True‐amplitude beam migration

Albertin, Uwe; Yingst, David; Kitchenside, Phil; Tcheverda, Vladimir

doi:10.1190/1.1845323

Cited by 35 publications

(19 citation statements)

References 3 publications

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“…That paper also provides formulas for inversion with Gaussian beams using beam-stacking. Albertin et al (2004) present a reasonable approximation for common-offset inversion with beam-stacking in 3D using Gaussian beams. The Beylkin determinant is computational intensive in this case; hence, Bleistein (2007) presents only the 2.5D commonoffset inversion.…”

Section: Other Inversion Formulasmentioning

confidence: 99%

“…Our ultimate objective is migration/inversion with Gaussian beams used to generate the propagators of the surface data into the Earth. Demonstrations of migration/inversion with Gaussian beams are presented in Albertin et al (2004), Hill (1990Hill ( , 2001, Gray (2005), andFerriera et al (2005). We seek true amplitude formulas in the same sense as Kirchhoff inversion.…”

Section: Introductionmentioning

confidence: 97%

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Modeling, migration and inversion with Gaussian beams, revisited

Gray

2007

SEG Technical Program Expanded Abstracts 2007

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Gaussian beams have been shown in some cases to provide smoother leading order asymptotic expansions of the solution of wave equations than classical ray theory provides. They do this through complexvalued traveltime functions that describe the propagating wave in a tube around some central ray. Quadratic exponential decay orthogonal to the central ray arising from the imaginary part of the traveltime provides a "skin depth" to the ray tube. Gaussian beams also have complex-valued amplitudes that avoid the vanishing ray Jacobians of classical ray theory in the neighborhood of caustics. By contrast, classical ray theory requires an extension to more general waveforms (Airy functions, for example) to describe the wavefield in the neighborhood of a caustic. Gaussian beam representations are influenced by the neighborhood of the ray through the sum over wavefields on nearby rays, whereas classical ray-theory produces a solution that depends only on the medium heterogeneity along a single ray, up to second derivatives of those functions. Further, no special tracking of a KMAH index is necessary for the phase shift through caustics to be effected by the sum/integral over Gaussian beams. This note presents a hierarchy of ray methods starting from classical ray theory, followed by dynamic ray tracing and modeling in ray-centered coordinates with real traveltime and amplitude and then with complex traveltime and amplitude leading to Gaussian beams. We introduce a sample application of the representations of wavefields-the Green's function-for source point and beam fan initial point coincident and non-coincident. Thereafter, we show how these wavefield representations can be used in seismic migration/inversion (M/I) for the common-shot configuration

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Section: Other Inversion Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Modeling, migration and inversion with Gaussian beams, revisited

Gray

2007

SEG Technical Program Expanded Abstracts 2007

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“…This is an advantage of Gaussian beam migration over other high-frequency migration approaches and is one of the reasons that Gaussian beam migration has become one of the principal migration tools in the petroleum industry. Nonetheless, even in the oil industry, Gaussian beam migration is primarily used for structural imaging and true amplitude formulas are still being developed (N. R. Hill, personal comm., 2003;Albertin et al, 2004).…”

Section: Introductionmentioning

confidence: 98%

Correlation Migration Using Gaussian Beams of Scattered Teleseismic Body Waves

Nowack

Dasgupta

Schuster

et al. 2006

Bulletin of the Seismological Society of America

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Correlation migration for structural imaging using Gaussian beams is described for the inversion of passively recorded teleseismic waves. Gaussian beam migration is based on an overcomplete frame-based representation of the seismic wave field and uses localized slant-stack windows of the data. Paraxial Gaussian beams are then utilized for the backpropagation of the seismic waves into the medium. The method can provide stable imaging of seismic data in smoothly varying background media where caustics and triplicated arrivals exist. We develop Gaussian beam migration for structural imaging, which allows for incident teleseismic waves from beneath the structure, using directly scattered or surface-reflected phases. The method is applied to synthetic data computed for a collisional-zone model, and the inversions show that the Gaussian beam migration can image structure using passive teleseismic data. The method is next applied to synthetic data that have been convolved with an observed pulse from the 1993 Cascadia experiment. The autocorrelation is computed and the autocorrelated data are migrated by using Gausian beams for direct P-to-S scattered waves and surface-reflected waves. Although the migrations of the autocorrelation data with the source pulse included have more noise than the migrations of the impulsive source data, the subduction zone structure can still be clearly identified in the migrated results without removal of the source pulses.

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“…That is why several authors ͑e.g.,Albertin et al, 2004;Valenciano, 2008͒ suggest computing a limited number of the Hessian off-diagonals to…”

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confidence: 99%

Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian

Tang

2009

GEOPHYSICS

188

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Prestack depth migration produces blurred images resulting from limited acquisition apertures, complexities in the velocity model, and band-limited characteristics of seismic waves. This distortion can be partially corrected using the model-space least-squares migration/inversion approach, where a target-oriented wave-equation Hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity. However, one difficulty is the cost of computing the explicit Hessian operator, which requires storing a large number of Green's functions, making it challenging for large-scale applications. A new method to compute the Hessian operator for the waveequation-based least-squares migration/inversion problem modifies the original explicit Hessian formula, enabling efficient computation of this operator. An advantage is that the method eliminates disk storage of Green's functions. The modifications, however, also introduce undesired crosstalk artifacts. Two different phase-encoding schemes, planewave-phase encoding and random-phase encoding, suppress the crosstalk. When the randomly phase-encoded Hessian operator is applied to the Sigsbee2A synthetic data set, an improved subsalt image with more balanced amplitudes is obtained.

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True‐amplitude beam migration

Cited by 35 publications

References 3 publications

Modeling, migration and inversion with Gaussian beams, revisited

Modeling, migration and inversion with Gaussian beams, revisited

Correlation Migration Using Gaussian Beams of Scattered Teleseismic Body Waves

Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian

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