Internal-wave time evolution effect on ocean acoustic rays

A range-dependent field of sound speed in the ocean, c(x,z), caused by internal waves, can give rise to instabilities in acoustic ray paths. Past work has shown the importance of the background, range-independent, sound-speed profile; the ray initial conditions; the source-receiver geometry (depths and range); and the strength of the internal waves. However, in the past the time evolution of the internal waves has been ignored on the grounds that the speed of internal waves is much slower than the speed of the acoustic wave. It is shown here by numerical simulation that two rays with identical initial conditions, traveling through an ocean with the same background profile and the same random realization of internal waves, but with the internal waves frozen in one case and evolving in the other, travel significantly different trajectories. The dependence of this "frozen-unfrozen" difference on the initial ray launch angle, the background profile, and the strength of the internal-wave spectrum, is investigated. The launch-angle difference that generates similar arrival-depth differences to those induced by internal-wave time evolution is on the order of 100 microrad. The pattern of differences is measured here by the arrival depth at the final range of 1000 km. The observed pattern as a function of launch angle, change in the background profile, and change in internal-wave strength is found to be nearly the same for "frozen-unfrozen" change as for a slight change in launch angle.     

Acoustic normal mode fluctuation statistics in the 1995 SWARM internal wave scattering experiment

In order to understand the fluctuations imposed upon low frequency (50 to 500 Hz) acoustic signals due to coastal internal waves, a large multilaboratory, multidisciplinary experiment was performed in the Mid-Atlantic Bight in the summer of 1995. This experiment featured the most complete set of environmental measurements (especially physical oceanography and geology) made to date in support of a coastal acoustics study. This support enabled the correlation of acoustic fluctuations to clearly observed ocean processes, especially those associated with the internal wave field. More specifically, a 16 element WHOI vertical line array (WVLA) was moored in 70 m of water off the New Jersey coast. Tomography sources of 224 Hz and 400 Hz were moored 32 km directly shoreward of this array, such that an acoustic path was constructed that was anti-parallel to the primary, onshore propagation direction for shelf generated internal wave solitons. These nonlinear internal waves, produced in packets as the tide shifts from ebb to flood, produce strong semidiurnal effects on the acoustic signals at our measurement location. Specifically, the internal waves in the acoustic waveguide cause significant coupling of energy between the propagating acoustic modes, resulting in broadband fluctuations in modal intensity, travel-time, and temporal coherence. The strong correlations between the environmental parameters and the internal wave field include an interesting sensitivity of the spread of an acoustic pulse to solitons near the receiver.     

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.     

Predicting acoustic effects of internal waves from the basic climatology of the world ocean

Internal waves of a given strength will produce acoustic effects that vary from water mass to water mass. Presented here is a means of predicting the strength of acoustic fluctuations due to internal waves, given the basic climatology, that is, measurements of depth, temperature, and salinity of an oceanic region. An acoustic fluctuation strength parameter F is defined as the ratio of the fractional potential sound-speed change to the fractional potential-density change. Here F is calculated at three depth levels (275, 550, and 850 m), on a one-degree grid of latitude and longitude, using NODC/OCL's World Ocean Atlas 1994. Representative values of F are presented for 15 upper water masses that range from F = 5 in the North Pacific to F = 34 in the North Atlantic, with a typical value for most of the upper waters being F = 15. Results for two depth levels within 12 intermediate water masses range from F = 7 in the North Pacific to F = 62 in the North Atlantic, with a typical value of F = 20, although there is considerable variation. In general, F exhibits higher values in the Atlantic Basin than in the Indian or Pacific, and has a maximum at 550 m. The main use of F will be the prediction of travel-time fluctuations in acoustic propagation experiments, which will be proportional to the value of F, given a universal strength of internal waves.     

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.     

南海东沙海域线性内波引起的声场统计特性

海洋内波对声传播及水声探测具有重要影响.利用南海东沙附近海域一次低频声传播起伏实验同步获取的声学与水文观测数据,从水文连续观测数据中提取了内波特征参数,验证了修正线性内波频谱公式,用蒙特卡洛方法统计分析了存在线性内波条件下的声场起伏特性,并用射线理论解释了声源与跃层相对位置对声场起伏的影响机理.结果 表明:随着频率、平...     

南海北部海域内波环境下声传播损失起伏统计特性

浅海内波会引起声传播能量随时间的起伏变化,进而影响水声设备的工作性能.本文利用2015年南海北部一次浅海声场起伏实验数据,对比分析了浅海线性内波和孤立子内波条件下的声传播损失统计特性.在孤立子内波条件下,声传播损失起伏明显加剧,可达11 dB,且分布明显展宽,相对于线性内波的环境,声传播损失起伏可增加5 dB.从简正波...     

Statistical moments of travel times at second order in isotropic and anisotropic random media

We study the high-frequency propagation of acoustic plane and spherical waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation distance observed with numerical experiments based on ray tracing. Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a general class of statistically anisotropic random media.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity: II

Well-known linearizations of Einstein's field equations and isomorphisms with electromagnetic theory allow one to demonstrate, in principle, the existence of gravitomagnetic (GM) and gravitoelectric (GE) wavefields generated by transient nongravitational sources—as in the spin-up of a rigid sphere by an external torque (Tolstoy, I. (2001). International Journal of Theoretical Physics 40(5), 1021–1031). Whereas such effects are currently too small to be measured in the laboratory, order of magnitude estimates suggest that major astrophysical events could generate signals (strains in the metric) observable by LIGO systems. GM/GE modes are entirely uncoupled from the quadrupole radiation of classic gravitational wave theory. However, both travel at light velocity c and, since quadrupole waves may be generated by, or in the neighborhood of, similar events, it is essential to demonstrate that LIGO array geometries can discriminate between them. This can be accomplished by determining arrival directions and polarization planes.     

内波、潮导致的声简正波幅度起伏及其深度分布

分析2005黄海声传播—内波实验传播起伏数据,观察（1）号声简正波幅度起伏及其深度分布特征。非线性内波（IW）通过接收阵可以导致脉冲峰值约5 dB起伏,幅度起伏垂向分布与简正波本征函数的微分分布吻合良好,（M2）潮致信号幅度起伏也满足相同深度分布特性。然而内波和潮致起伏的垂向相位变化明显不同:前者本征函数峰值两侧起伏信号反相,而后者近乎同相。前者由接收器与简正波分布的相对移动决定,而后者取决于简正波和水听器位置变化的复合效应。      

浅海内波环境下声场时间相关特性*

浅海内波是导致声场时间相关半径减小的一个重要原因,利用2015年南海声传播起伏实验,对比分析了线性内波以及孤立子内波环境下声场时间相关半径的统计特性。实验数据表明大振幅孤立子内波的存在极大的降低了声场的时间相关半径,声场时间相关半径从线性内波环境下的1小时-3小时,降低为孤立子内波环境下的小于20分钟。利用RAM程序仿真模拟了内波环境下的声场时间相关半径,理论预报结果与实验结果相符。     

Parameter sensitivity of a T-junction sea model; the importance of the internal damping loss factors

For a typical building acoustics configuration, a T-junction of plates formed by a light weight wall placed on a heavy floor, a statistical energy analysis (SEA) model is presented. Only structural systems (i.e., no acoustic wavefields) are considered. Besides bending waves also in-plane waves, quasi-longitudinal and plane transverse waves, in particular, are included in the calculation. A parametric survey is conducted on the T-junction model—for one frequency (1000 Hz) only—in order to find the sensitivity of the SEA model to the inaccuracies of its parameters. It is shown that, when using reverberation time measurements of the plates to determine the internal damping loss factors, the worst case variations of the internal damping loss factors cause variations in the junction dampings of bending waves of about one order higher than any of the other parameters. Therefore, the conclusion is that in cases where the internal damping loss factors are large with respect to the coupling loss factors, it is necessary to obtain more accurate estimates for the internal damping loss factors than are found with simple reverberation time measurements of plates.     

利用声场频谱频率漂移监测内波的算法改进和实验验证

声场频谱的频率漂移曲线可以用来监测内波。由于简正波幅度剧烈起伏带来的干扰,目前尚无从实验数据中提取频移曲线的有效算法.提出了一种依据实测声学传播数据提取频移曲线的算法。借助于简正波过滤技术,该算法利用相关法从简正波相角之差中提取频率漂移曲线。利用该算法提取的频移曲线与内波导致的跃层起伏具有很高的相似性,这在2011年黄海实验中得到了验证。该算法的优点是可以保留简正波相位差变化导致的频移曲线信息,同时又能有效地抑制简正波幅度起伏带来的干扰,但是需要良好的接收阵阵型来保证简正波分离。      

Stability and accuracy of spatial approximations for wave equation tidal models

Amplitude and phase characteristics for numerical approximations to the shallow water wave equation are obtained for linear and quadratic finite elements, for finite difference approximations, for non-constant bathemetry, and for uneven node spacing. Stability is shown to require non-zero friction as well as satisfaction of a Courant constraint. Lumping is shown to reduce the Courant constraint for stability while higher order and quadratic finite element approximations require a more restrictive constraint than their second order and linear finite element counterparts. The amplitude of the propagation factor for stable schemes and propagating waves is seen to be independent of the Courant number and type of numerical approximation. Although the higher order and quadratic schemes provide better propagation of the low and moderate frequency waves, the highest frequency waves (2Δx) are better propagated by low order numerical methods.     

Sound fluctuations resulting from mode coupling in shallow-water internal waves

We conduct a theoretical analysis and numerical simulation of fluctuations of low-frequency signals propagating in shallow water in the presence of nonlinear internal waves moving approximately along the acoustic track. It is believed that mode coupling causes the fluctuations. We show that in the fluctuation spectra there are characteristic frequencies that are proportional to the motion velocity of solitons along the track. We calculate the sound field using single- and multimode sources and analyze the frequency-mode composition of the field responsible for the maximum and minimum fluctuations. We analyze the so-called dominant fluctuation frequency introduced previously by the authors, which corresponds to fluctuations with the maximum amplitude in the given frequency range and for the given set of modes. We compare the calculation results with estimates obtained previously by the authors within the framework of ray theory.     

Evidence of Doppler-shifted Bragg scattering in the vertical plane by ocean surface waves

A set of narrowband tones (280, 370, 535, and 695 Hz) were transmitted by an acoustic source mounted on the ocean floor in 10 m deep water and received by a 64-element hydrophone line array lying on the ocean bottom 1.25 km away. Beamformer output in the vertical plane for the received acoustic tones shows evidence of Doppler-shifted Bragg scattering of the transmitted acoustic signals by the ocean surface waves. The received, scattered signals show dependence on the ocean surface wave frequencies and wavenumber vectors, as well as on acoustic frequencies and acoustic mode wavenumbers. Sidebands in the beamformer output are offset in frequency by amounts corresponding to ocean surface wave frequencies. Deviations in vertical arrival angle from specular reflection agree with those predicted by the Bragg condition through first-order perturbation theory using measured directional surface wave spectra and acoustic modes measured by the horizontal hydrophone array.     

Determining tomographic arrival times based on matched filter processing: considering the impact of ocean waves

Reflection of high-frequency acoustic signals from an air-sea interface with waves is considered in terms of determining travel times for acoustic tomography. Wave-induced, multi-path rays are investigated to determine how they influence the assumption that the time of the largest matched filter magnitude between the source and receiver signals is the best estimate of the arrival time of the flat-surface specular ray path. A simple reflection model is developed to consider the impact of in-plane, multi-path arrivals on the signal detected by a receiver. It is found that the number of multi-path rays between a source and receiver increases significantly with the number of times the ray paths strike the ocean surface. In test cases, there was always one of the multi-path rays that closely followed the flat-surface specular ray path. But all the multi-path rays arrive at the receiver almost simultaneously, resulting in interference with the signal from the flat-surface specular ray path. As a result, multi-path arrivals due to open ocean surface waves often distort the received signal such that maxima of matched filtering magnitudes will not always be a reliable indicator of the arrival time of flat-surface specular ray paths.     

Characteristics of sound signals on a quasi-stationary track between the Josephine and Ampere Seamounts

Experimental data are presented on the measurement of the cross-correlation coefficients and the differences in the arrival times (temporal spectra) of acoustic signals transmitted through a 210-km-long quasi-stationary track in the Atlantic Ocean. At the summit of the Josephine Seamount, a continuous pseudonoise signal was emitted in the one-third-octave band with a mean frequency of 630 Hz. The signal was received at the Ampere Seamount by a 40-m flexible vertical array with a directivity pattern in the form of a static fan of 32 lobes. The width of each lobe was ～3°. At a signal-to-noise ratio of about 3 dB and with an incomplete resolution of multipath signals by the array, the correlation coefficients reached a value of 0.48. The rms fluctuations of the differences in the arrival times varied from 1.8 to 3.1 ms depending on the signal arrival angles. The factors responsible for the low correlation coefficients and the relatively high fluctuations of the arrival time differences are discussed. Apparently, one of the factors is the presence of short-period internal waves.     

Computed narrow-band time-reversing array retrofocusing in a dynamic shallow ocean

A time-reversing array (TRA) can retrofocus acoustic energy, in both time and space, to the original sound-source location without any environmental information. This unique capability may be degraded in time-dependent or noisy acoustic environments, or when propagation losses are prevalent. In this paper, monochromatic propagation simulations (based on the parabolic equation code, RAM) are used to predict TRA retrofocusing performance in shallow-water sound channels having characteristics similar to those measured during the recent SWARM (shallow-water acoustics in a random medium) experiment. Results for the influence of source-array range, source depth, acoustic frequency, bottom absorption, internal wave strength, and round-trip time delay are presented. For a fixed channel geometry, higher frequencies, deeper sources, and lower bottom absorption improve TRA performance and allow retrofocusing at longer ranges. In a dynamic shallow-water channel containing a random superposition of linear internal waves, the size of the retrofocus is slightly decreased and sidelobes are suppressed compared to the static channel results. These improvements last for approximately 1 to 2 min for source-array ranges near 10 km at a frequency of 500 Hz. For longer time delays, the internal waves cause significant TRA retrofocus amplitude decay, and the decay rate increases with increasing internal wave activity and acoustic frequency.     

Reversal of waves in forward-scattering location

Potentialities of the pulsed acoustic forward-scattering location with the use of time separation of the intense direct and weak scattered signals propagating at a small angle to one another are considered. Two types of interference are taken into account: nonstationary observation conditions under the effect of currents, which affect the arrival times of the direct and scattered signals, and nonstationary reverberation. It is shown that, in the presence of these interferences, the application of the correlation transformation equivalent to the time reversal of waves has an advantage over the conventional location technique based on the determination of the signal travel times.