Reciprocity properties of one‐way propagators

Wapenaar, Kees

doi:10.1190/1.1444473

Cited by 47 publications

(41 citation statements)

References 10 publications

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“…The original Bremmer series (Bremmer, 1951) is a geometric-optical series for stratified media, which can be considered as a higher order extension to the regular WKBJ solution (the first order term). Later it was generalized to 3-D inhomogeneous media, and was named the generalized Bremmer series (Corones, 1975;De Hoop, 1996;Wapenaar, 1996Wapenaar, , 1998Van Stralen et al, 1998;Thomson, 1999;Le Rousseau and De Hoop, 2001). The zero order term (the leading term) of the GBS is a high-frequency asymptotic solution (a WKBJ-like solution or Rytov-like solution) (De Hoop, 1996), and used as the Green's function for deriving the higher order terms.…”

Section: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

“…The key difference between these approaches is how to define a reference Green's function for constructing one-way propagators. The generalized Bremmer series (GBS) approach (Corones, 1975;De Hoop, 1996;Wapenaar, 1996Wapenaar, , 1998Van Stralen et al, 1998;Thomson, 1999;Le Rousseau and De Hoop, 2001) adopts an asymptotic solution of the acoustic or elastic wave equation in the heterogeneous medium as the Green's function, i.e. the one-way propagator in the preferred direction.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

Section: Introductionmentioning

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 inverse wavefield extrapolation operatorF + (z A , z B ) in equation (2) is closely related to the forward propagatorW − (z A , z B ) as (Wapenaar, 1998):…”

Section: Theorymentioning

confidence: 99%

“…Here,L ± 1 andL ± 2 represent submatrices of the energy flux-normalized composition matrixL that depend on the medium properties at the receiver level (e.g. Wapenaar (1998)). In principle, any normalization of the composition matrix will work.…”

Section: Theorymentioning

confidence: 99%

Wavefield Decomposition of Field Data, Using a Shallow Horizontal Downhole Sensor Array and a Free-surface Constraint

et al. 2014

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SUMMARYSeparation of recorded wavefields into downgoing and upgoing constituents is a technique that is used in many geophysical methods. The conventional, multi-component (MC) wavefield decomposition scheme makes use of different recorded wavefield components. In recent years, land acquisition designs have emerged that make use of shallow horizontal downhole sensor arrays. Inspired by marine acquisition designs that make use of recordings at multiple depth levels for wavefield decomposition, we have recently developed a multi-depth level (MDL) wavefield decomposition scheme for land acquisition. Exploiting the underlying theory of this scheme, we now consider conventional, multi-component (MC) decomposition as an inverse problem, which we try to constrain in a better way. We have overdetermined the inverse problem by adding an MDL equation that exploits the Dirichlet free-surface boundary condition. To investigate the successfulness of this approach, we have applied both MC and combined MC-MDL decomposition to a real land dataset acquired in Annerveen, the Netherlands. Comparison of the results of overdetermined MC-MDL decomposition with the results of MC wavefield decomposition, clearly shows improvements in the obtained one-way wavefields, especially for the downgoing fields.

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“…L is a composition operator that involves forward Fourier transformation, applying pseudo-differential operators (for expressions, see Wapenaar (1998)) and inverse Fourier transformation. Some freedom exist in the scaling of L, depending on what we want the decomposed wavefields p + and p − to represent.…”

Section: Theorymentioning

confidence: 99%

Up/Down Wavefield Decomposition by Sparse Inversion

Neut¹,

Herrmann

2012

Proceedings

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SUMMARYExpressions have been derived for the decomposition of multi-component seismic recordings into up-and downgoing constituents. However, these expressions contain singularities at critical angles and can be sensitive for noise. By interpreting wavefield decomposition as an inverse problem and imposing constraints on the sparseness of the solution, we arrive at a robust formalism that can be applied to noisy data. The method is demonstrated on synthetic data with multi-component receivers in a horizontal borehole, but can also be applied for different configurations, including OBC and dual-sensor streamers.

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Reciprocity properties of one‐way propagators

Cited by 47 publications

References 10 publications

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

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

Wavefield Decomposition of Field Data, Using a Shallow Horizontal Downhole Sensor Array and a Free-surface Constraint

Up/Down Wavefield Decomposition by Sparse Inversion

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