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Randomized marine acquisition with compressive sampling matrices
Author(s) -
Mansour Hassan,
Wason Haneet,
Lin Tim T.Y.,
Herrmann Felix J.
Publication year - 2012
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2012.01075.x
Subject(s) - compressed sensing , computer science , dither , data acquisition , sampling (signal processing) , fourier transform , algorithm , matrix (chemical analysis) , mathematics , computer vision , materials science , bandwidth (computing) , telecommunications , mathematical analysis , filter (signal processing) , operating system , composite material
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.