Wide‐angle elastic wave one‐way propagation in heterogeneous media and an elastic wave complex‐screen method

Wu, Ru‐Shan

doi:10.1029/93jb02518

Cited by 179 publications

(134 citation statements)

References 32 publications

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“…Here u + t (x, z) is the total wavefield composed of incident field u + 0 (x, z) and the scattered field U + (x, z) caused by the heterogeneities within the slab (see Wu, 1994;Wu et al, 2000a). If we put the slab entrance at x = x and the wavefield on the entrance surface…”

Section: Conformal Coordinate Transform Methods For Smoothly Varying Tmentioning

confidence: 99%

“…To introduce the P-SV elastic screen propagator for a flat free surface, the basic idea is to incorporate plane wave reflection calculation into elastic screen method (Wu, 1994;Wu et al, 2000c). The half space is extended upward in vertical direction from free surface.…”

Section: P-sv Casementioning

confidence: 99%

“…The one-return approximation is also called the De Wolf approximation (De Wolf, 1971, which neglects the reverberation between screens and can simulate multiple-forescattering-singlebackscattering (MFSB). Significant progress has been made on the development of an elastic complex screen (ECS) method for modeling elastic wave propagation and scattering in arbitrarily complicated structures (Wu, 1994(Wu, , 1996Xie andWu, 1995, 2001;Wild and Hudson, 1998;. The method is two to three orders of magnitude faster than the elastic finite-difference method for a medium sized 3-D problem.…”

Section: Introductionmentioning

confidence: 99%

“…For detailed derivation and the physical meaning of the MFSB approximation and the generalized screen method, see Chapter 5 of this volume. The screen method has been successfully used in forward modeling (Wu, 1994;Xie and Wu, 1995Wu, 2001, 2005) and as backpropagators for seismic wave imaging/migration in both acoustic and elastic media (e.g., Wu and Xie, 1994;Huang and Wu, 1996;Huang et al, 1999aHuang et al, , 1999bXie andWu, 1998, 2005;Xie et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

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Simulation of High-Frequency Wave Propagation in Complex Crustal Waveguides Using Generalized Screen Propagators

Xie

2007

Advances in Wave Propagation in Heterogenous Earth

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In the crustal waveguide environment, the major part of wave energy is carried by forward propagating waves, including forward scattered waves. Therefore, neglecting backscattered waves in numerical modeling will not modify the main features of regional waves in most cases. By neglecting backscattering in the theory, the wave modeling becomes a forward marching problem in which the next step of propagation depends only on the present values of the wavefield in a transverse cross-section and the heterogeneities between the present cross-section and the next one (wavefield extrapolation interval). The saving of computation time and computer memory is enormous. A half-space screen propagator (generalized screen propagator) has been developed to accommodate the free-surface boundary condition for modeling SH wave propagation in complex crustal waveguides. The SH screen propagator has also been extended to handle irregular surface topography using conformal or nonconformal topographic transforms. The screen propagator for modeling regional SH waves has been calibrated extensively against some full-wave methods, such as the wavenumber integration, finite-difference and boundary element methods, for different crustal models. Excellent agreement with these full-wave methods demonstrated the validity and accuracy of the new one-way propagator method. For medium size problems, the screen-propagator method is 2-3 orders of magnitude faster than finite-difference methods. It has been used for the simulation of Lg propagation in crustal models with random heterogeneities and the related energy partition, attenuation and blockage. It is found that the leakage attenuation of Lg waves caused by large-angle forward scattering by random heterogeneities, which scatters the guided waves out of the trapped modes and leaking into the mantle, may contribute significantly to Lg attenuation and blockage in some regions. In the case of P-SV elastic screen propagators, plane wave reflection calculations have been incorporated into the elastic screen method to handle the free surface. Body waves, including the reflected and converted waves, can be calculated by real wavenumber integration; while surface waves (Rayleigh waves) can be obtained with imaginary wavenumber integration. Numerical tests proved the validity of the theory and methods.

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Section: Conformal Coordinate Transform Methods For Smoothly Varying Tmentioning

confidence: 99%

Section: P-sv Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of High-Frequency Wave Propagation in Complex Crustal Waveguides Using Generalized Screen Propagators

Xie

2007

Advances in Wave Propagation in Heterogenous Earth

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“…One-way approximation for wave propagation has been introduced and widely used as propagators in forward and inverse problems of scalar, acoustic and elastic waves (e.g., Claerbout, 1970Claerbout, , 1976Landers and Claerbout, 1972;Flatté and Tappert, 1975;Corones, 1975;Tappert, 1977;McCoy, 1977;Hudson, 1980;Ma, 1982;Wales and McCoy, 1983;McCoy, 1984, 1985;Wales, 1986;McCoy and Frazer, 1986;Collins, 1989Collins, , 1993Collins and Westwood, 1991;Stoffa et al, 1990;Fisk and McCartor, 1991;Wu and Huang, 1992;Ristow and Ruhl, 1994;Wu, 1994Wu, , 1996Wu, , 2003Wu and Xie, 1994;Huang and Wu, 1996;Wu and Jin, 1997;Grimbergen et al, 1998;Van Stralen et al, 1998;Wild and Hudson, 1998;Huang et al, 1999aHuang et al, , 1999bThomson, 1999Thomson, , 2005De Hoop et al, 2000;Lee et al, 2000;Wild et al, 2000;Wu et al, 2000aWu et al, , 2000bLe Rousseau and De Hoop, 2001;Wu, 2001, 2006;Wu, 2001, 2005;…”

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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Modeling 3‐D Scalar Waves Using the Fourier Finite‐Difference Method

Zhang¹,

Wang²,

Zhao³

et al. 2007

Chinese J of Geophysics

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Fourier finite‐difference (FFD) operator has both of the advantages of Fourier and finite‐difference methods, it can handle the wave propagations in complex media with large velocity contrasts and wide propagation angles. In 3‐D case, however, two‐way splitting may cause artificial azimuthal anisotropy. In this paper, we handle the remnants of the conventional two‐way splitting technique by Fourier transforms, and the azimuthal anisotropy is removed. Based on the dual‐domain scheme of the FFD method, the proposed algorithm significantly reduces computational cost caused by error correction. Compared with the finite‐difference method by the zero‐offset records and shot profiles based on 3‐D modified French model, the proposed method can properly model the primary reflected waves and is much more attractive in both computational cost and storage demand.

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Wide‐angle elastic wave one‐way propagation in heterogeneous media and an elastic wave complex‐screen method

Cited by 179 publications

References 32 publications

Simulation of High-Frequency Wave Propagation in Complex Crustal Waveguides Using Generalized Screen Propagators

Simulation of High-Frequency Wave Propagation in Complex Crustal Waveguides Using Generalized Screen Propagators

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

Modeling 3‐D Scalar Waves Using the Fourier Finite‐Difference Method

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