Matrix Completion on Unstructured Grids - 2-D Seismic Data Regularization and Interpolation

Kumar, Rajiv; López, Oscar; Esser, Ernie; Herrmann, Felix J.

doi:10.3997/2214-4609.201413448

Cited by 8 publications

(2 citation statements)

References 6 publications

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“…By choosing a value for h, we now deal with a single offset (or offset bin) volume, resulting in a 3D dataset. Some low-rank approaches for data recovery attempt to honour the true coordinates (Kumar et al, 2015;Carozzi and Sacchi, 2021), often through a combination with other procedures, such as the irregular Fourier transform. Here we only consider irregularly spaced data at a regular interval (regular grid) in x i = i x, i = 1, .…”

Section: Multidimensional Seismic Datamentioning

confidence: 99%

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Cavalcante

Porsani

2021

Geophysical Prospecting

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Low-rank reconstruction methods assume that noiseless and complete seismic data can be represented as low-rank matrices or tensors. Therefore, denoising and recovery of missing traces require a reduced-rank approximation of the data matrix/tensor. To calculate such approximation, we explore the CUR matrix decompositions, which use actual columns and rows of the data matrix, instead of the costly singular vectors derived from singular value decomposition. By allowing oversampling columns and rows, CUR decompositions obviate the need for the exact rank. We evaluate three different procedures for randomly selecting columns and rows to obtain the CUR. Once the low-rank approximation is estimated, data reconstruction is achieved by an iterative optimization scheme. To demonstrate the effectiveness of CUR matrix decompositions for multidimensional seismic data recovery, we present examples of 3D and 4D synthetic and field data. Results derived by CUR compare well to conventional eigenimage-family methods.

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Section: Multidimensional Seismic Datamentioning

confidence: 99%

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Cavalcante

Porsani

2021

Geophysical Prospecting

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“…This work builds upon the ideas of off-the-grid regularized matrix completion for seismic data with missing traces in Kumar et al (2014) and extends the regularization approach to the 3D data case. Other approaches to regularized interpolation include the Antileakage Fourier Transform (AFT) in Xu et al (2005), Interpolated Compressed Sensing (ICS) in Li et al (2012), and Non-uniform Curvelets (NCT) in Hennenfent et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Off the Grid Tensor Completion for Seismic Data Interpolation

Silva¹,

Herrmann²

2015

Proceedings

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The practical realities of acquiring seismic data in a realistic survey are often at odds with the stringent requirements of Shannon-Nyquist-based sampling theory. The unpredictable movement of the ocean's currents can be detrimental in acquiring exactly equally-spaced samples while sampling at Nyquist-rates are expensive, given the huge dimensionality and size of the data volume. Recent work in matrix and tensor completion for seismic data interpolation aim to alleviate such stringent Nyquist-based sampling requirements but are fundamentally posed on a regularly-spaced grid. In this work, we extend our previous results in using the so-called Hierarchical Tucker (HT) tensor format for recovering seismic data to the irregularly sampled case. We introduce an interpolation operator that resamples our tensor from a regular grid (in which we impose our low-rank constraints) to our irregular sampling grid. Our framework is very flexible and efficient, depending primarily on the computational costs of this operator. We demonstrate the superiority of this approach on a realistic BG data set compared to using low-rank tensor methods that merely use binning.

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Ultrasonic detection of contour node represented voids and cracks

Yan

2018

Nondestructive Testing and Evaluation

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Matrix Completion on Unstructured Grids - 2-D Seismic Data Regularization and Interpolation

Cited by 8 publications

References 6 publications

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Off the Grid Tensor Completion for Seismic Data Interpolation

Ultrasonic detection of contour node represented voids and cracks

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