Wave propagation in a random medium layer with rough boundaries

The large-scale behavior of the spatial distribution of radiation in a random medium is investigated under the assumption of strong internal reflection from its boundaries. The qualitative variations of the angular coherent backscattering spectrum and long-range spatial intensity correlations in the transmitted and reflected radiation fluxes are predicted.

Wave propagation in random media

The propagation of electromagnetic waves from satellites to the earth is influenced by the electrically anisotropic behavior of the ionosphere. Fluctuating ionospheric parameters cause perturbations in the signal. To calculate the ground field of arbitrarily shaped linear antennas of geostationary satellites for polar regions, the passage of a carrier wave through a homogeneous, electrically anisotropic, stochastic ionosphere imbedded in a two-dimensional three-layer model (near-earth space, ionosphere, atmosphere) is considered. Perturbations due to the ionospheric fluctuations are treated using B.J. Uscinski's multiple scatter theory (see The Elements of Wave Propagation in Random Media, McGraw Hill, 1977) which has been extended to anisotropic media. Finally, the theory of E. Arbel and L.B. Felsen (see Electromagnetic Theory and Antennas Part I, Pergamon, 1963, p.391-420) is applied to derive field representations for the more realistic case of a homogeneously stratified anisotropic ionosphere.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A theory of wave propagation in random media must actually refer to a suite of predictive models of the effects of a random heterogeneity. This is because a single general formalism, suitable for all stochastic experiments, would be too complicated for realistic scenarios to have any computational capability. Thus predictive models expressed in partial descriptors of a propagating radiation field, intended for specific experiments are acceptable. In this talk, a number of thought experiments for the propagation of waves in random media will be presented. The point of this is to highlight a richness in the observations one might expect to obtain as a result of random heterogeneity, and to provide a discussion of the possible physical bases for these observations. Appropriate descriptors of the radiation field for each of the thought experiments will be considered, as will be the derivation of prediction models expressed in these measures. A number of specific issues to be addressed are: the possibility of ...

In 1973 A. J. Chorin [Math. Comp., 27 (1973), pp. 1–15] reported quadrature formulas for the approximation of a class of Wiener path integrals by n-fold ordinary integrals with an error Similar formulas are presented here for certain stochastic Wiener function space integrals in which n-fold integral approximations result in errors $O( n^{ - 2} )$ or $O( n^{ - 3/ 2} )$. Stochastic Wiener integrals arise in the physics of wave propagation in random media and in signal estimation problems in communication theory. The present formulas provide simple, accurate computational tools for these applications, among others. This point is illustrated by several examples in the paper.

First Page

We propose optical path-length spectroscopy as a new approach to obtaining information from media that exhibit multiple light scattering. By using a backscattering technique based on low-coherence interferometry, we are able to determine the optical path-length distribution for light reflected from a random medium and to infer the value of the transport mean free path. We illustrate how a diffusion approximation model leads to a satisfactory description of depth-resolved profiles of the backscattered intensity and discuss potential applications of this technique.

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

We develop a stochastic approach for the description of wave propagation in random media and present a derivation of the time independent bilocal radiative transport equation which generalizes the Boltzmann transport equation by taking into account wave scattering effects by correlated scatterers. We obtain an expression for the extinction coefficient that includes effects of correlation.

In this paper we consider the Ito-Schrodinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width. As applications we prove that the centered fourth-order moments of the field satisfy the Gaussian summation rule, we derive the covariance function of the intensity of the transmitted beam, and the variance of the smoothed Wigner transform of the transmitted field. The second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the Wigner transform.

Asymptotic solution of the Bethe-Salpeter equation and the Green-Kubo formula for the diffusion constant for wave propagation in random media

We present an original numerical approach for investigation of time-dependent wave propagation in random media. We review different results in 2D, including subdiffusive regime characterization, NDE in the multiple scattering regime and Anderson localization in presence of a nonlinear local gain.

The amplitude of a seismic wavefront travelling through a heterogeneous rock matrix decreases due to (1) absorption or intrinsic attenuation, i.e. conversion of seismic energy to heat, and (2) apparent attenuation by scattering, i.e . transfer of seismic energy to later arrival times and other propagation directions. For a lithologic interpretation of seismic data it is highly desireable to separate both effects, for example by analyzing VSP or cross-hole data.

We present a new method for efficient, accurate calculations of transport properties of random media. It is based on the principle that the wave energy density should be uniform when averaged over length scales larger than the size of the scatterers. This scheme captures the effects of resonant scattering of the individual scatterer exactly, as well as the multiple scattering in a mean-field sense. It has been successfully applied to both ``scalar'' and ``vector'' classical wave calculations. Results for the energy transport velocity are in agreement with experiment. This approach is of general use and can be easily extended to treat different types of wave propagation in random media.

In this paper we revisit the parabolic approximation for wave propagation in random media by taking into account backscattering. We obtain a system of transport equations for the moments of the components of reflection and transmission operators. In the regime in which forward scattering is strong and backward scattering is weak, we obtain closed form expressions for physically relevant quantities related to the reflected wave, such as the beam width, the spectral width and the mean spatial power profile. In particular, we analyze the enhanced backscattering phenomenon, that is, we show that the mean power reflected from an incident quasi-plane wave has a maximum in the backscattered direction. This enhancement can be observed in a small cone around the backscattered direction and we compute the enhancement factor as well as the shape of the enhanced backscattering cone.