Fourth moments of acoustic waves forward scattered by a rough ocean surface

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

低频水下声信号的激光探测

根据表面波声光效应的原理,提出了一种低频水下声信号的激光探测技术,并建立了实验装置。在几十赫兹的低频段,对水下声源所产生的表面声波进行了探测。实验过程中,利用MATLAB软件对拍摄的衍射图样进行扫描分析,得到了衍射图样中条纹的像素差。根据波长与条纹间距的解析关系式,得到了低频液体表面声波波长,其大小在毫米量级。利用计算机编程,根据最小二乘法拟合色散关系的回归曲线,测量结果与理论色散关系吻合。该方法具有实时、非接触的特点。     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

Abstract

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Space-time structure of the low-frequency acoustic field in an underwater sound channel

Experimental data are presented on the fine structure of the sound field in an underwater sound channel for low and infralow sound frequencies. The experiments are performed in the Black Sea, on a 600-km-long path, with explosive sound sources. The intensity, space-time, and frequency characteristics of the sound field are analyzed. The geometric dispersion of the first normal wave is experimentally studied. The role of the channel inhomogeneities in the violation of the sound field coherence is determined for different frequency bands. On the basis of the experimental data, the vertical distribution of the critical frequencies of the waveguide is obtained, and the validity limits are established for the wave and ray calculation methods. The applicability of the phase methods for calculating the sound fields in waveguides with dispersion is discussed. The frequency-angular dependence of the effective sound attenuation coefficient in an underwater waveguide is revealed and explained.     

Simultaneous detection of the acoustic-field aberration and Doppler shift in forward acoustic scattering

The aberration in the received acoustic field and the Doppler shift in the forward scattered field are simultaneously induced when a submerged target crosses the source–receiver line. Formulations for the two variations are developed upon an ideal forward scattering configuration. Both the field aberration and the Doppler shift are expressed as functions of the same argument — the target motion time. An experimental validation was carried out in a tank, in which the continuous wave was transmitted. The field aberration and the Doppler shift were extracted from the collected data by the simple Hilbert transform and a hybrid technique, respectively. The measured aberration and Doppler shift agree with the theoretical results.Simultaneous detection outputs are beneficial to enhance the reliability on target detection by providing both the aberrations in the received acoustic field and the Doppler shift in the forward scattered field.     

Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Theory of radio wave scattering at a rough sea surface

The problem of the reflection of a plane single-frequency electromagnetic wave from a statistically rough dielectric boundary with arbitrary is solved in the perturbation approximation. The statistical characteristics (scattering cross section, change of polarization, and frequency spectrum) of a radar signal reflected from a rough sea surface are investigated. The model used for the surface—a small ripple superimposed on large waves—enables the perturbation theory approach to be extended to the decimeter and centimeter wave band.Izvestiya VUZ. Radiofizika, Vol. 9, No. 5, pp. 876–887, 1966     

Correlation of Bragg scattering from the sea surface at different polarizations

The phase interference fading in Bragg backscattering from the sea surface at moderate incidence angles is considered using both moment method calculation of the scattering from measured water profiles and an implementation of the slightly rough, tilted facet model. The fading of the instantaneous scattering cross-section is shown to be independent of the instantaneous phase of the illuminating signal. The vertical and horizontal polarization fading responses are therefore strongly correlated when identical carrier frequencies and modulations are used at both polarizations since the electromagnetic energy is Bragg resonant with the same small-scale roughness in both cases, independent of whether the polarization channels are phase locked. Instantaneous horizontally polarized Bragg backscattering (HH) exceeding that at vertical polarization (VV) is extremely unlikely in this case. Use of an offset in the frequencies of monochromatic signals used at the two polarizations can lead to reduced correlation between the fading if the illumination footprint length is sufficiently large so that the frequency shift introduces a significant additional phase shift between the scattering from the leading and trailing edges of the footprint. The fading shows only a very weak correlation when this phase shift exceeds 400°. HH Bragg backscattering exceeding VV will be much more common under these specialized conditions.     

A time domain rough surface scattering model based on wedge diffraction: application to low-frequency backscattering from two-dimensional sea surfaces

A time domain method for calculating the acoustic impulse response of impenetrable, rough, two-dimensional (2D) surfaces is presented. The method is based on an extension of the wedge assemblage (WA) method to 2D surfaces and objects. Like the WA method for one-dimensional (1D) surfaces, the approach for 2D surfaces uses Biot's and Tolstoy's exact solution for the impulse response of an infinite impenetrable wedge [J. Acoust. Soc. Am. 29, 381-391 (1957)] as its fundamental building block. The validity of the WA method for backscattering from 2D sea surfaces is assessed through comparisons with calculations based on Milder's operator expansion (OE) method [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Average intensities for backscattering from 2D fully developed seas (20 m/s wind speed) were computed by the WA and OE methods using 50 surface realizations and compared at 11 frequencies between 100 and 200 Hz. A single, moderately low grazing angle of incidence (20 degrees) and several scattered grazing angles (90 degrees, 45 degrees, 20 degrees , and 10 ) were considered. Excellent overall agreement between the two models was obtained. The utility of the WA method as a tool to describe the physics of the scattering process is also discussed.     

The effects of shadowing on modelling forward radar propagation over a rough sea surface

In order to accurately predict the effects of ocean roughness on forward radar propagation, it is important to incorporate the relevant physical scattering mechanisms. Shadowing is one such mechanism that is particularly important for low-grazing incidence yet it is often not taken into account. One broad class of approximations defines a roughness reduction factor in terms of an ensemble average over surface heights of a Rayleigh phase factor. The widely used Ament approximation and Miller–Brown approximation are two examples from this class of approximations that do not incorporate shadowing. In this paper, we use this class of approximations to develop a ‘shadowed’ approximation that implements a probability density function (PDF) for a rough sea surface illuminated at grazing incidence. A rigorous method of moments calculation is used to compare and quantitatively assess the accuracy of the Ament, Miller–Brown, and shadowed approximations at horizontal polarization. It is shown that the shadowed approximation yields significantly more accurate results than either the Ament or Miller–Brown approximation. In addition, these three approximations are compared with experimental data and it is shown that the shadowed approximation is in good agreement with the data. Finally, numerical curve fitting is used to develop a simple analytical expression for a roughness reduction factor that incorporates shadowing.     

Forward scattering of pulses from a rough sea surface by Fourier synthesis of parabolic equation solutions

A variable depth step implementation of the range-dependent acoustic model (RAM) is applied to the modeling of forward scattering from a rough sea surface. The sea surface is treated within RAM simply as an internal interface between a water layer and an air upper halfspace. A comparison with a numerically exact integral equation is undertaken for the scattering of single frequencies from Pierson-Moskowitz sea surfaces. The method is extended to model the variability of linear frequency modulated pulses from a series of frozen sea surfaces in a shallow water waveguide. The subsequent effect of rough boundary scattering on the replica correlation process is investigated.     

Investigation on global positioning system signal scattering and propagation over the rough sea surface

This paper is devoted to the study of polarization properties, scattering properties and propagation properties of global positioning system (GPS) scattering signal over the rough sea surface. To investigate the polarization and the scattering properties, the scattering field and the bistatic scattering coefficient of modified Kirchhoff approximation with using the tapered incident wave is derived in detail. In modeling the propagation properties of the GPS scattering signal in the evaporation duct, the initial field of parabolic equation traditionally computed by the antenna pattern with using fast Fourier transform (FFT) is replaced by the GPS scattering field. And the propagation properties of GPS scattering signal in the evaporation duct with different evaporation duct heights and elevation angles of GPS are discussed by the improved discrete mixed Fourier transform with taking into account the sea surface roughness.     

基于正交频分复用的水声通信中克服频率偏移影响的方法

OFDM(正交频分复用)是一种适合于在频率选择性衰落信道中进行高速传输的技术。水下信 道中存在着严重的多普勒频率偏移,限制了这种技术在水下的应用。本文分析了频率偏移对OFDM 系统性能的影响,提出了利用循环前缀补偿频率偏移引起的相位偏移方法来克服频偏的影响。试验 证明了这种方法的有效性。     

Visualization of surface acoustic wave scattering by dislocations

Stroboscopic X-ray topography at the synchrotron beam line was used to visualize the propagation of a 580 MHz surface acoustic waves (SAW) in LiNbO3 crystals. For this purpose, the X-ray bursts coming from the synchrotron storage ring with periodicity of 5.68 MHz were synchronized with the SAW frequency in a phase-locked mode. This method allowed us to "stop" the SAW in time and to observe the X-ray diffraction contrast caused by the dynamic deformation field of SAW. The X-ray topographic images showed well-resolved individual acoustic wave fronts of 6 microm SAW as well as their distortions due to SAW scattering by linear dislocations. Some of the images revealed an exceptional contrast of the concentric rings about the dislocation line, which is caused by coherent interaction of the secondary elastic waves. This contrast is similar to the Fresnel zones in optics, and this conclusion is confirmed by direct summation of secondary waves emitted by local elements of a vibrating dislocation string.