Diffuse waves in a random medium layer with rough boundaries

Abstract

The problem of scattering from a random medium layer with rough boundaries is formulated as an integral equation in which the random fluctuations are represented as a zero-mean random operator. The analysis for the diffuse fields is based on the ladder-approximated Bethe–Salpeter equation. An integral equation for the diffuse intensities thus derived displays the various multiple-scattering processes involved in our problem. Transport equations are also derived and several special cases are considered to illustrate the characteristics of the results and to compare them with those in the literature.     

Scattering from a rough layer of a random medium

This paper deals with scattering from a random-medium layer with rough boundaries. The fluctuations of the surface heights and medium permittivity are assumed to be small and smooth. All random quantities are assumed to be stationary and independent of each other. After the introduction of approximate boundary conditions, the system of partial differential equations is transformed into an integral equation where the fluctuations of the problem are represented as a zero-mean random operator. Employing smoothing, integral equations for the coherent fields are obtained. Use of the Helmholtz operator leads to solution for the coherent propagation constant while the boundary operators lead to coherent Fresnel coefficients. The characteristics of the results are illustrated by considering several examples.     

Reflection of radiofrequency waves by a two-layer medium with randomly rough boundaries

Using perturbation theory, we have investigated the electromagnetic field reflected by a two-layer medium with rough boundaries. To first order in perturbation theory with respect to the asperities on the boundaries, we consider the scattering fading effect. To a second approximation, we have obtained analytical expressions for the perturbations of the mean field reflected and transmitted into the medium, and also analytical expressions for the second moment of the field with orthogonal polarization scattered in the plane of incidence. We have investigated the dependences of the second moment of the field on the character of the asperity spectrum, the frequency of the radiation, and the layer thickness.Scientific-Research Institute of Physics at Rostov University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1483–1498, December, 1994.     

Strong scattering of radio waves by a two-layer medium with rough boundaries and inhomogeneous permittivity of the layer

An analytical expression for the two-frequency correlation function of reflected radiation is derived in the framework of the Kirchhoff approximation, assuming that the mean square roughness heights _1,2 of the upper (₁) and lower (₂) boundaries are large compared to the wavelength and taking account of large-scale permittivity fluctuations in the layer. The condition under which p cannot be small when _i ^{2 2} is specified. In particular, it is shown that if the scattering is only at the upper boundary of the layer (when ₁ 0, ₂ = = 0), then this condition is , where m, n=0, 1,.... The potential of the layered medium sounding methods based on the relations obtained is estimated.Institute of Physics, State University, Rostov-on-Don. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 7, pp. 619–630, July, 1995.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Statistics of waves propagating in a random medium

We present a review of part of the results obtained by the authors for the statistics of coherent radiation propagating in a random medium both in the framework of diagrammatic techniques and random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient for the diffusive transport and the crossover between the diffusive and ballistic regimes are obtained.The authors acknowledge the financial support of the Israeli Academy of Sciences and of the Schottenstein Center.     

1D waves in a random poroelastic medium with large fluctuations

We examine the problem of wave propagation in a random poroelastic medium. The porous medium is modelled as a Biot poroelastic solid whose constitutive parameters fluctuate substantially over finite distances. Our main results are asymptotic analytical expressions for the mean velocity-stress wave; this solution incorporates two distinct length scales. The effect of the fluctuations appears on the regular depth coordinate while the parameters of the effective medium arise on a shorter scale of distance. Thus the method that we apply, the theory of averaging, allows us to give a rigorous derivation of the effective medium parameters. It also provides the correction terms which are caused by the fluctuations in the random medium; we find that the relative effect of the latter increases in proportion to ω^1/2 where ω denotes the wave frequency. We also show that the fluctuations introduce significant attenuation of the fast Biot compressional wave and dispersion of the slow Biot wave. These results are illustrated by numerical examples using real oilfield data.     

How hertzian solitary waves interact with boundaries in a 1D granular medium

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.     

Strong scattering of radio waves by a two-layered medium with a rough boundary

Radiowave scattering by a two-layered medium with a rough boundary is studied in the Kirchhoff approximation. We consider the case of oblique incidence of waves and mean square heights of the upper boundary roughnesses, which are nonsmall compared with the wavelength λ. An analytical expression and the conditions under which P₁ turns out to be large are derived for the term P₁ of the two-frequency correlation function P = (E_m(w₁)E_n(w₂)), which is proportional to the first degree of the coefficient of reflection from the lower boundary. Such effect is shown to emerge only for the resonant frequency relation. In particular, the following resonant relationship is written for the mirror reflection direction: w_2,1(√ε-sin²θ/cosθ-1), where θ is the incidence angle and ε is the layer permittivity. Research Institute of Physics, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 6, pp. 733–743, June, 1997.     

Transmission of waves by a nonlinear random medium

We study analytically and numerically the effect of nonlinearity on transmission of waves through a random medium. We introduce and analyze quantities associated with the scattering problem that clarify the lack of uniqueness due to the nonlinearity as well as the localization of waves due to the random inhomogeneities. We show that nonlinearity tends to delocalize the waves and that for very large scattering regions the average transmitted energy is small.     

Radar cross sections of a random medium layer

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.     

Radar cross sections of a random medium layer

Abstract

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.     

Scattering of radio waves by a two-layer medium with a weakly reflecting rough boundary

The average reflected field and the second moment of the scattered field of the main polarization are found and analyzed in the approximation of a small jump of the dielectric constant when a horizontally polarized wave is reflected by a two-layer medium with a rough upper boundary. It is shown that the oscillations due to frequency changes predicted by perturbation theory do not exist when the scattering parameter is large. Sounding at close angles of incidence and scattering is the most efficient method of layer thickness determination by the scattered radiation. Institute of Physics, State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 889–903, July, 1998.