Why Ricker wavelets are successful in processing seismic data: Towards a theoretical explanation

Gholamy, Afshin; Kreinovich, Vladik

doi:10.1109/cies.2014.7011824

Cited by 45 publications

(24 citation statements)

References 17 publications

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“…for an example of approximating equation using equation . Besides effectively capturing the support of equation , equation is a multi‐variate generalisation of Ricker wavelet, whose practical success was supported with the recent theoretical study (Gholamy and Kreinovich ).…”

Section: Numerical Example In (1 + 1)dmentioning

confidence: 94%

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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Section: Numerical Example In (1 + 1)dmentioning

confidence: 94%

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

Yarman

Kumar

2017

Geophysical Prospecting

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“…Zhou et al (2016) following Rosa and Ulrych (1991) approximated a smooth wavelet amplitude spectrum with a low order exponentiated polynomial up to seventh order. In this paper, inspired by the original Ricker's paper (Ricker, 1953) and the more recent discussions on Ricker wavelet by Gholamy and Kreinovich (2014), Multi-Ricker wavelet spectral modeling (MRA) is proposed in approximating the smooth wavelet amplitude spectrum at each time sample in the S-transform domain. In this scheme, the signal spectrum is simply described as a linear combination of Ricker wavelet spectra with different peak frequencies as shown in Figures 4 and 5.…”

Section: Estimation Of Time-variant Wavelet Using Multi-ricker Spectrmentioning

confidence: 99%

Multi-Ricker Spectral Modeling in the S-transform Domain for Enhancing Vertical Resolution of Seismic Reflection Data

Winardhi

Pranowo

2019

Indonesian J. Geosci.

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A relatively straightforward methodology is presented for extending seismic bandwidth, and hence enhancing the seismic resolution by performing time-variant deconvolution. The generalized S-transform (GST) approach is used in order to properly compute the time-frequency components of the seismic reflection trace. In estimating the time-variant wavelet, a spectral modeling method is proposed, named multi-Ricker spectral approximation (MRA). After obtaining the estimated wavelet spectrum at each time sample, a deconvolution filter can then be built and applied in the S-transform domain. This proposed time-variant seismic enhancement method needs neither information on subsurface attenuation model nor assumption that the subsurface reflectivity is random. It is a data-driven methodology which is based on the seismic data only. This proposed method is validated on a noise-free and noisy synthetics and also applied to a field data. Results show that, after enhancement, overall seismic bandwidth can be extended resulting in a higher vertical resolution. Correlation with VSP corridor stack at well location ensures that the generated reflection details after enhancement are geologically plausible.

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“…The shape of the transmitted signal is Ricker Wavelet [35]. Combining this with the hall of mirrors effect results in a "wavy" signal, where the multiple wavelets are visible in the A-Scan.…”

Section: Multi Layered Mediummentioning

confidence: 99%

Automated Target Detection for Geophysical Applications

Peer

2017

IEEE Trans. Geosci. Remote Sensing

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Why Ricker wavelets are successful in processing seismic data: Towards a theoretical explanation

Cited by 45 publications

References 17 publications

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

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

Multi-Ricker Spectral Modeling in the S-transform Domain for Enhancing Vertical Resolution of Seismic Reflection Data

Automated Target Detection for Geophysical Applications

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