Generalized Bremmer series with rational approximation for the scattering of waves in inhomogeneous media

Stralen, M.J.N. van; Hoop, Maarten V. de; Blok, H.

doi:10.1121/1.423615

Cited by 19 publications

(33 citation statements)

References 45 publications

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“…Unlike the DWS, which is a series in terms of medium velocity variation, the GBS is in terms of the spatial derivatives of the medium properties (De Hoop, 1996). Because of the asymptotic nature of its Green's function, the media need to be "smooth" on the scale of the irradiating pulse (De Hoop, 1996;Van Stralen et al, 1998;Thomson, 1999). Some authors used an equivalent medium averaging process to smooth the medium before the application of the method (Van Stralen et al, 1998).…”

Section: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

“…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%

“…Because of the asymptotic nature of its Green's function, the media need to be "smooth" on the scale of the irradiating pulse (De Hoop, 1996;Van Stralen et al, 1998;Thomson, 1999). Some authors used an equivalent medium averaging process to smooth the medium before the application of the method (Van Stralen et al, 1998). Wapenaar's approach (1996Wapenaar's approach ( , 1998 is to get an asymptotic solution, without averaging the medium, using the flux normalized decomposition of wavefield.…”

Section: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

“…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%

“…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%

See 4 more Smart Citations

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: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

Section: The De Wolf Series and Generalized Bremmer Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Semiclassical Approximation

Cao¹,

Yin²

2013

Advances in One-Dimensional Wave Mechanics

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The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

Angus

2013

Surv Geophys

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The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green's function for wavefield propagation, and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operatorroot one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency dependent shear-wave splitting modeling, and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications.

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Generalized Bremmer series with rational approximation for the scattering of waves in inhomogeneous media

Cited by 19 publications

References 45 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

Semiclassical Approximation

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

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