Beating Level-Set Methods for 5-D Seismic Data Interpolation: A Primal-Dual Alternating Approach

Abstract

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to 'fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques.We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume using matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5D seismic data volume, generated from the geologically complex synthetic 3D Compass velocity model, where 80% of the data has been removed.

Spectral Gap-Based Seismic Survey Design

“…To address 1), several reorganizations and transformations of seismic data tensors into matrices have been shown to expunge low-rank structure [22,16]. Furthermore, for 2) efficient methodologies have been proposed to solve the matrix completion problem with large matrices [1,23,21], including on parallel architectures [4,15]. However, it is not clear how to fulfill 3) in an practical manner.…”

Anti-Aliasing Add-On For Deep Prior Seismic Data Interpolation

“…Besides traditional processing methods such as transform representations [4,5,6], low-rank approximation [7], multichannel singular spectrum analysis (MSSA) [8] and its interpolated version I-MSSA [9], many seismic interpolation methods based on Convolutional Neural Networks (CNNs) have been proposed [10,11,12,13] A different approach has been proposed interpreting the CNN architecture as a Deep Prior, in the framework of inverse problems, to address tasks such as interpolation, denoising or super-resolution [14]. In this paradigm, the CNN learns the inner structure of a 2D image from the corrupted data itself, without pre-training: this prevents any over-fitting issue as well as the need for training data.…”

“…Besides traditional processing methods such as transform representations [4,5,6], low-rank approximation [7], multichannel singular spectrum analysis (MSSA) [8] and its interpolated version I-MSSA [9], many seismic interpolation methods based on Convolutional Neural Networks (CNNs) have been proposed [10,11,12,13]. However, the vast majority of CNN-based methods work according to a training paradigm.…”

Basis Pursuit Denoise With Nonsmooth Constraints

“…Seismic data is a key use case [3], [15], [9], where acquisition is prohibitively expensive and interpolation techniques are used to fill in data volumes by promoting parsimonious representations in the Fourier [19] or Curvelet [12] domains. Matricization of the data leads to low-rank interpolation schemes [3], [15], [9], [24].…”

“…BPDN and the closely related LASSO formulation have applications to compressed sensing [18], [6] and machine learning [11], [10], as well as to applied domains including MRI [16]. Seismic data is a key use case [3], [15], [9], where acquisition is prohibitively expensive and interpolation techniques are used to fill in data volumes by promoting parsimonious representations in the Fourier [19] or Curvelet [12] domains. Matricization of the data leads to low-rank interpolation schemes [3], [15], [9], [24].…”