Renormalization of EM fields in application to large-angle scattering from randomly continuous media and sparse particle distributions

Wolf, D. de

doi:10.1109/tap.1985.1143632

Cited by 45 publications

(21 citation statements)

References 15 publications

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“…In the appendix, we give a brief derivation of De Wolf approximation using formal operator algebra (DE WOLF, 1985). In this section, we will adopt an intuitive approach of derivation to discerns the physical meaning of the approximation.…”

Section: De Wolf Approximationmentioning

confidence: 99%

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

Wu¹

2003

Pure appl. geophys.

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Dual-domain one-way propagators implement wave propagation in heterogeneous media in mixed domains (space-wavenumber domains). One-way propagators neglect wave reverberations between heterogeneities but correctly handle the forward multiple-scattering including focusing/defocusing, diffraction, refraction and interference of waves. The algorithm shuttles between space-domain and wavenumber-domain using FFT, and the operations in the two domains are self-adaptive to the complexity of the media. The method makes the best use of the operations in each domain, resulting in efficient and accurate propagators. Due to recent progress, new versions of dual-domain methods overcame some limitations of the classical dual-domain methods (phase-screen or split-step Fourier methods) and can propagate large-angle waves quite accurately in media with strong velocity contrasts. These methods can deliver superior image quality (high resolution/high fidelity) for complex subsurface structures. One-way and one-return (De Wolf approximation) propagators can be also applied to wave-field modeling and simulations for some geophysical problems. In the article, a historical review and theoretical analysis of the Born, Rytov, and De Wolf approximations are given. A review on classical phase-screen or split-step Fourier methods is also given, followed by a summary and analysis of the new dual-domain propagators. The applications of the new propagators to seismic imaging and modeling are reviewed with several examples. For seismic imaging, the advantages and limitations of the traditional Kirchhoff migration and time-space domain finite-difference migration, when applied to 3-D complicated structures, are first analyzed. Then the special features, and applications of the new dual-domain methods are presented. Three versions of GSP (generalized screen propagators), the hybrid pseudo-screen, the wide-angle Pade´-screen, and the higherorder generalized screen propagators are discussed. Recent progress also makes it possible to use the dualdomain propagators for modeling elastic reflections for complex structures and long-range propagations of crustal guided waves. Examples of 2-D and 3-D imaging and modeling using GSP methods are given.

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Section: De Wolf Approximationmentioning

confidence: 99%

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

Wu¹

2003

Pure appl. geophys.

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“…These high-order derivatives are similar to the high-order scattering terms in the Born series. The De Wolf approximation in scattering series corresponds to neglect the multiple backscattering (reverberations), i.e., drop all the terms containing two or more backscattering operators but keep all the forward scattering terms untouched (De Wolf, 1971, 1985Wu, 1994; for a summary and review, see Wu et al, 2007). In the forward direction, scattered fields of  and  have the opposite signs, so that the resulted scattering response is for the velocity perturbation; while in the backward direction, the scattered fields of  and  have the same sign, which corresponds to a response of impedance perturbation.…”

Section:   S S Smentioning

confidence: 99%

Nonlinear Fréchet derivative and its De Wolf approximation

Zheng

2012

SEG Technical Program Expanded Abstracts 2012

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SummaryWe introduce and derive the nonlinear Fréchet derivative for the acoustic wave equation. It turns out that the high order Fréchet derivatives can be realized by consecutive applications of the scattering operator and a zero-order propagator to the source. We prove that the higher order Fréchet derivatives are not negligible and the linear Fréchet derivative may not be appropriate in many cases, especially when forward scattering is involved for large scale perturbations. Then we derive the De Wolf approximation (multiple forescattering and single backscattering approximation) for the nonlinear Fréchet derivative. We split the linear derivative operator (i.e. the scattering operator) onto forward and backward derivatives, and then reorder and renormalize the nonlinear derivative series before making the approximation by dropping the multiple backscattering terms. Numerical simulations for a Gaussian ball model show significant difference between the linear and nonlinear Fréchet derivatives.

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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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Renormalization of EM fields in application to large-angle scattering from randomly continuous media and sparse particle distributions

Cited by 45 publications

References 15 publications

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

Nonlinear Fréchet derivative and its De Wolf approximation

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

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