Wave Scattering and Coherence

An analytical study of the propagation of coherent sound waves through an atmosphere containing both mean and fluctuating flow variables is presented. The general flow problem is formulated as a time-dependent wave propagation in a half-space containing the turbulent medium. The coherent acoustic waves are analyzed by a smoothing technique, assuming that mean flow variables vary with the height only. The general equations for the coherent waves are derived, and then applied to two special cases, corresponding to uniform and shear mean flow, respectively. The results show that mean shear and turbulence introduce pronounced effects on the propagation of coherent acoustic disturbances.

This paper deals with the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers. We assume same-size cylindrical inclusions and same-thickness interface layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equation which depends only upon the scattering amplitude of the single scattering problem. Effective elastic constants can be obtained from phase velocities of coherent waves. Numerical calculations for an SiC-fiber-reinforced Al composite are carried out, and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant is shown graphically.

Scattering of waves causes the coherent wave field to be attenuated and dispersed. These phenomena express the fact that the pulse loses coherence by which incoherent coda energy is created. First-order scattering theory violates the law of energy conservation and therefore cannot be used when the wave field is strongly distorted. An approximation is proposed which estimates the interaction between different scatterers by considering only multiple forward scattering interactions. Internal of a single scatterer all multiple interactions are maintained. This approximation can only be valid for the first part of the wave field and sufficiently weak scattering conditions. The heterogeneous medium can then be described as an effective medium that is a function of the scatterer density and forward scattering amplitude and the background medium. Simulations of the multiple scattering process with isotropic scatterers in two dimensions show that the discrepancies between the exact and approximate solution are small compared to the difference with the undisturbed wave field, even when the pulse is severely attenuated. Contrary to single scattering theory multiple scattering maintains the propagation of a stable and localized coherent wave. Apparently the nonlinear multiple scattering interactions cause a tendency for the coherent wave field to become insensitive to the specific scatterer distribution.

The scattering of a plane electromagnetic wave obliquely incident on a layer of dense medium consisting of dielectric spherical particles of finite sizes and with size distributions is studied. The spherical particles are of sizes comparable to wavelength so that Mie scattering is used to describe the single particle scattering characteristics. The coherent wave is studied with quasicrystalline approximation using the cross pair distribution functions of multiple sizes governed by Percus-Yevick approximation. The incoherent scattered wave is calculated with the distorted Born approximation with the result expressed in terms of a product of the T-matrices of particles of different sizes and permittivities and the Fourier transform of the cross pair distribution functions. The coherent wave effective propagation constants, the attenuation rates and the backscattering coefficients are illustrated numerically, with examples chosen to illustrate microwave and millimeter wave scattering from snow cover in the f...

An investigation is conducted how the geometrical properties of a crack distribution in a fault fracture zone and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident seismic waves. All cracks are assumed to be either aligned or randomly oriented. The crack width is assumed to obey a power law distribution, according to seismological knowledge. The crack surface is assumed to be stress-free, or to undergo viscous friction. To deal with cracks under high confining pressure, the latter case will be more realistic than the stress-free crack, due to the existence of fluid in the earth's crust and the viscoelastic response of contacting solid material to seismic waves under high confining pressure. When the crack distribution is statistically homogeneous, the calculated dispersion and attenuation exhibit that the variance of crack size affects in different way the coherent wave. The analysis on the effect of the friction shows that the crack scattering decreases as the viscosity increases, which is expected since for high viscosity, the crack faces remain almost welded to each other. The results obtained in this work will be applicable to the state close to the occurrence time in large earthquakes.

This paper is concerned about coherent waves in a random medium layer with randomly rough boundaries which on the average are parallel planes. The fluctuations of the problem are assumed to be small and smooth. All the statistical parameters of the problem are stationary and independent of each other. The bottom surface is assumed to be perfectly conducting. Using transferred boundary conditions the problem of electromagnetic wave scattering from this layer is formulated as a single integral equation where the random fluctuations of the problem are represented as a zero mean random operator. Smoothing leads to an integral equation for the coherent fields. Various operators are employed to this equation to obtain expressions for the principal parameters of the coherent fields such as propagation constants and Fresnel coefficients. Some examples are considered to illustrate the characteristics of our results.

: The effect of multiple scattering on the coherent wave propagation is discrete random media is studied for spherical and non-spherical dielectric scatterers as a function of frequency and volume concentration of scatterers. The first and second order probability distribution functions are specified and a self-consistent T-matrix approach together with Lax's quasi-crystalline approximation is used to derive dispersion equations whose singular solutions yield the complex propagation constant of the 'effective medium'. Various forms of pair-correlations were considered in the analysis; the self-consistent pair-correlation function is found to be well suited for a wide range of concentration of scatterers. The formalism is also found to be applicable for very high frequencies. The theoretical results obtained by this formalism were compared with experimental findings and the agreement is excellent. (Author)

Scattering of Coherent Sound Waves by Atmospheric Turbulence

The influence of a geostrophically balanced or potential vorticity (PV) containing background flow on the propagation of a coherent gravity wave is examined in a rotating shallow-water model. Over inertial time scales, we find that the gravity wave energy is scattered into other modes of similar wavelength, but with different directions of propagation. We attribute this response to nonlinear resonant interactions between the PV and gravity wave modes, despite the absence of any exchange of energy between the two, and show that the response is consistent with resonant triad theory. We first consider the scattering of a gravity wave mode due to a single PV mode, and compare the theoretical response to numerical solutions. This is followed by consideration of the propagation of a coherent gravity mode through a turbulent PV background. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.

This study considers the phase velocity and attenuation of time harmonic axial shear waves in a piezoelectric fibrous composite with slip at interfaces subjected to a steady-state in-plane electrical load. Scattering of plane axial shear waves by a circular piezoelectric fiber with slip is analyzed. We apply the results of the single scattering problem to the propagation of any desired finite frequency waves in a composite containing a dilute concentration of circular piezoelectric fibers. Numerical results for some piezoelectric fibrous composites are obtained and the effects of interfacial slippages and electroelastic interactions on the phase velocity and attenuation of coherent plane waves are discussed in detail.

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.The coherent or average wave is assumed to be propagating in a homogeneous continuum characterized by a bulk complex wavenumber. This wavenumber depends on the frequency of the probing waves; and on the physical properties and the concentration of discrete scatterers, causing the effective medium to be dispersive. With the help of multiple scattering theory, we are able to analytically predict the attenuation of the transmitted wave intensity as well as the dispersion of the phase velocity. These two sets of data are valuable to the study of the inverse scattering problems in seismology. Some numerical results are presented and also compared, if possible, with experimental measurements.

Scattering of in-plane compressional (P) and shear (SV) waves by a polygonal inclusion is studied by using the boundary-element method. We apply the results of the single scattering problem to the propagation of elastic waves in a composite containing a dilute concentration of polygonal inclusions. Numerical calculations are carried out for a moderately wide range of frequencies, and the effect of inclusion shape on the scattering cross sections, and the phase velocities and attenuations of coherent waves and the effective elastic moduli for a dilute composite are shown graphically.

Multiple Scattering of SH Waves by Randomly Distributed Dissimilar Scatterers

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.

Active and passive microwave remote sensing has been used for monitoring the soil moisture and snow water equivalent. In the interactions of microwaves with bare soil, the effects are determined by scattering of electromagnetic waves by random rough surfaces. In the interactions of microwaves with terrestrial snow, the effects are determined by volume scattering of dense media characterized by densely packed particles. In this paper, we review the electromagnetic full-wave simulations that we have conducted for such problems. In volume scattering problems, one needs many densely packed scatterers in a random medium sample to simulate the physical solutions. In random rough surface scattering problems, one needs many valleys and peaks in the sample surface. In random media and rough surface problems, the geometric characterizations of the media and computer generations of statistical samples of the media are also challenges besides electromagnetic computations. In the scattering of waves by soil surfaces, we consider the soil to be a lossy dielectric medium. The random rough surface is characterized by Gaussian random processes with exponential correlation functions. Surfaces of exponential correlation functions have fine-scale structures that cause significant radar backscattering in active microwave remote sensing. Fine-scale features also cause increase in emission in passive microwave remote sensing. We apply Monte Carlo simulations of solving full 3-D Maxwell's equations for such a problem. A hybrid UV/PBTG/SMCG method is developed to accelerate method of moment solutions. The results are illustrated for coherent waves and incoherent waves. We also illustrate bistatic scattering, backscattering, and emissivity which are signatures measured in microwave remote sensing. For the case of scattering by terrestrial snow, snow is a dense medium with densely packed ice grains. We have used two models: densely packed particles and bicontinuous media. For the case of densely packed particles, we used the Metropolis shuffling method to simulate the positions of particles. The particles are also allowed to have adhesive properties. The Foldy-Lax equations of multiple scattering are used to study scattering from the densely packed spherical particles. The results are illustrated for the coherent waves and incoherent waves. For the case of bicontinuous media, the method developed by Cahn is applied to construct the interfaces from a large number of stochastic sinusoidal waves with random phases and directions. The volume scattering problem is then solved by using CGS-FFT. We illustrate the results of frequency and polarization dependence of such dense media scattering.