Downward Continuation of Moveout‐corrected Seismograms

Claerbout, Jon F.; Doherty, Stephen M.

doi:10.1190/1.1440298

Cited by 198 publications

(105 citation statements)

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“…It is easy to implement, it is not demanding computationally, and it is widely used in several applied areas such as seismic imaging [9,10,3,2], radar imaging [15,7], and nondestructive evaluation of materials [34]. There are, of course, more accurate broadband imaging methods such as full wave migration [2,Chapter 4] and full least squares inversion [2,Chapter 9].…”

mentioning

confidence: 99%

Edge Illumination and Imaging of Extended Reflectors

Borcea¹,

Papanicolaou²,

Vasquez³

2008

SIAM J. Imaging Sci.

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Abstract. We use the singular value decomposition of the array response matrix, frequency by frequency, to image selectively the edges of extended reflectors in a homogeneous medium. We show with numerical simulations in an ultrasound regime, and analytically in the Fraunhofer diffraction regime, that information about the edges is contained in the singular vectors for singular values that are intermediate between the large ones and zero. These transition singular vectors beamform selectively from the array onto the edges of the reflector cross-section facing the array, so that these edges are enhanced in imaging with travel-time migration. Moreover, the illumination with the transition singular vectors is done from the sources at the edges of the array. The theoretical analysis in the Fraunhofer regime shows that the singular values transition to zero at the index N (ω) = |A||B|/(λL) 2 . Here |A| and |B| are the areas of the array and the reflector cross-section, respectively, ω is the frequency, λ is the wavelength, and L is the range. Since (λL) 2 /|A| is the area of the focal spot size at range L, we see that N (ω) is the number of focal spots contained in the reflector cross-section. The ultrasound simulations are in an extended Fraunhofer regime. The simulation results are, however, qualitatively similar to those obtained theoretically in the Fraunhofer regime. The numerical simulations indicate, in addition, that the subspaces spanned by the transition singular vectors are robust with respect to additive noise when the array has a large number of elements.

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mentioning

confidence: 99%

Edge Illumination and Imaging of Extended Reflectors

Borcea¹,

Papanicolaou²,

Vasquez³

2008

SIAM J. Imaging Sci.

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“…Finite-difference migration was first proposed by Claerbout and Doherty (1972) using a continued-fraction expansion of the one-way wave equation. An important advantage of finite-difference migration is that it can deal with lateral velocity variations because it extrapolates wavefields in the space domain.…”

Section: Wavefield-continuation Methodsmentioning

confidence: 99%

Least-Squares Reverse-Time Migration

Yao

Jakubowicz

2012

SEG Technical Program Expanded Abstracts 2012

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Conventional migration methods, including reverse-time migration (RTM) have two weaknesses: first, they use the adjoint of forward-modelling operators, and second, they usually apply a crosscorrelation imaging condition to extract images from reconstructed wavefields. Adjoint operators, which are an approximation to inverse operators, can only correctly calculate traveltimes (phase), but not amplitudes. To preserve the true amplitudes of migration images, it is necessary to apply the inverse of the forward-modelling operator. Similarly, crosscorrelation imaging conditions also only correct traveltimes (phase) but do not preserve amplitudes. Besides, the examples show crosscorrelation imaging conditions produce strong sidelobes. Least-squares migration (LSM) uses both inverse operators and deconvolution imaging conditions. As a result, LSM resolves both problems in conventional migration methods and produces images with fewer artefacts, higher resolution and more accurate amplitudes. At the same time, RTM can accurately handle all dips, frequencies and any type of velocity variation. Combining RTM and LSM produces least-squares reverse-time migration (LSRTM), which in turn has all the advantages of RTM and LSM.In this thesis, we implement two types of LSRTM: matrix-based LSRTM (MLSRTM) and non-linear LSRTM (NLLSRTM). MLSRTM is a matrix formulation of LSRTM and is more stable than conventional LSRTM; it can be implemented with linear inversion algorithms but needs a large amount of computer memory. NLLSRTM, by contrast, directly expresses migration as an optimisation which minimises the ‫ܮ‬ 2 norm of the residual between the predicted and observed data. NLLSRTM can be implemented using non-linear gradient inversion algorithms, such as non-linear steepest descent and non-linear conjugated-gradient solvers.We demonstrate that both MLSRTM and NLLSRTM can achieve better images with fewer artefacts, higher resolution and more accurate amplitudes than RTM using three synthetic examples. The power of LSRTM is also further illustrated using a field dataset. Finally, a simple synthetic test demonstrates that the objective function used in LSRTM is sensitive to errors in the migration velocity.As a result, it may be possible to use NLLSRTM to both refine the migrated image and estimate the migration velocity.

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“…That is, given an initial wavefield and its derivative, that wavefield can be extrapolated or propagated using a variety of numerical means. This type of wavefield extrapolation has been found particularly useful in the migration of seismic data [47]. The above parabolic approximations are commonly referred to as 'reference phase' approaches.…”

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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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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Downward Continuation of Moveout‐corrected Seismograms

Cited by 198 publications

References 0 publications

Edge Illumination and Imaging of Extended Reflectors

Edge Illumination and Imaging of Extended Reflectors

Least-Squares Reverse-Time Migration

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

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