Operator-oriented CRS interpolation

Hoecht, G.; Ricarte, Patrice; Bergler, S.; Landa, Evgeny

doi:10.3997/2214-4609.201404918

Cited by 13 publications

(22 citation statements)

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“…We here provide a brief note on terminology. In this paper, the term attribute refers to the kinematic wave field parameters in the CRS traveltime equation (Hoecht et al 2009). Examples include the curvatures and emergence angles in the CRS traveltime.…”

Section: O M M O N -O F F S E T C O M M O N -R E F L E C T I O N -Smentioning

confidence: 99%

“…As mentioned before, this is achieved with the CO CRS stacking operator, which approximates finite-offset reflection events in the vicinity of a given finite-offset central ray. Another benefit of the CRS operator is the seismic data regularization (Hoecht et al 2009;Xie and Gajewski 2016) by interpolating seismic traces to positions with missing or null traces. This benefit is also observed and extended to the pre-stack data in the CO CRS method.…”

Section: Introductionmentioning

confidence: 99%

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Common‐offset common‐reflection‐surface attributes estimation with differential evolution

Barros

Lopes

Krummenauer

et al. 2019

Geophysical Prospecting

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Common‐reflection surface is a method to describe the shape of seismic events, typically the slopes (dip) and curvature portions (traveltime). The most systematic approach to estimate the common‐reflection surface traveltime attributes is to employ a sequence of single‐variable search procedures, inheriting the advantage of a low computational cost, but also the disadvantage of a poor estimation quality. A search strategy where the common‐reflection surface attributes are globally estimated in a single stage may yield more accurate estimates. In this paper, we propose to use the bio‐inspired global optimization algorithm differential evolution to estimate all the two‐dimensional common‐offset common‐reflection surface attributes simultaneously. The differential evolution algorithm can provide accurate estimates for the common‐reflection surface traveltime attributes, with the benefit of having a small set of input parameters to be configured. We apply the differential evolution algorithm to estimate the two‐dimensional common‐reflection surface attributes in the synthetic Marmousi data set, contaminated by noise, and in a land field data with a small fold. By analysing the stacked and coherence sections, we could see that the differential evolution based common‐offset common‐reflection surface approach presented significant signal‐to‐noise ratio enhancement.

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Section: O M M O N -O F F S E T C O M M O N -R E F L E C T I O N -Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Common‐offset common‐reflection‐surface attributes estimation with differential evolution

Barros

Lopes

Krummenauer

et al. 2019

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…For this task, there are mainly three classes of approaches: (i) greedy methods such as matching pursuit and its variants (Mallat and Zhang 1993;Pati, Rezaiifar and Krishnaprasad 1993;Tropp and Gilbert 2007;Donoho et al 2012); (ii) iterative hard thresholding (Blumensath and Davies 2008;Fornasier and Rauhut 2008;Blumensath 2012); and (iii) basis pursuit, also referred to as iterative soft thresholding (Chen, Donoho and Saunders 1998;Candès and Wakin 2008;Yin et al 2008;Candès et al 2011;Andersson, Carlsson and Tenorio 2012) or its variants (Andersson et al 2012). In order to avoid local minima of the cost function with respect to P, one may need to globally sample the non-linear parameter, sometimes densely, depending on the oscillatory behaviour of J with respect to P. As the number of samples for non-linear parameters increases, so does the computational complexity of finding the optimal values for D. This especially constitutes a challenge with the introduction of curvature, window size, and other parameters into the formation of the library (Hoecht et al 2009).…”

Section: Literaturementioning

confidence: 99%

A model‐based data‐driven dictionary learning for seismic data representation

Yarman

Kumar

2017

Geophysical Prospecting

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A B S T R A C TPlanar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised "signal cones". In this work, we consider a space-time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone-limited (C-limited) functions (functions whose Fourier transform lives within a cone) or C-Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non-linear optimisation problem, which we address by a fixed-point method that utilises a variable projection method with 1 constraints on the linear parameters and bound constraints on the non-linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C-limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C-Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity-promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity-promoting plane-wave decomposition methods.

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“…We propose here a different data-driven approach based on CRS attributes, that does not need to make assumptions about the linearity of seismic events. Another CRS-based approach (Hoecht et al 2009) was proposed recently as an operator-oriented interpolation scheme, that is more intended at regularize irregular data geometry, looking for coherencies in common-offset volumes. We feel that our approaches are complementary, since our interpolation scheme can be used from sparse data only.…”

Section: Real Data Setmentioning

confidence: 99%

Inverse Common-Reflection-Surface

Perroud¹,

Tygel

Freitas³

2010

Geophysical Journal International

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S U M M A R YThe Common-Reflection-Surface (CRS) stack method is a powerful tool to produce highquality stacked images of multicoverage seismic data. As a result of the CRS stack, not only a stacked section, but also a number of attributes defined at each point of that section, are produced. In this way, one can think of the CRS stack method as a transformation from data space to attribute space. Being a purely kinematic method, the CRS stack lacks amplitude information that can be useful for many purposes. Here we propose to fill this gap by means of a combined use of a zero-offset section (that could be a short-offset or amplitude-corrected stacked section) and common midpoint gather. We present an algorithm for an inverse CRS transformation, namely one that (approximately) transforms the CRS attributes back to data space. First synthetic tests provide satisfying results for the two simple cases of single dippingplane and single circular reflectors with a homogeneous overburden, and provide estimates of the range of applicability, in both midpoint and offset directions. We further present an application for interpolating missing traces in a near-surface, high-resolution seismic experiment, conducted in the alluvial plain of the river Gave de Pau, near Assat, southern France, showing its ability to build coherent signals, where recording was not available. A somewhat unexpected good feature of the algorithm, is that it seems capable to reconstruct signals even in muted parts of the section.The Common-Reflection-Surface (CRS) stack method is a recent data-driven time imaging process (see, e.g. Hubral 1999;Jäger et al. 2001 and also references therein) that has been originally proposed as an alternative to the classical normal moveout (NMO)-dip moveout (DMO) chain (Yilmaz 2000) to build seismic stacked, simulated zero-offset (ZO) time images of the subsurface. As already discussed elsewhere (Perroud & Tygel 2005), the CRS stack method has both advantages and disadvantages with respect to its alternative approaches. In fact, the adoption of the CRS stack method by the geophysical community has been until now only limited, because the classical NMO-DMO chain already provides good-quality robust results, so the need for a change is not obvious.However, the CRS stack method does not provide only ZO images, but also a set of wavefield attributes (also called CRS parameters: emergence angles and wave front curvatures) that have been exploited in several applications. These include, for example, velocity model building (Della-Moretta et al. 2001;Klüver 2006), multiple attenuation (Prüssmann et al. 2006) or residual statics correction (Koglin et al. 2006).The CRS stack method can be seen as a transformation from the data space (seismic amplitudes as a function of position and time) into attribute space (wavefield attributes as a function of position and time). Note that data space position variables include both midpoint and offset coordinates, while the attribute space position variables consist in the midpoint coordinat...

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Operator-oriented CRS interpolation

Cited by 13 publications

References 0 publications

Common‐offset common‐reflection‐surface attributes estimation with differential evolution

Common‐offset common‐reflection‐surface attributes estimation with differential evolution

A model‐based data‐driven dictionary learning for seismic data representation

Inverse Common-Reflection-Surface

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