Randomized marine acquisition with compressive sampling matrices

Abstract

Seismic data acquisition in marine environments is a costly process that calls for the adoption of simultaneous‐source or randomized acquisition ‐ an emerging technology that is stimulating both geophysical research and commercial efforts. Simultaneous marine acquisition calls for the development of a new set of design principles and post‐processing tools. In this paper, we discuss the properties of a specific class of randomized simultaneous acquisition matrices and demonstrate that sparsity‐promoting recovery improves the quality of reconstructed seismic data volumes. We propose a practical randomized marine acquisition scheme where the sequential sources fire airguns at only randomly time‐dithered instances. We demonstrate that the recovery using sparse approximation from random time‐dithering with a single source approaches the recovery from simultaneous‐source acquisition with multiple sources. Established findings from the field of compressive sensing indicate that the choice of the sparsifying transform that is incoherent with the compressive sampling matrix can significantly impact the reconstruction quality. Leveraging these findings, we then demonstrate that the compressive sampling matrix resulting from our proposed sampling scheme is incoherent with the curvelet transform. The combined measurement matrix exhibits better isometry properties than other transform bases such as a non‐localized multidimensional Fourier transform. We illustrate our results with simulations of ‘ideal’ simultaneous‐source marine acquisition, which dithers both in time and space, compared with periodic and randomized time‐dithering.

Efficient least‐squares imaging with sparsity promotion and compressive sensing

“…Because our formulation includes contributions from the wave-equation Hessian more theoretical work will be necessary to (i) compensate for the 'colouring' by this operator, e.g., by solving weighted 1 -norm problems and (ii) analyse the coherence and restricted-isometry properties of the dimensionality reduced Hessian, using practical techniques recently developed by Mansour et al (2011). These latter results are particularly exciting because they allow for:…”

Separation of simultaneous source data via iterative rank reduction

“…Coherent pass filters in τ − p, f − k and f − x domains were developed to filter out incoherent interferences (Akerberg et al, 2008;Moore et al, 2008;Huo et al, 2009;Maraschini et al, 2012). Better separation was achieved with inversion methods based on projecting the data to other domains where the coherent constraints can be effectively implemented (Abma et al, 2010;Mahdad et al, 2011;Lin and Herrmann, 2009;Mansour et al, 2012).…”

Time-jittered ocean bottom seismic acquisition

“…With the appropriate data transformation, we can capture this structure by a small number of significant transform coefficients resulting in a sparse representation of data. In our work, we rely on the CS literature to analyze a physically realizable time-jittered (multiplesource) marine acquisition scheme, and recover the canonical sequential single-source (interference-free/deblended) data by solving a sparsity-promoting problem (Mansour et al, 2012;Wason and Herrmann, 2012). Hence, we develop the relation between blended acquisition design and (curvelet-based) sparse recovery, within the CS framework.…”