Modeling of bottom backscattering from three-dimensional volume inhomogeneities and comparisons with experimental data

In this paper, backscattering from 3D volume inhomogeneities in the seabed is modeled and the results compared with experimental data at 250-650 Hz. The experiment was part of the Acoustic Reverberation Special Research Program (ARSRP) and the data were obtained in a sediment pond on the western flank of the Mid-Atlantic Ridge. A volume scattering model based on first-order perturbation theory is developed incorporating contributions from both sound speed and density fluctuations. With the propagators, i.e., the Green's functions, handled accurately through numerical wave number integration and random fluctuations generated effectively by a new scheme modified from the spectral method, the model is capable of simulating monostatic, backscattered fields in the frequency domain as well as in the time domain owing to 3D volumetric sediment inhomogeneities. The model compares favorably and consistently with the ARSRP backscattering data over the entire frequency band, with the fluctuations of sound speed and density in two irregular sediment layers, identified from the data analysis, described by a power-law type of power spectrum.     

Spectral integral representations of volume scattering in sediments in layered waveguides

In situ measurements of scattering strength are often obtained by analyzing the early-time, high-angle reverberation from bottom and subbottom features. In order to provide insight into the mechanisms which cause bottom reverberation, and to their distinguishing characteristics, it is necessary to have a capability for modeling both the rough surface and the volume scattering mechanisms. For high-angle, early-time backscatter, the most appropriate approach is to use a spectral integral representation, which naturally includes the continuous spectrum important for this angular regime. A rough surface scattering theory developed earlier in this framework has provided important insights into wave scattering and penetration physics at the seafloor. Here a consistent representation for the subbottom scattering is developed and examples are provided which illustrate the observable differences between the two scattering mechanisms.     

Spectral representations of Lorentz invariant distributions and scale transformation

An approach to the theory of Lorentz invariant distributions is developed in terms of covariant spectral representations. The behaviour of singular invariant distributions under a change of scale is analyzed. It is shown that the conventional extension of homogeneous singular functions into distributions inR ⁴, followed by a breakdown of homogeneity, is incomplete. Homogeneous extensions depending on an arbitrary scaling parameter are introduced, calculation techniques are developed and various formulae having applications in quantum field theory are derived.Supported by the Deutsche Forschungsgemeinschaft.     

Investigation of correlation properties of backscattering by discrete inhomogeneities

Physical modeling of acoustic signal backscattering by discrete random inhomogeneities is performed. The behavior of the transverse correlation radius of the scattered field amplitude is studied. Its experimental dependences on the transducer aperture, on the angle of sounding of an inhomogeneity-containing plane, and on the correlation properties of the scatterer position on this plane are derived. Qualitative theoretical models in the framework of the theory of single scattering are proposed which provide an explanation to the phenomena observed.State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 106–109, January–February, 1995.     

Enhanced backscattering of vortex waves from volume scattering media

The effect of phase vortices on the enhanced coherent backscattering from volume scattering media is studied theoretically and experimentally. The experimental results are well described by a theoretical model based on the diffusion approximation corrected for small path lengths contributions. Based on this approach, a self-referencing method for measuring the optical characteristics of a multiple scattering medium can be developed.     

Study of acoustic wave backscattering by discrete inhomogeneities of different sizes

The influence of the distribution statistics on the sizes of discrete random bottom inhomogeneities on the mean intensity of acoustic signal backscattering is studied. The simultaneous presence of two effects leading to an increase in the mean intensity of backscattering are considered: the correlation in the positional relationship of particles on the plane of the bottom and their size distribution.     

火焰烟黑三维温度场和浓度场同时重建实验研究

利用电荷耦合器件摄像机采用烟黑温度场和浓度场同时重建模型对自由火焰烟黑的三维温度场和浓度场进行了同时重建实验研究,所利用的重建模型是基于区域重建的方法.将重建的烟黑温度场和浓度场与文献结果进行了对比,而且还将重建温度场与热电偶所测量的温度场进行了对比.结果表明,重建的烟黑温度场和浓度场与文献结果趋势相一致,重建温度值与热电偶测量值符合较好.因此,同时重建模型可以较好地重建出火焰烟黑的三维温度场和浓度场. 关键词： 火焰烟黑 温度场 浓度场 三维同时重建     

Spectral distributions of thomson-scattered photons from high-intensity pulsed lasers

General formulas for the far-field spectral distribution of photons Thomson scattered by a single electron have been obtained. Effects due to the pulsed nature of the laser beam are explicitly allowed, simultaneously with intensity high enough that harmonic generation is possible. For realistic pulsed photon beams, the spectrum of backscattered radiation is considerably broadened because of changes in the longitudinal velocity of the electrons during the pulse. Such ponderomotive broadening is especially pronounced at higher harmonics, eventually leading to a continuous emission spectrum.     

Statistical properties of perturbative nonlinear random diffusion from stochastic integral representations

Nonlinear diffusions on bounded intervals perturbed by gaussian white noise are considered. Terms in the expansion of the solution satisfy a recursive sequence of linear stochastic partial differential equations with the same kernel. Their solutions may be found as stochastic integrals. Thus expressions are obtained for the mean to order ϵ² and for the covariance and spectral density to order ϵ³.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

Determination of non-homogeneous high-concentration depth distributions using elastic backscattering data

A computer program has been developed by which the depth concentration distribution of a two-element bulk sample can be determined from elastic backscattering data. The presented calculative procedure can be applied to non-homogeneous high concentrations, where the composition variation as a function of depth has to be considered to obtain correct distributions. Two samples with different compositions, nitrogen in titanium and gold in silicon, were analysed with 2MeVH⁺ and He⁺ ions, respectively, to illustrate the versatility of the calculative program.     

Spectral brightness distributions in spectrometric monitoring of the earth from space

The effect of the atmosphere on the spectral reflection and scattering of visible and near IR solar radiation by different natural surfaces observed from space and the earth is examined. The shift in the spectral brightness maximum of the emerging radiation relative to the maximum of the solar constant is analyzed. The data are compared with theoretical calculations of the brightness of the emerging radiation.     

Inversion of the backscattering data and a problem of integral geometry

The backscattered acoustic field from an inhomogeneity is known on a plane P for all frequencies. These data determine the inhomogeneity uniquely. An analytical formula for the inversion is given. The integral geometry problem which consists in finding a compactly supported function from the knowledge of its integrals over the spheres S(x¹, R) of various R centered at x¹, 0 < R < ∞, x¹ ? P, is solved analytically explicitly. The backscattered field known at any finite number of frequencie s does not determine the inhomogeneity uniquely.     

Spectral representations and the density matrix of subsystems

A regular method is indicated which makes it possible, under conditions of thermodynamic equilibrium, to find in a constructive manner the density matrix of a subsystem which, in general, is in strong interaction with its surroundings.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 81–87, May, 1978.I am grateful to the participants of the seminar led by V. L. Bonch-Bruevich for discussion of the work.     

Fock space representations of affine lie algebras and integral representations in the Wess-Zumino-Witten models

Fock space representations of affine Lie algebras are studied. Explicit forms of correction terms adding to the currentsF _i (z) are determined. It is proved that the Sugawara energy-momentum tensor on the Fock spaces is quadratic in free bosons. Furthermore, screening operators are constructed. This implies the existence of generalized hypergeometric integrals satisfying the Knizhnik-Zamolodchikov equation.     

Spectral moment estimates of broadband backscattering acoustic wave in moving medium

I.IntroductionSincemiddle198o's,theacousticDopplercurrentprofiler(ADCP)hasbeenusedinvariousaspects.Itnormallytransmitsasine-modulatedpulse,thenmeasurestheechoofmanylayersinaprofile.TheDopplerfrequencyshiftofeachlayeriscalculatedwhilethevesseliscruisingandADCPiscontinuallytransmittingpulsesandreceivingechoes.BystatisticallyaveragingtheDopplerfrequencyshiftofeachlayerinmultipletransmissions,theestimateofDopplerfrequencyshiftofthatlayerisobtained,thenthevelocityestimatesofmanydepthbinsinapr…     

宽带运动介质反向散射声信号的谱矩估计

本文假设宽带运动介质反向散射信号和噪声是彩色高斯信号,在大样本的假设下,用协方差法求得了信号谱矩一阶矩和二阶矩的均值和方差,推广了文献^[8]的工作。发射信号是伪随机编码信号,它由两个相同的子序列组成,为了简化问题,又设信号和噪声的带宽和中心频率相同,得到了易用的公式。公式表明,一阶谱矩估计的均值是无偏估计,估计的方差与子序列间的相关系数ρ,信噪比S/N和ΔfTL有关,其中Δf、T和L分别对应子序列中码元的带宽、长度和总个数。分析了约3000组窄带信号的海上实验数据,给出了ρ的变化范围。这些工作对研制宽带多普勒流速剖面仪(BBADCP)是很有用的。     

Volume integral equation for analysis of three-dimensional scattering from dielectric frequency-selective structures

The space-domain volume integral equation method is presented for the analysis of three-dimension scattering from dielectric frequency-selective structures involving homogeneous and inhomogeneous lossy materials. The method directly solves for the electric field in order to easily enable the periodic boundary conditions in the spatial domain. The special basis and test functions are introduced to deal with the current continuity in periodic boundaries. The computation of the spatial domain periodic Green’s function (PGF) is accelerated by the modified Ewald transformation, so that a very thick periodic structure can also be analyzed efficiently and accurately. The PGF mentioned above is of free-space type and very smooth and amenable to interpolation. Thus, optimized interpolation procedures for the PGFs can be applied, resulting in a considerable reduction of matrix-filling time without any significant influence on the accuracy. A study of the scattering parameters of a multilayered dielectric periodic structure is accomplished by imposing the boundary conditions in terms of the multimode scattering matrix. Numerical examples show the reliability and accuracy of the proposed method.     

The angular dependence of the coefficient of sound reflection from anisotropic volume inhomogeneities of the ocean

The small perturbation method is used to consider the scattering of sound by random volume inhomogeneities of the ocean. The inhomogeneities are assumed to be horizontally anisotropic with their horizontal dimensions far exceeding the vertical ones. Expressions are obtained for the angular dependence of the scattering coefficient. Vertical and horizontal sections of the scattering pattern are presented, and the angular widths of its maxima are analytically estimated.