none 10.1190/1.3506147 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 46189994 5981 2025121111482688000 10.1190 2025-12-11T16:48:37Z 2010-12-22T19:24:35Z 171 Geophysics 1942-2156 0016-8033 11 2010 01 01 2010 75 6 Felix J. Herrmann 1University of British Columbia, Department of Earth and Ocean Sciences, Seismic Laboratory for Imaging and Modeling, Vancouver, Canada. E-mail: fherrmann@eos.ubc.ca. Abstract Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. Although this approach has been extremely successful in the past, current efforts toward higher-resolution images in increasingly complicated regions of the earth continue to reveal fundamental shortcomings in our workflows. Chiefly among these is the so-called “curse of dimensionality” exemplified by Nyquist's sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continue to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing toward seismic acquisition and processing for data that are traditionally considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are no longer determined by overly stringent sampling criteria, such asNyquist. At the heart of our approach lies randomized incoherent sampling that breaks subsampling related interferences by turning them into harmless noise, which we subsequently remove by promoting transform-domain sparsity. Now, costs no longer grow significantly with resolution and dimensionality of the survey area, but instead depend only on transform-domain sparsity. Our contribution is twofold. First, we demonstrate by means of carefully designed numerical experiments that compressive sensing can successfully be adapted to seismic exploration. Second, we show that accurate recovery can be accomplished for compressively sampled data volumes sizes that exceed the size of conventional transform-domain data volumes by only a small factor. Because compressive sensing combines transformation and encoding by a single linear encoding step, this technology is directly applicable to acquisition and to dimensionality reduction during processing. In either case, sampling, storage, and processing costs scale with transform-domain sparsity. We illustrate this principle by means of number of case studies. 11 2010 01 01 2010 12 22 2010 WB173 WB187 10.1190/1.3506147 https://pubs.geoscienceworld.org/geophysics/article/75/6/WB173/73891/Randomized-sampling-and-sparsity-Getting-more https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/75/6/WB173/3235525/gsgpy_75_6_WB173.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/75/6/WB173/3235525/gsgpy_75_6_WB173.pdf http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.3506147 Geophysics Abma 71 6 E91 2006 10.1190/1.2356088 3D interpolation of irregular data with a POCS algorithm Presented at the Allerton Conference on Communication, Control, and Computing Asif 2009 10.1109/ALLERTON.2009.5394881 Random channel coding and blind deconvolution The Leading Edge Beasley 27 914 2008 10.1190/1.2954033 A new look at marine simultaneous sources 68th Annual International Meeting Beasley 133 1998 A new look at simultaneous sources Berg 2008 Probing the Pareto frontier for 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