a noisy environment by hyperbolic curves in quefrency domain

Time Difference of Arrivals (TDOAs) of sound waves between microphones have to do with source localization. How well a sound source can be localized depends on how precisely the TDOAs are estimated. Although many ways to estimate TDOA have been proposed, noise always prevents us from finding exact time differences more or less in practice. Cross correlation has been the most prevalent way to estimate time difference, and various cross correlations robust to noise have also been developed. Nevertheless, much remains to be done for exact TDOA estimation under noisy environments. A novel way to show time delays in quefrency domain by removing noise has been proposed, which is called Minimum Variance Cepstrum (MVC). In particular, it is practically desirable to visualize source position with as few number of sensors as possible. Once TDOAs are obtained precisely, it is enough to show the source position in a 2-D plane using hyperbolic curves with only three sensors. In this work, the MVC is adopted to accurately estimate TDOAs under noise, and a way to localize an acoustic source by intersecting hyperbolic curves using the TDOAs between three microphones is proposed. Numerical simulations on TDOA estimation and source localization with white Gaussian noise demonstrated that the proposed method worked well under the noisy environment, and we compared the results with those of other old but well-established cross correlation estimators. In addition, experiments to detect a leaking point on a pipe successfully showed where the leak sound was generated.