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.     

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.     

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.     

Pekeris waveguide comparisons of methods for predicting acoustic field amplitude uncertainty caused by a spatially uniform environmental uncertainty (L)

Acoustic field calculations in underwater environments are often uncertain because the environmental parameters required for such calculations are uncertain. This letter compares the accuracy of direct simulations, the field shifting approximation, and polynomial chaos expansions for predicting acoustic amplitude uncertainty in 100-m-deep Pekeris waveguides having spatially uniform uncertain water-column sound speed. When this sound speed is Gaussian-distributed with a standard deviation of 1 m/s, direct simulations and polynomial chaos expansions, based on 21 field calculations, are more accurate than the field shifting approximation, based on two field calculations. This ranking reverses as the sound-speed standard deviation increases to 20 m/s.     

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.     

Calculation of temporal, angular, and intensity characteristics of the sound field in a coastal area with an arbitrary bottom relief and a constant sound speed in the medium

Computational algorithms and some computed data are presented for the total sound field in a waveguide whose depth arbitrarily depends on two horizontal coordinates. The sound speed is supposed to be constant, and the bottom slopes are considered as small. The algorithm involves three steps. First, horizontal rays, i.e., horizontal projections of the real rays multiply bottom-and surface-reflected, are calculated. Second, the horizontal rays are set up to a point. Third, the real rays are set up to a point. The computational accuracy is analyzed for a homogeneous wedge lying on a halfspace. Calculations are carried out for a coastal region of the ocean.     

Comparison between ocean-acoustic fluctuations in parabolic-equation simulations and estimates from integral approximations

Line-integral approximations to the acoustic path integral have been used to estimate the magnitude of the fluctuations in an acoustic signal traveling through an ocean filled with internal waves. These approximations for the root-mean-square (rms) fluctuation and the bias of travel time, rms fluctuation in a vertical arrival angle, and the spreading of the acoustic pulse are compared here to estimates from simulations that use the parabolic equation (PE). PE propagations at 250 Hz with a maximum range of 1000 km were performed. The model environment consisted of one of two sound-speed profiles perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model with strengths of 0.5, 1, and 2 times the GM reference energy level. Integral-approximation (IA) estimates of rms travel-time fluctuations were within statistical uncertainty at 1000 km for the SLICE89 profile, and in disagreement by between 20% and 60% for the Canonical profile. Bias estimates were accurate for the first few hundred kilometers of propagation, but became a strong function of time front ID beyond, with some agreeing with the PE results and others very much larger. The IA structure functions of travel time with depth are predicted to be quadratic with the form theta(2)vc0(-2)deltaz(2), where deltaz is vertical separation, c0 is a reference sound speed, and thetav is the rms fluctuation in an arrival angle. At 1000 km, the PE results were close to quadratic at small deltaz, with values of thetav in disagreement with those of the integral approximation by factors of order 2. Pulse spreads in the PE results were much smaller than predicted by the IA estimates. Results imply that acoustic tomography of internal waves at ranges up to 1000 km can use the IA estimate of travel-time variance with reasonable reliability.     

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。      

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.     

Ray chaos and ray clustering in an ocean waveguide

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a randomlike sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincare maps, plots of variations of the action per ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a randomlike multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.     

Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System

Systematic improvements in algorithmic design of regional ocean circulation models have led to significant enhancement in simulation ability across a wide range of space/time scales and marine system types. As an example, we briefly review the Regional Ocean Modeling System, a member of a general class of three-dimensional, free-surface, terrain-following numerical models. Noteworthy characteristics of the ROMS computational kernel include: consistent temporal averaging of the barotropic mode to guarantee both exact conservation and constancy preservation properties for tracers; redefined barotropic pressure-gradient terms to account for local variations in the density field; vertical interpolation performed using conservative parabolic splines; and higher-order, quasi-monotone advection algorithms. Examples of quantitative skill assessment are shown for a tidally driven estuary, an ice-covered high-latitude sea, a wind- and buoyancy-forced continental shelf, and a mid-latitude ocean basin. The combination of moderate-order spatial approximations, enhanced conservation properties, and quasi-monotone advection produces both more robust and accurate, and less diffusive, solutions than those produced in earlier terrain-following ocean models. Together with advanced methods of data assimilation and novel observing system technologies, these capabilities constitute the necessary ingredients for multi-purpose regional ocean prediction systems.     

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.     

Ray stability in weakly range-dependent sound channels

Ray stability is investigated in environments consisting of a range-independent background sound-speed profile on which a range-dependent perturbation is superimposed. Theoretical arguments suggest and numerical results confirm that ray stability is strongly influenced by the background sound speed profile. Ray instability is shown to increase with increasing magnitude of alpha(I)=(I/omega)d omega/dI, where 2pi/omega(I) is the range of a ray double loop and I is the ray action variable. This behavior is illustrated using internal-wave-induced scattering in deep ocean environments and rough surface scattering in upward refracting environments.     

深海海底反射区声场的相干结构及其有源声呐估距

有源声呐在探测深海海底反射区的目标时,由于声线大掠射角弯曲且声速沿声线传播路径不断变化,造成了常规估距方法产生较大的误差。有效声速法是减小常规估距方法误差的有效途径,但由于需要预先计算空间每一位置点的"声线时延有效声速"对,复杂度高,实时性差。针对有效声速法的实时性问题,本文基于深海海底反射区声场的相干结构,提出一种改进的有效声速估距方法.首先指出深海声场能量沿声源出射角强弱相间变化及其引起的海底反射区离散声呐可探测区现象,并利用深海近水面声源的声线干涉效应解释了该现象的物理机理,建立了声呐可探测区与高能量声线的量化关系。在此基础上,计算声呐可探测区边界位置的"声线时延-有效声速"对,并线性拟合出可探测区所有位置点对应的值。经仿真验证,该方法与传统的有效声速法均可实现对常规估距方法估距误差的有效校正。虽然该方法估距精度较传统的有效声速法略有增大,但计算复杂度和计算时间显著减小,实时性好,具有良好的工程应用前景。      

Focused sound from three-dimensional sound propagation effects over a submarine canyon

Ship noise data reveal an intensification of the near-surface sound field over a submarine canyon. Numerical modeling of sound propagation is used to study the effect. The noise data were collected during an ocean acoustic and physical oceanography experiment northeast of Taiwan in 2009. In situ measurements of water sound-speed profiles and a database of high-resolution bathymetry are used in the modeling study. The model results suggest that the intensification is caused by three-dimensional sound focusing by the concave canyon seafloor. Uncertainties in the model results from unsampled aspects of the environment are discussed.     

Range dependence of the vertical structure of the sound field in the ocean

In the ocean without fluctuations, the sound field is calculated by the method of geometrical acoustics with allowance for purely water-path rays in a sound channel of canonical shape with a thickness of 4 km for distances of 500 and 2000 km. The sound field is determined as a sum of individual rays arriving at a given point with their own amplitudes and phases. It is shown that the vertical structure of the sound field consists of a number of caustics separated by regions with a quasi-random distribution of the field whose amplitude is much smaller than that in the caustics. At a fixed distance, the number of caustics is equal to the difference between the numbers of the ray turning points at the boundaries of the departure angle range. As the distance from the source increases, the number of caustics increases proportionally to distance.     

Underwater acoustic scattering from a radially layered cylindrical obstacle in a 3D ocean waveguide

A solution based on coupled mode expansions is presented for the 3D problem of acoustic scattering from a radially layered penetrable cylindrical obstacle in a shallow-water plane-horizontal waveguide. Each cylindrical ring is characterized by a general, vertical sound speed and density profile (ssdp), the ocean environment around the obstacle can be also considered horizontally stratified with a depth-arbitrary ssdp, and the bottom is assumed to be rigid. The total acoustic field generated by an harmonic point source is represented as a normal-mode series expansion. The expansion coefficients are calculated exploiting the matching conditions at the cylindrical interfaces, which results in an infinite linear system. The system is appropriately truncated and numerically solved by using a recursive relation, which involves the unknown coefficients of two successive rings. Results concerning the transmission loss outside and inside obstacles consisting of three cylindrical rings are given for a typical depth-dependent ocean sound-speed profile. The presented solution can serve as a benchmark solution to the general problem of 3D acoustic scattering from axisymmetric inhomogeneities in ocean waveguides at low frequencies.     

基于射线模型的超声声速层析算法研究进展

得益于超声换能器硬件的进步和数据采集速度的提升,超声层析成像近年来得到了越来越多的关注,特别是在乳腺成像领域.超声层析成像中的声速图像分布可以为乳腺组织表征提供良好的定量分析数据,进而使得超声层析成像在乳腺癌的诊断方面有着良好的应用前景.目前,超声声速层析重建方法主要包括基于射线模型和全波模型的两大类算法.基于射线模型...     

The possibility of reconstructing the seasonal variability of the ocean using acoustic tomography methods

The possibility of reconstructing by acoustic methods the typical annual variations of the sound velocity profile in different regions of the ocean is investigated. The effect of local seasonal variations of the sound velocity profile on the field received by a system of vertical arrays is simulated for an acceptable number of such systems. The latter is attained by using a mosaic basis, which considerably simplifies the solution of the direct problem, the construction of the perturbation matrix, and the subsequent solution of the inverse problem, as well as by describing the vertical structure of the sound velocity profile within the Karhunen-Loéve basis. The field representation in the vertical modes-horizontal rays approximation is used.