The Double Focal Transformation and its Application to Seismic Data Reconstruction

Kutscha, H.

doi:10.3997/2214-4609.20148302

Cited by 3 publications

(9 citation statements)

References 52 publications

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“…Every row vector of

R (z_{m})

contains a convolution operator that applies the angle‐dependent reflection to the incident wavefield related to one spatial location. For more information about the reflectivity matrix, see Berkhout (), de Bruin, Wapenaar, and Breakout (), Doulgeris, Mahdad, and Blacquiere (), and Kutscha (). The reflected wavefield is then upward propagated to the receivers at the surface.…”

Section: Theory and Implementationmentioning

confidence: 99%

“…This would lead to a rough estimate of

\overset{x}{true}

. Another possibility is to solve for

\overset{x}{true}

by least squares (LS) inversion or by sparse inversion, which is also investigated in Kutscha and Verschuur () and Kutscha (). This paper will focus solely on the case of sparse inversion as this shows the best reconstruction results for coarse input data.…”

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

“…In the work of Kutscha (), it is shown how de aliasing filters can be generated for simple data that are coarsely sampled in a regular fashion. These filters can be used to mute the noise area in the focal domain, for instance, by setting to zero the energy in the red shapes in Fig.…”

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

“…(). Another option is to use a weighting function for the model space, which allows a more flexible suppression of aliasing noise (see Kutscha ). However, a more robust way is to estimate the focal domain from the coarse input data by sparse inversion.…”

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

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The utilization of the double focal transformation for sparse data representation and data reconstruction

Kutscha

Verschuur

2016

Geophysical Prospecting

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In many cases, seismic measurements are coarsely sampled in at least one dimension. This leads to aliasing artefacts and therefore to problems in the subsequent processing steps. To avoid this, seismic data reconstruction can be applied in advance. The success and reliability of reconstruction methods are dependent on the assumptions they make on the data. In many cases, wavefields are assumed to (locally) have a linear space–time behaviour. However, field data are usually complex, with strongly curved events. Therefore, in this paper, we propose the double focal transformation as an efficient way for complex data reconstruction. Hereby, wavefield propagation is formulated as a transformation, where one‐way propagation operators are used as its basis functions. These wavefield operators can be based on a macro velocity model, which allows our method to use prior information in order to make the data decomposition more effective. The basic principle of the double focal transformation is to focus seismic energy along source and receiver coordinates simultaneously. The seismic data are represented by a number of localized events in the focal domain, whereas aliasing noise spreads out. By imposing a sparse solution in the focal domain, aliasing noise is suppressed, and data reconstruction beyond aliasing is achieved. To facilitate the process, only a few effective depth levels need to be included, preferably along the major boundaries in the data, from which the propagation operators can be calculated. Results on 2D and 3D synthetic data illustrate the method's virtues. Furthermore, seismic data reconstruction on a 2D field dataset with gaps and aliased source spacing demonstrates the strength of the double focal transformation, particularly for near‐offset reflections with strong curvature and for diffractions.

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“…Every row vector of

R (z_{m})

Section: Theory and Implementationmentioning

confidence: 99%

“…This would lead to a rough estimate of

\overset{x}{true}

. Another possibility is to solve for

\overset{x}{true}

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

Section: The Double Focal Transformation As An Inverse Problemmentioning

confidence: 99%

See 2 more Smart Citations

The utilization of the double focal transformation for sparse data representation and data reconstruction

Kutscha

Verschuur

2016

Geophysical Prospecting

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“…Conventionally, seismic processing is implemented as an open-loop process, in which information about the inconsistency between output and input is not taken into account. Recently, the so-called feedback-loop process has been introduced, see, e.g., Kutscha and Verschuur (2012) and Verschuur et al (2012) for data reconstruction, Lopez and Verschuur (2012) for multiple elimination and primary estimation, Soni et al (2012) and Davydenko et al (2012) for full wavefield migration, and Berkhout (2012) for joint migration inversion. The feedback-loop is described by an inversion problem of its own model parameters in each processing.…”

Section: Introductionmentioning

confidence: 99%

Dispersive multi-modal mud-roll elimination using feedback-loop approach

Ishiyama

2013

SEG Technical Program Expanded Abstracts 2013

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SummaryIn a shallow water environment, mud-rolls are often dominant and appear as a prevailing coherent noise in OBC seismic data. Their complex properties make the noise elimination notably challenging in seismic processing. To address these challenges, we propose a dispersive multimodal mud-roll elimination method using a feedback-loop approach with a sparse inversion of focal/Radon transformation. In this paper, we illustrate the proposed method, and show some examples on synthetic seismic data to demonstrate its virtues.

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Separating Simultaneous Seismic Sources using Robust Inversion of Radon and Migration Operators

Ibrahim¹

2016

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The Double Focal Transformation and its Application to Seismic Data Reconstruction

Cited by 3 publications

References 52 publications

The utilization of the double focal transformation for sparse data representation and data reconstruction

The utilization of the double focal transformation for sparse data representation and data reconstruction

Dispersive multi-modal mud-roll elimination using feedback-loop approach

Separating Simultaneous Seismic Sources using Robust Inversion of Radon and Migration Operators

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