Scale invariance of the intensity anomaly induced by the ice cover in the sound field of a tone source in an arctic waveguide

On the basis of the normal mode method and the theory of sound scattering by a stochastically rough surface of an elastic layer, the specific features of the frequency dependence of the intensity anomaly induced by the ice cover in the sound field generated by a tone source in an arctic waveguide are studied. The anomaly is determined by the difference between the level (in dB) of the coherent component of the sound intensity that occurs in the waveguide with the ice cover and the intensity level in a waveguide with an ice-free surface. Using the WKB approach, it is shown that the intensity anomaly is invariant for all values of the frequency, the mean ice thickness, and the rms amplitude and correlation radius characterizing the rough undersurface of ice on the condition that the ratios of all the aforementioned geometric parameters to the sound wavelength in water remain constant. This property is confirmed by precise calculations of the anomaly by the mode program and explained by the specific features of the frequency dependence of attenuation coefficients and their distribution in the numbers of normal modes. Possible practical applications of the revealed property of the intensity anomaly are suggested.     

WKB approximation in complex time

The WKB approximation to the one particle Schrödinger equation in time is used to obtain the wavefunction at a given point as a sum of semiclassical terms, each corresponding to a different classical trajectory (real or complex) but ending up at the same point. A method to find out reflection coefficient for processes involving one and two turning points is developed and it is shown that the semiclassical complex analysis reproduces exactly the reflection coefficient that is obtained through the exact solution of the problem. The connection between pair production and reflection amplitude is also shown. The pair production amplitude in a time dependent gravitational background is calculated and it is shown that the vacuum considered in complex trajectory WKB analysis refers to adiabatic vacuum.     

Modeling and characterizing the typical under-ice acoustic channel for the Arctic

The properties of arctic underwater acoustic channel were researched using BurkeTwersky(BT) model and ray theory.In the BT model,sea ice ridge is assumed as a set of semi-elliptical cylinder randomly distributed on a stress-free surface.By approximation of low frequency and high frequency of the BT model,the reflection coefficients were calculated at different frequencies.On the basis of ray theory,the acoustic field was calculated and the properties of underwater acoustic channel was analyzed.Compared to underwater acoustic channel properties when the boundary is air,the results show that under the ice surface some sound rays disappear during transmission,because the ice surface reflection coefficients is less than absolute soft surface.Especially,the higher the frequency,the higher the under-ice transmission loss.As a result,under-ice condition is unfavourable for acoustic signals to travel far.Besides,as to the channel structure,the reflection coefficient of ice layer is smaller,the channel multi-path structure is not significant compared to water-air interface without ice.The research results are valuable for our understanding of hydroacoustic channel and the prediction of the sonar system working in the polar region.     

A relation between multipath group velocity, mode number, and ray cycle distance

Weston's ray invariant or "characteristic time" in a range-dependent environment is exactly equivalent to the Wentzel-Kramers-Brillouin phase integral for ducted normal modes. By considering a ray element it is shown that the ray invariant can also be written in terms of ray cycle distance and cycle time. This leads to a useful formula for group velocity in terms of cycle distance and mode number. Drawing a distinction between the ray and wave interpretation, the Airy phase (i.e., the existence of a group velocity minimum) can be included in this approach. Favorable comparisons are made with group velocities derived from a normal mode model. The relationship is valid for variable sound speed and variable bathymetry, and this is demonstrated numerically. The formula is applicable to active sonar, multipath pulse shape, target signatures, reverberation, tomography, and underwater communications.     

修正反射系数的Kirchhoff近似方法计算高斯起伏冰面三维声散射

针对随机起伏冰面的声散射计算问题,利用修正反射系数的Kirchhoff近似方法计算了高斯起伏冰面的三维声散射。在计算模型中引入了冰面局部统计平均反射系数的概念,将二维高斯起伏冰面的散射分为相干散射和非相干散射,分别得到两类散射成分的散射系数公式,计算了高斯起伏冰面三维声散射的散射强度。分析了散射强度与随机起伏冰面的均方根高度、声波入射角度及频率的关系。通过实验室水池中高斯起伏冰面的散射强度测量实验,对理论模型的计算结果进行了验证。将实验结果分别与采用冰面局部统计平均反射系数的模型计算结果和文献中采用平整冰面镜反射系数的模型计算结果进行了对比,采用冰面局部统计平均反射系数的模型计算结果与实验测量值吻合较好。     

On the accuracy of the WKB approximation in optical dielectric waveguides

Eigenvalues and field distributions for optical waveguides obtained from the WKB approximation have been compared with those found from geometrical optics and from more rigorous weakly-guiding LP mode theories in the cases of the step-index and parabolic-index profiles. In all cases it is found that the zero-order WKB approximation yields very accurate eigenvalues provided care is taken in the choice of phase factors in the eigenvalue equation. Expressions are deduced for the required phase factors for guides of arbitrary index profile in both two- and three-dimensions, and physical interpretations are given in terms of ray optics. The first-order WKB field distributions are found to give good agreement with the mode fields everywhere except in the vicinity of the caustics.     

海面冰层对声波的反射和散射特性

北极海面冰层复杂多变,其对声波的反射和散射严重影响冰下水声信道的传输特性,建立海面冰层的声波反射和散射模型对冰下水声通信研究具有重要意义.假设海面冰层为多层固体弹性介质且冰-水界面粗糙,满足微扰边界条件,导出声波从海水介质入射到海面冰层时相干反射系数满足的线性方程组.对相干反射系数随声波频率、掠射角、冰层厚度的变化进行数值分析.进一步引入根据散射声场功率谱密度计算散射系数的方法,改变掠射角,对冰层厚度、散射掠角对散射系数的影响进行研究.     

北极典型冰下声信道建模及特性

将Burke-Twersky (BT)散射模型与射线理论相结合研究北极典型冰下的水声信道特性。BT模型将极地冰水界面的冰脊视为随机分布在自由表面的半椭圆柱。首先根据BT模型分别对高频和低频情况下的冰面反射系数取近似,计算不同频率的冰面反射系数。然后结合射线理论计算冰下声场并分析冰下信道特性,并与相同条件下绝对软界面的水声信道进行对比研究。结果显示,由于冰界面的存在,冰水界面与绝对软界面相比,冰面反射系数较小,使得部分声线不会传播很远,且随频率的增加衰减越发严重,因此不利于声信号远距离传播;此外在信道结构上,由于冰层反射系数较小,冰下信道多径相较于无冰的水-空气界面其多途现象不明显。研究结果对认知极地冰下水声信道特性以及开展极地水声系统性能预报具有一定意义。     

Temporal coherence of sound transmissions in deep water revisited

This paper examines the signal coherence loss due to internal waves in deep water in terms of the signal coherence time and compare to data reported in the literature over the past 35 years. The coherence time of the early raylike arrivals was previously modeled by Munk and Zachariasen ["Sound propagation through a fluctuating stratified ocean: Theory and observation," J. Acoust. Soc. Am. 59, 818-838 (1976)] using the supereikonal approximation and by Dashen et al. ["Path-integral treatment of acoustic mutual coherence functions for arrays in a sound channel," J. Acoust. Soc. Am. 77, 1716-1722 (1985)] using the path integral approach; a -1 [corrected] power frequency dependence and a -1/2 [corrected] power range dependence were predicted. Recent data in shallow water in downward refractive environments with internal waves suggested that the signal coherence time of the mode arrivals follows a -3/2 power frequency dependence and a -1/2 power range dependence. Since the temporal coherence of the acoustic signal is related to the temporal coherence of the internal waves, based on the observation that the (linear) internal waves in deep and shallow waters have a similar frequency spectrum, it is argued that the modelike arrivals in deep water should exhibit a similar frequency dependence in deep and shallow waters. This argument is supported by a brute-force application of the path integral to mode arrivals based on the WKB relation between the ray and mode. It is found that the data are consistent with the -3/2 power frequency dependence but more data are needed to further test the hypothesis.     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型。利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度。数值计算模型中,将冰面认为是局部阻抗表面,直接代入起伏冰面局部反射系数进行散射声场的计算,避免了解析计算模型中对反射系数的近似处理。对比分析了数值和解析计算模型在小粗糙起伏冰面、大粗糙起伏冰面及不同声波入射角和不同声波频率时的散射强度。相比解析模型计算结果,数值模型计算结果与实测结果更吻合。     

Multipath structure of the typical under-ice sound channel in the Arctic:theory and experiment

Considering the typical acoustic environment of the Arctic, this paper proposes a method based on OASES-Bellhop coupled model to rapidly analyze the multipath structure of the under-ice sound channel. Firstly the proposed model refers to ice plate as stratified elastic media with some roughness. Secondly,it uses the perturbation method and Kirchhoff approximation theory to solve the scattering loss due to the sea ice inhomogeneity. Finally, the model predicts the multipath structure of the under-ice channel through Ray theory. The results of the numerical simulation and experiment indicate that the typical Arctic sound channel presents multipath structures due to the sea ice and seabed in the range of 6 km, respectively.The sea ice reflection paths are stable,with a short multipath spread within 14 ms. The seabed reflection paths have relatively weak strength. The proposed OASES-Bellhop coupled model successfully predicts the amplitude and delay of the multipath structure with small error,which indicates the proposed model is able to analyze and predict the multipath structure of the observed acoustic environment in experiment.     

A modified warping operator based on BDRM theory in homogeneous shallow water

In this paper, a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode (BDRM) theory is presented. According to the BDRM theory, the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide. A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes. The derived dispersion formula can be applied to the homogeneous shallow water waveguide. Theoretically, the formula is related to the phase of the reflection coefficient and suitable for various bottom models. Furthermore, based on the derived dispersion relation, the modified warping operator is developed to obtain linear modal structures. For the Pekeris model, the formulae for the phase of the reflection coefficient are derived in this work. By taking account of the effect of the bottom attenuation on the reflection coefficient, the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom. Performance and accuracy of different formulae are evaluated and compared. The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.     

Formation of a weakly diverging caustic beam in an underwater sound channel open to the bottom

The paper studies the patterns manifesting themselves in the formation and propagation of caustic and weakly diverging beams using the geometric acoustic approximation and mode theory applied to the simplest model of an underwater sound channel open to the bottom in the form of the bilinear dependence of the square of the refractive index on depth. It is established that when a vertical array emitting a tonal sound signal is located at a certain critical depth, the multimode caustic beam which forms near the reference ray horizontally departing from its center and which predominates in intensity is simultaneously the most weakly diverging beam. It is shown that the reference ray of such a weakly diverging caustic beam corresponds to the smoothest minimum for the dependence of the length of the ray cycle on their angle of departure from the center of the array and to the depth level of revolution at the critical depth characteristic of the given oceanic waveguide.     

Features of the Invariant of the Spatial–Frequency Interference Structure of Acoustic Fields in Oceanic Waveguides

The paper considers the regular patterns that can be manifested in the behavior of the invariant of the spatial–frequency interference structure of an acoustic field in oceanic waveguides that are homogeneous and inhomogeneous along a track. Using the WKB and adiabatic approximations, an analytic expression is obtained for the invariant that, when certain conditions are fulfilled, reduces to the well-known classical expression independent of the mode numbers, their parity, or the emission frequency. It has been established that the approximate classical expression for the invariant correctly describes the slope of interference lines only in ranges of variation in the grazing angles of modes where the dependence of the cycle length of their corresponding Brillouin waves on the ray parameter is quite smooth and monotonic. The paper studies the formation of the spatial–frequency interference structure of an acoustic field propagating from a shallowwater isovelocity waveguide to a relatively deep-water waveguide with a near-surface sound channel.     

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采用等离子体分层模型,利用WKB近似研究了离子回旋共振加热(ICRH)天线发射谱n||对离子回旋波在托卡马克等离子体的表面功率反射系数、吸收衰减的影响,数值模拟了不同天线发射谱n||条件下快波少数离子加热的效果.模拟结果表明,当其它实验参数一定时,ICRH天线发射合适的n||能提高天线与等离子体的耦合效率,增强少数离子加热的效果.     

充水管道声分隔片消声性能研究Ⅰ.理论分析

本文对在充水管道中加入声分隔片的消声结构的消声性能进行了理论研究,用模式匹配法计算了有限和蔗声分隔片的传递损失和功率反射系数。研究结果表明,声分隔片的消声效果优于通常所采用在管壁加吸声衬怪的结构,并且其功率反射系数很小。     

典型北极冰下声信道多途结构分析及实验研究

针对北极海域典型声场环境,提出了基于OASES-Bellhop耦合模型的冰下声信道多途结构快速分析方法。模型将海冰等效为具有粗糙界面的弹性分层介质,利用微扰法与Kirchhoff近似,估计海冰界面不均匀造成的散射损失,结合射线传播理论对典型北极冰下声信道多途结构进行分析与预报。数值仿真与实验结果表明,在6 km距离处,典型北极冰下声信道由于海冰与海底反射分别形成多途结构,海冰多次反射路径叠加形成的多途结构较为稳定,时延扩展在14 ms范围内,海底反射路径强度相对较弱。OASES-Bellhop模型对冰下声信道多途结构幅度和时延预测误差较小,能够较好的解释及预报实验观测到的多途结构环境特性。     

Acoustic Parameters of the Bottom In Lake Baikal

A technique for estimating the effective acoustic parameters of the bottom in shallow water areas under ice cover has been developed. The methodology compares the experimental and simulated dependences of the sound field amplitude on depth at a distance from the source about an order of magnitude greater than the depth of the water area. The effective parameters are the values of the sound speed in the bottom, density, and attenuation coefficient of acoustic waves, which provide maximum agreement with experimental data in the calculations. The methodology was tested in a field experiment on Lake Baikal and can be recommended for developing autonomous acoustic monitoring systems.

     

A numerical halynometry experiment on an acoustic path in the Arctic ocean

It is shown that, in the Arctic-type deep-water waveguide, the first water mode can be used for acoustic halynometry at frequencies of about 40 Hz and higher. For this task, the stochastic sound scattering by the ice cover and the frequency dispersion of modes are the interfering factors. The data of numerical modeling are presented for the levels of the regular and stochastic components of the pseudo-noise signal and for the impulse response of the waveguide to narrow-band and broadband transmissions. To suppress the stochastically scattered component of the sound field, one can use a horizontal extended array. However, choosing the experimental site in a region with a mainly smooth ice cover may be more advantageous. It is shown that the frequency band of the received signal can be broadened by introducing a frequency-time correction of the propagation time of the first mode as a function of the sound frequency.