Computation of wave fields in inhomogeneous media -- Gaussian beam approach

Červený, Vlastislav; Popov, M. M.; Pšenčı́k, Ivan

doi:10.1111/j.1365-246x.1982.tb06394.x

Cited by 508 publications

(206 citation statements)

References 5 publications

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“…) is the windowed data The form of the beams can be taken as Gaussian beams (e.g., Cerveny, 1982). If the beam widths are infinite, then we have plane wave extrapolation such as the double-square-root operator, plane wave migration, offset plane waves etc.…”

Section: Methods and Theorymentioning

confidence: 99%

Efficient Double-beam Characterization for Fractured Reservoir

Zheng¹,

Fang²,

Fehler³

et al. 2012

Proceedings

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We proposed an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.

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Section: Methods and Theorymentioning

confidence: 99%

Efficient Double-beam Characterization for Fractured Reservoir

Zheng¹,

Fang²,

Fehler³

et al. 2012

Proceedings

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“…The accuracy of the beam off the central ray is determined by the truncation error of Taylor expansion, and the approximate solution is given by a sum of all the beams (see [4,13,25]). The accuracy of the Taylor expansion was studied by Motamed and Runborg [24], and Tanushev [30] developed and analyzed higher order Gaussian beams giving better accuracy of the approximations.…”

Section: )mentioning

confidence: 99%

Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations

Jin

Yang

2008

Communications in Mathematical Sciences

129

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Abstract. The solution to the Schrödinger equation is highly oscillatory when the rescaled Planck constant ε is small in the semiclassical regime. A direct numerical simulation requires the mesh size to be O(ε). The Gaussian beam method is an efficient way to solve the high frequency wave equations asymptotically, outperforming the geometric optics method in that the Gaussian beam method is accurate even at caustics.In this paper, we solve the Schrödinger equation using both the Lagrangian and Eulerian formulations of the Gaussian beam methods. A new Eulerian Gaussian beam method is developed using the level set method based only on solving the (complex-valued) homogeneous Liouville equations. A major contribution here is that we are able to construct the Hessian matrices of the beams by using the level set function's first derivatives. This greatly reduces the computational cost in computing the Hessian of the phase function in the Eulerian framework, yielding an Eulerian Gaussian beam method with computational complexity comparable to that of the geometric optics but with a much better accuracy around caustics.We verify through several numerical experiments that our Gaussian beam solutions are good approximations to Schrödinger solutions even at caustics. We also numerically study the optimal relation between the number of beams and the rescaled Planck constant ε in the Gaussian beam summation.

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“…(1) is comprised of a Gaussian distribution with a linear phase-term which causes the beam to tilt with respect to the z = 0 plane. The tilted GBs in [24] were obtained by introducing a novel non-orthogonal coordinate system which is a priori matched to distribution (1). In this system r b = (x b 1 , x b 2 , z b ) where the z b -axis is in the beam-axis propagation direction and the transverse coordinates, x b 1 and x b 2 , lie on a plane parallel to the (x 1 , x 2 ) plane and are centered at its intersection with the z b -axis (see Fig.…”

Section: Tilted Gaussian Beamsmentioning

confidence: 99%

“…This feature is significantly advantageous for propagation and scattering and results in simplified analytic expressions for the beam fields. Locality considerations have been utilized for solving beam-type waveobjects propagation in generic media profiles such as inhomogeneous [1][2][3], anisotropic [4][5][6][7][8][9][10][11], and for time-dependent pulsed beams, in dispersive media [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Parameterization of the Tilted Gaussian Beam Waveobjects

Hadad¹,

Melamed²

2010

PIER

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Abstract-Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field's planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associated with them. Specific types of tilted Gaussian beams that are characterized by their aperture complex curvature matrices, are parameterized in term of beam-widths, waist-locations, collimationlengths, radii of curvature, and other features. Emphasis is placed on the difference in the parameterization between the conventional (orthogonal coordinates) beams and the tilted ones.

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Computation of wave fields in inhomogeneous media -- Gaussian beam approach

Cited by 508 publications

References 5 publications

Efficient Double-beam Characterization for Fractured Reservoir

Efficient Double-beam Characterization for Fractured Reservoir

Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations

Parameterization of the Tilted Gaussian Beam Waveobjects

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