Fast high‐resolution Radon transforms by greedy least‐squares method

Wang, Juefu; Ng, Mark; Perz, Mike

doi:10.1190/1.3255506

Cited by 14 publications

(5 citation statements)

References 7 publications

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“…for increasing the resolution of the migrated seismic images [32]. The interpolation of seismic data based on sparse transforms constitutes the most popular methods, such as the Fourier [34,32,25], Radon [38], and curvelet transform [30]. Noise attenuation can be classified into random noise attenuation [33,9] and correlated noise attenuation, such as multiple [37,16] and ground-roll attenuation [31].…”

Section: 2mentioning

confidence: 99%

Geometric mode decomposition

Yu¹,

Ma²,

Osher³

2018

Inverse Problems &Amp; Imaging

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We propose a new decomposition algorithm for seismic data based on a band-limited a priori knowledge on the Fourier or Radon spectrum. This decomposition is called geometric mode decomposition (GMD), as it decomposes a 2D signal into components consisting of linear or parabolic features. Rather than using a predefined frame, GMD adaptively obtains the geometric parameters in the data, such as the dominant slope or curvature. GMD is solved by alternatively pursuing the geometric parameters and the corresponding modes in the Fourier or Radon domain. The geometric parameters are obtained from the weighted center of the corresponding mode's energy spectrum. The mode is obtained by applying a Wiener filter, the design of which is based on a certain band-limited property. We apply GMD to seismic events splitting, noise attenuation, interpolation, and demultiple. The results show that our method is a promising adaptive tool for seismic signal processing, in comparisons with the Fourier and curvelet transforms, empirical mode decomposition (EMD) and variational mode decomposition (VMD) methods.

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Section: 2mentioning

confidence: 99%

Geometric mode decomposition

Yu¹,

Ma²,

Osher³

2018

Inverse Problems &Amp; Imaging

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“…The most commonly used transformations are the Fourier transform ͑Sacchi and Ulrych, 1996; Sacchi et al, 1998;Duijndam et al, 1999;Xu et al, 2005;Zwartjes andGisolf, 2006͒, the Radon transform ͑Darche, 1990;Kabir and Verschuur, 1995;Trad et al, 2002͒, the local Radon transform ͑Sacchi et al, 2004Wang et al, 2009͒, andthe curvelet transform ͑Hennenfent andHerrmann and Hennenfent, 2008͒. Another group of signal-processing interpolation methods relies on prediction-error filtering techniques ͑Wig-gins and Miller, 1972͒.…”

Section: Introductionmentioning

confidence: 98%

Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data

2010

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We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform. In a first pass, the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data. The aforementioned coefficients are divided into two groups of scales: alias-free and alias-contaminated scales. The alias-free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias-contaminated scale coefficients. The mask function is incorporated into the inversion via a minimum norm least-squares algorithm that determines the curvelet coefficients of the desired aliasfree data. Once the alias-free coefficients are determined, the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions. The proposed method can be used to reconstruct regularly and irregularly sampled seismic data. We believe that our exposition leads to a clear unifying thread between f-x and f-k beyond-alias interpolation methods and curvelet reconstruction. As in f-x and f-k interpolation, we stress the necessity of examining seismic data at different scales ͑frequency bands͒ to come up with viable and robust interpolation schemes. Synthetic and real data examples are used to illustrate the performance of the proposed curvelet interpolation method.

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“…These include Radon transform (e.g. Lu, 1985; Turner, 1990; Trad et al ., 2002; Sacchi et al ., 2004; Yu et al ., 2007; Wang et al ., 2009; Ibrahim et al ., 2015), curvelet transform (e.g. Herrmann & Hennenfent, 2008; Naghizadeh & Sacchi, 2010), seislet transform (Liu & Fomel, 2010; Gan et al ., 2015, 2016), and also shaping regularization techniques (e.g.…”

Section: Introductionmentioning

confidence: 99%

Oriented extrapolation of common‐midpoint gathers in the absence of near‐offset data using predictive painting

Khoshnavaz

2022

Geophysical Prospecting

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Seismic reconstruction of missing traces is an extremely important subject in seismic data processing. It includes both interpolation and extrapolation of sparsely recorded data. Extrapolation is often performed in the absence of near-offset seismic data recorded through marine acquisition. Several reconstruction methods have been designed to circumvent this sparsity in time-offset, frequency-offset and timefrequency domains. In this research, I propose an oriented extrapolation workflow to reconstruct near-offset missing traces. The term oriented or velocity-independent refers to those techniques that are based on the use of local slopes. In the proposed workflow, I use an oriented time-warping algorithm called predictive painting. This algorithm is suitable to predict two-way traveltimes between two distinctive points of an event. Seismic events recorded by an off-end array very rarely contain dips of both signs with respect to their zero-offset location in common-midpoint domain. This makes the domain an ideal choice to run the algorithm. The proposed algorithm is demonstrated on synthetic and field data examples. I decimate near-offset seismic traces and reconstruct them through the algorithm. The reconstruction results are compared with the original data before decimation. Furthermore, insensitivity of the proposed workflow to the presence of class II amplitude-versus-offset anomalies is demonstrated on a synthetic example. I also perform a velocity-dependent (a normalmoveout-based) technique on the field data and compare the corresponding outcomes with the results achieved by the application of the proposed velocity-independent approach. All the results suggest that the proposed technique has the potential to be used in the exploration industry.

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Fast high‐resolution Radon transforms by greedy least‐squares method

Cited by 14 publications

References 7 publications

Geometric mode decomposition

Geometric mode decomposition

Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data

Oriented extrapolation of common‐midpoint gathers in the absence of near‐offset data using predictive painting

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