Least‐squares wave‐equation migration for AVP/AVA inversion

Kühl, Henning; Sacchi, Mauricio D.

doi:10.1190/1.1543212

Cited by 211 publications

(62 citation statements)

References 25 publications

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“…However, to ensure convergence, the two subroutines have to be conjugate-transpose (adjoint) to one other (Nemeth et al, 1999;Kühl, and Sacchi, 2003). This can be confirmed using a dot-product test.…”

Section: Discussionmentioning

confidence: 96%

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Least-squares Reverse-time Migration

Yao¹,

Jakubowicz²

2012

Proceedings

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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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Section: Discussionmentioning

confidence: 96%

“…This suggests that the aliasing artefacts can be further suppressed using a roughness constraint (Kühl and Sacchi, 2003). …”

Section: Aliasingmentioning

confidence: 99%

Least-squares Reverse-time Migration

Yao¹,

Jakubowicz²

2012

Proceedings

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“…L 1 -or entropy-norms, on the other hand, preserve sparseness and this explains the current resurgence of sparseness-constrained inversion techniques [Kuhl andSacchi, 2003, Schonewille andDuijndam, 2001], which has led to successful spike-train solutions of the deconvolution problem. In this paper, we allow for a more general types of transitions that go beyond Earth models that consist of isolated jump-discontinuities.…”

Section: Seismic Deconvolutionmentioning

confidence: 99%

“…Seismic imaging roughly consists of two main steps. First, kinematic effects of the wave propagation are removed by a process called migration, which corresponds to applying the adjoint of the linearized forwardscattering operator to seismic data [Brandsberg-Dahl and de Hoop, 2003, Kuhl and Sacchi, 2003, ten Kroode et al, 1998]. Remaining source-function , Oldenburg et al, 1981, Robinson, 1957, Scheuer, 81, Ulrych and Walker, 1982, imaging [Hu et al, 2001] and propagation influences are removed during a second step, which is designed to improve the resolution as well as amplitude characteristics of the image.…”

Section: Introductionmentioning

confidence: 99%

Seismic deconvolution by atomic decomposition: A parametric approach with sparseness constraints

Herrmann

2005

ICA

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In this paper an alternative approach to the blind seismic deconvolution problem is presented that aims for two goals namely recovering the location and relative strength of seismic reflectors, possibly with super-localization, as well as obtaining detailed parametric characterizations for the reflectors. We hope to accomplish these goals by decomposing seismic data into a redundant dictionary of parameterized waveforms designed to closely match the properties of reflection events associated with sedimentary records. In particular, our method allows for highly intermittent non-Gaussian records yielding a reflectivity that can no longer be described by a stationary random process or by a spike train. Instead, we propose a reflector parameterization that not only recovers the reflector's location and relative strength but which also captures reflector attributes such as its local scaling, sharpness and instantaneous phase-delay. The first set of parameters delineates the stratigraphy whereas the second provides information on the lithology. As a consequence of the redundant parameterization, finding the matching waveforms from the dictionary involves the solution of an ill-posed problem. Two complementary sparseness-imposing methods Matching and Basis Pursuit are compared for our dictionary and applied to seismic data.

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“…Kirchhoff-based LSM uses a ray-theory based forward modeling operator; its derivation and application is discussed in Nemeth et al (1999) and Duquet et al (2000). LSM has also been applied to a wave-equationbased forward modeling operator, as shown by Kühl and Sacchi (2003). Clapp (2005) describes two methods for choosing a regularization scheme in the LSM context where the image is constrained to be smooth either along geological features predetermined by a seismic interpreter or along the ray-parameter axis.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous estimation of reflectivity and geologic texture: Least-squares migration with a hierarchical Bayesian model

Zamanian¹,

Kane

Rodi³

et al. 2013

SEG Technical Program Expanded Abstracts 2013

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SUMMARYIn many geophysical inverse problems, smoothness assumptions on the underlying geology are utilized to mitigate the effects of poor resolution and noise in the data and to improve the quality of the inferred model parameters. Within a Bayesian inference framework, a priori assumptions about the probabilistic structure of the model parameters impose such a smoothness constraint or regularization. We consider the particular problem of inverting seismic data for the subsurface reflectivity of a 2-D medium, where we assume a known velocity field. In particular, we consider a hierarchical Bayesian generalization of the Kirchhoff-based least-squares migration (LSM) problem. We present here a novel methodology for estimation of both the optimal image and regularization parameters in a least-squares migration setting. To do so we utilize a Bayesian statistical framework that treats both the regularization parameters and image parameters as random variables to be inferred from the data. Hence rather than fixing the regularization parameters prior to inverting for the image, we allow the data to dictate where to regularize. In order to construct our prior model of the subsurface and regularization parameters, we define an undirected graphical model (or Markov random field) where vertices represent reflectivity values, and edges between vertices model the degree of correlation (or lack thereof) between the vertices. Estimating optimal values for the vertex parameters gives us an image of the subsurface reflectivity, while estimating optimal edge strengths gives us information about the local "texture" of the image, which, in turn, may tell us something about the underlying geology. Subsequently incorporating this information in the final model produces more clearly visible discontinuities in the final image. The inference framework is verified on a 2-D synthetic dataset, where the hierarchical Bayesian imaging results significantly outperform standard LSM images.

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Least‐squares wave‐equation migration for AVP/AVA inversion

Cited by 211 publications

References 25 publications

Least-squares Reverse-time Migration

Least-squares Reverse-time Migration

Seismic deconvolution by atomic decomposition: A parametric approach with sparseness constraints

Simultaneous estimation of reflectivity and geologic texture: Least-squares migration with a hierarchical Bayesian model

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