Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media

Bamberger, A.; Engquist, Björn; Halpern, Laurence; Joly, Patrick

doi:10.1137/0148006

Cited by 175 publications

(124 citation statements)

References 5 publications

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“…For instance, the difference between equation (60) and its transpose leads to three independent equations for the antisymmetric part of P α . Adding equation (60) and its transpose leads to six equations for the symmetric part of P α .…”

Section: Narrow-angle Approximationmentioning

confidence: 99%

“…This is unacceptable because coupling between wave modes can be important, especially at interfaces or for long propagation distances. [59] and [60] introduce higher order Padé series expansions to the splitoperators which allow even wider angles of propagation. More importantly though, these higher order expansions allow wave speeds to differ substantially from the chosen reference speed (or phase).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Narrow-angle Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Angus

2013

Surv Geophys

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“…a profuse num ber of developm ents have been carried out to improve the accuracy and efficiency of the approxim ation [2,[44][45][46][47][48][49][50][51][52][53], and to expand i t 's applicability to more realistic conditions [54][55][56][57][58][59][60][61]. T he parabolic equation was originally lim ited to narrow -angle propagation; th e energy outside the angle of propagation is neglected.…”

Section: P Arabolic E Quation M Eth O Dmentioning

confidence: 99%

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

Rolla

Rice

2006

Journal of Sound and Vibration

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“…where the symbols In equations 7 and 8 the Green functions are computed by means of the one-way wave equation (Ehinger et al, 1996) and the extrapolation is performed using the adequate paraxial wave equations (flux conservation) (Bamberger et al, 1988).…”

Section: Subsurface-offset Hessianmentioning

confidence: 99%

Wave-Equation Angle-Domain Hessian

Valenciano¹,

Biondi²

2006

68th EAGE Conference and Exhibition Incorporating SPE EUROPEC 2006

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A regularization in the reflection angle dimension (and, more generally in the reflection and azimuth angles) is necessary to stabilize the wave-equation inversion problem. The angle-domain Hessian can be computed from the subsurface-offset Hessian by an offsetto-angle transformation. This transformation can be done in the image space following the Sava and Fomel (2003) approach. To perform the inversion, the angle-domain Hessian matrix can be used explicitly, or implicitly as a chain of the offset-to-angle operator and the subsurface offset Hessian matrix.

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Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media

Cited by 175 publications

References 5 publications

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

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

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

Wave-Equation Angle-Domain Hessian

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