The application of wide angle screen propagator to 2D and 3D depth migrations

Xie, Xiao‐Bi; Mosher, Charles C.; Wu, Ru Shan

doi:10.1190/1.1816213

Cited by 13 publications

(11 citation statements)

References 5 publications

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“…The coefficients can also be optimized to obtain better accuracy for large propagation-angle waves (e.g., Huang and Fehler 2000;Xie, Mosher and Wu 2000).…”

Section: Conventional One-way Propagatormentioning

confidence: 99%

Lateral velocity variation related correction in asymptotic true‐amplitude one‐way propagators

Cao

2010

Geophysical Prospecting

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A B S T R A C TIt was mathematically proved that the asymptotic true-amplitude one-way wave equation could provide the same amplitude as the full-wave equation in heterogeneous lossless media in the sense of high-frequency asymptotics. Much work has been done on the vertical velocity variation related amplitude correction term but the lateral velocity variation related term has not received much attention, even being excluded in some asymptotic true-amplitude one-way propagator formulations. Here we analyse the effects of different amplitude correction terms in the asymptotic true-amplitude one-way propagator, especially the effect related to the lateral velocity variation, by comparing the wavefield amplitude from the one-way propagator with that from full-wave modelling. We derive a dual-domain wide-angle screen type asymptotic true-amplitude one-way propagator and evaluate two implementations of the amplitude correction. Numerical examples show that the lateral velocity variation related correction term can play a significant role in the asymptotic true-amplitude oneway propagator. Optimization of the expansion coefficients in the asymptotic trueamplitude one-way propagator can improve both the amplitude and phase accuracy for wide-angle waves. I N T R O D U C T I O NConventional one-way wave equations do not pay much attention to the correctness of amplitude information and cannot provide accurate amplitudes even at the level of leading order asymptotic Wentzel-Kramers-Brillonin-Jeffreys or ray theory (Zhang, Zhang and Bleistein 2003). Wentzel-KramersBrillonin-Jeffreys amplitudes have long been introduced into the conventional one-way wave propagator (e.g., Clayton and Stolt 1981). Traditionally the Wentzel-Kramers-BrilloninJeffreys solution was derived by asymptotic approximation in smoothly varying v(z) media (e.g., Morse and Feshbach 1953;Aki and Richards 1980;Clayton and Stolt 1981;Stolt and Benson 1986). It has also been obtained by approximately factorizing the full-wave operator into one-way wave operators in heterogeneous media (Zhang 1993). It has been mathemat- *

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“…The coefficients can also be optimized to obtain better accuracy for large propagation-angle waves (e.g., Huang and Fehler 2000;Xie, Mosher and Wu 2000).…”

Section: Conventional One-way Propagatormentioning

confidence: 99%

Lateral velocity variation related correction in asymptotic true‐amplitude one‐way propagators

Cao

2010

Geophysical Prospecting

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“…One approach to achieve better accuracy for the large propagation-angle waves is to use higher-order expansion. However, it will bring extra computation cost, so here we focus on the other approach, to optimize the expansion coefficients in the rational functions, which has been studied extensively in the traditional one-way 'phase' propagator (e.g., Lee & Suh, 1985;Ristow & Rühl, 1994;Huang & Fehler, 2000;Xie et al, 2000). For the conventional 45 º FD equation Lee & Suh (1985) proposed a least-squares optimization scheme.…”

Section: Optimizations In True-amplitude One-way Propagatorsmentioning

confidence: 99%

“…Quite a few methods have been proposed to improve the wide-angle accuracy of one-way wave propagators (Collins and Westwood, 1991;Ristow and Ruhl, 1994;Wu, 1994Wu, , 1996Xie and Wu, 1998;Grimbergen et al, 1998;Jin et al, 1998Jin et al, , 2002Huang et al, 1999a, b;Xie et al, 2000;De Hoop et al, 2000;Le Rousseau et al, 2001;Han and Wu, 2005;Thomson, 2005). In spite of these progresses, the accuracy of wide-angle waves for strong contrast media is still a serious problem and put a practical limitation on applying these methods to steep reflector imaging.…”

Section: Introductionmentioning

confidence: 99%

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

Wu¹,

Xie²

2008

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“…The other approach, i.e. the generalized screen propagator (GSP) approach (Wu, 1994(Wu, , 1996(Wu, , 2003Xie, 1993, 1994;Wild and Hudson, 1998;De Hoop et al, 2000;Wild et al, 2000;Xie et al, 2000;Wu, 2001, 2005), on the other hand, does not use asymptotic solutions. Instead, the approach uses the multiple-forward-scattering (MFS) corrected one-way propagator as the Green's function.…”

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 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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The application of wide angle screen propagator to 2D and 3D depth migrations

Cited by 13 publications

References 5 publications

Lateral velocity variation related correction in asymptotic true‐amplitude one‐way propagators

Lateral velocity variation related correction in asymptotic true‐amplitude one‐way propagators

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

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

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