Seislet transform and seislet frame

Fomel, Sergey; Liu, Yang

doi:10.1190/1.3380591

Cited by 373 publications

(106 citation statements)

References 43 publications

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“…Prediction and update operators for the OC-seislet transform are specified by modifying the biorthogonal wavelet construction in equations 2 and 4 as follows (Fomel, 2006;Fomel and Liu, 2010):…”

Section: Oc-seislet Structurementioning

confidence: 99%

“…We design the transform in the log-stretch-frequency domain, where each frequency slice can be processed independently and in parallel. We expect the new seislet transform to perform better than the previously proposed seislet transform by plane-wave destruction, PWD-seislet transform (Fomel and Liu, 2010), in cases of moderate velocity variations and complex structures that generate conflicting dips in the data.…”

Section: Introductionmentioning

confidence: 99%

“…The curvelet transform in particular has found important applications in seismic imaging and data analysis (Douma and de Hoop, 2007;Chauris and Nguyen, 2008;. Fomel (2006) and Fomel and Liu (2010) investigated the possibility of designing a wavelet-like transform tailored specifically to seismic data and introduced it under the name of the seislet transform. Based on the digital wavelet transform (DWT), the seislet transform follows patterns of seismic events (such as local slopes in 2-D and frequencies in 1-D) when analyzing those events at different scales.…”

Section: Introductionmentioning

confidence: 99%

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OC-seislet: Seislet transform construction with differential offset continuation

Liu

Fomel

2010

GEOPHYSICS

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Many of the geophysical data analysis problems, such as signal-noise separation and data regularization, are conveniently formulated in a transform domain, where the signal appears sparse. Classic transforms such as the Fourier transform or the digital wavelet transform, fail occasionally in processing complex seismic wavefields, because of the nonstationarity of seismic data in both time and space dimensions. We present a sparse multiscale transform domain specifically tailored to seismic reflection data. The new wavelet-like transform -the OC-seislet transform -uses a differential offset-continuation (OC) operator that predicts prestack reflection data in offset, midpoint, and time coordinates. It provides high compression of reflection events. In the transform domain, reflection events get concentrated at small scales. Its compression properties indicate the potential of OC-seislets for applications such as seismic data regularization or noise attenuation. Results of applying the method to both synthetic and field data examples demonstrate that the OC-seislet transform can reconstruct missing seismic data and eliminate random noise even in structurally complex areas.

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Section: Oc-seislet Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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OC-seislet: Seislet transform construction with differential offset continuation

Liu

Fomel

2010

GEOPHYSICS

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“…• F (forward operator) applies predictive painting (Fomel, 2010) to spread information using a known dip field and then subsamples in time (Figure 4.2).…”

Section: Methodsmentioning

confidence: 99%

Improving resolution of NMO stack using shaping regularization

Regimbal

Fomel

2015

SEG Technical Program Expanded Abstracts 2015

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“…where R can be any suitable sparse transform of choice such that the magnitude-sorted coefficients of the vector Rm are of rapid decay (Herrmann et al, 2008;Fomel and Liu, 2010). The optimization problem in equation 2 minimizes the L1-norm of the model in the transformed domain, and ϵ is the tolerance level to which the L2-norm data misfit is minimized.…”

Section: S76 Dutta Et Almentioning

confidence: 99%

Least-squares reverse time migration with local Radon-based preconditioning

et al. 2017

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Least-squares migration (LSM) can produce images with better balanced amplitudes and fewer artifacts than standard migration. The conventional objective function used for LSM minimizes the L2-norm of the data residual between the predicted and the observed data. However, for field-data applications in which the recorded data are noisy and undersampled, the conventional formulation of LSM fails to provide the desired uplift in the quality of the inverted image. We have developed a leastsquares reverse time migration (LSRTM) method using local Radon-based preconditioning to overcome the low signal-tonoise ratio (S/N) problem of noisy or severely undersampled data. A high-resolution local Radon transform of the reflectivity is used, and sparseness constraints are imposed on the inverted reflectivity in the local Radon domain. The sparseness constraint is that the inverted reflectivity is sparse in the Radon domain and each location of the subsurface is represented by a limited number of geologic dips. The forward and the inverse mapping of the reflectivity to the local Radon domain and vice versa is done through 3D Fourier-based discrete Radon transform operators. The weights for the preconditioning are chosen to be varying locally based on the relative amplitudes of the local dips or assigned using quantile measures. Numerical tests on synthetic and field data validate the effectiveness of our approach in producing images with good S/N and fewer aliasing artifacts when compared with standard RTM or standard LSRTM.

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Seislet transform and seislet frame

Abstract: We introduce a digital wavelet-like transform, which is tailored specifically for representing seismic data.

Cited by 373 publications

References 43 publications

OC-seislet: Seislet transform construction with differential offset continuation

OC-seislet: Seislet transform construction with differential offset continuation

Improving resolution of NMO stack using shaping regularization

Least-squares reverse time migration with local Radon-based preconditioning

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