Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

Wolf, D. de

doi:10.1109/tap.1971.1139894

Cited by 190 publications

(55 citation statements)

References 13 publications

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“…The interference terms may be expected to vanish, ā p a p ′ = 0, yielding the uniform average intensity that is familiar to us from the view of most natural objects like clouds. In the context of light scattering, it was first realized by Watson [17], de Wolf [18] and others, however, that each multiple scattering sequence visiting N scatterers in a given order (1, . .…”

Section: Enhanced Backscattering Of Lightmentioning

confidence: 99%

Weak localization of light by cold atoms: The impact of quantum internal structure

et al. 2001

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Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single and double scattering contributions to the intensity in the weak localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.

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Section: Enhanced Backscattering Of Lightmentioning

confidence: 99%

Weak localization of light by cold atoms: The impact of quantum internal structure

et al. 2001

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“…The multiple scattering theory has been developed since 1960 in particular, and applied to many practical cases (e.g., see references (1) (6) ). Backscattering enhancement of waves in random media has been investigated from an academic point of view in about two decades from 1971 to 1993 (7) (16) . It has thereby been said to be a fundamental phenomenon in disordered media (14) (16) and to be produced by statistical coupling of incident and backscattered waves due to the effect of double passage (8) .…”

Section: Introductionmentioning

confidence: 99%

Scattering by Conducting Bodies in Random Media

2004

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This paper presents that scattering by a body in a random medium consists of the following two issues; one is scattering of spatially partially coherent wave by the body and the other is coupling between incident and scattered waves through the random medium. Investigating separately each issue makes the scattering more understandable. The numerical analysis of scattered power by conducting cylinders leads to the radar cross-sections quite different from those in free space, under the condition that the radar cross-section of the random medium is negligibly small. The causes of the difference are explained on the basis of above separation of the scattering, and we emphasize that the spatial coherence length of incident wave is one of key parameters for estimating the cross sections.

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“…We hope that some sub-series can be summed up theoretically so that the divergent elements of the series can be removed. The De Wolf approximation splits the scattering potential into forescattering and backscattering parts and renormalizes the incident field and Green's function into the forward propagated field and forward propagated Green's function (forward propagator), respectively (De Wolf, 1971, 1985. The forward propagated field u f is the sum of an infinite sub-series including all the multiple forescattered fields.…”

Section: De Wolf Approximationmentioning

confidence: 99%

One-way and one-return approximations (de wolf approximation) for fast elastic wave modeling in complex media

Wu¹,

Xie²,

Wu³

2007

Advances in Wave Propagation in Heterogenous Earth

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The De Wolf approximation has been introduced to overcome the limitation of the Born and Rytov approximations in long range forward propagation and backscattering calculations. The De Wolf approximation is a multiple-forescattering-singlebackscattering (MFSB) approximation, which can be implemented by using an iterative marching algorithm with a single backscattering calculation for each marching step (a thin-slab). Therefore, it is also called a one-return approximation. The marching algorithm not only updates the incident field step-by-step, in the forward direction, but also the Green's function when propagating the backscattered waves to the receivers. This distinguishes it from the first order approximation of the asymptotic multiple scattering series, such as the generalized Bremmer series, where the Green's function is approximated by an asymptotic solution. The De Wolf approximation neglects the reverberations (internal multiples) inside thin-slabs, but can model all the forward scattering phenomena, such as focusing/defocusing, diffraction, refraction, interference, as well as the primary reflections.In this chapter, renormalized MFSB (multiple-forescattering-single-backscattering) equations and the dual-domain expressions for scalar, acoustic and elastic waves are derived by using a unified approach. Two versions of the one-return method (using MFSB approximation) are given: one is the wide-angle, dual-domain formulation (thin-slab approximation) (compared to the screen approximation, no small-angle approximation is made in the derivation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be clearly seen that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, are mainly controlled by impedance perturbations. Later in this chapter the validity of the thin-slab and screen methods, and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface, derived from numerical simulations by the wide-angle method, are shown to match the theoretical curves well up to critical angles. The methods are applied to the fast calculation of synthetic seismograms. The results are compared with finite difference (FD good agreement between the two methods verifies the validity of the one-return approach. However, the one-return approach is about 2-3 orders of magnitude faster than the elastic FD algorithm. The other example of application is the modeling of amplitude variation with angle (AVA) responses for a complex reservoir with heterogeneous overburdens. In addition to its fast computation speed, the one return method (thin-slab and complex-screen propagators) has some special advantages when applied to the thin-bed and random layer responses.

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Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

Cited by 190 publications

References 13 publications

Weak localization of light by cold atoms: The impact of quantum internal structure

Weak localization of light by cold atoms: The impact of quantum internal structure

Scattering by Conducting Bodies in Random Media

One-way and one-return approximations (de wolf approximation) for fast elastic wave modeling in complex media

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