Sparsity-promoting recovery from simultaneous data: a compressive sensing approach

Seismic data acquisition forms one of the main bottlenecks in seismic imaging and inversion. The high cost of acquisition work and collection of massive data volumes compel the adoption of simultaneous-source seismic data acquisition - an emerging technology that is developing rapidly, stimulating both geophysical research and commercial efforts. Aimed at improving the performance of marine- and land-acquisition crews, simultaneous acquisition calls for development of a new set of design principles and post-processing tools. Leveraging developments from the field of compressive sensing the focus here is on simultaneous-acquisition design and sequential-source data recovery. Apart from proper compressive sensing sampling schemes, the recovery from simultaneous simulations depends on a sparsifying transform that compresses seismic data, is fast, and reasonably incoherent with the compressive-sampling matrix. Using the curvelet transform, in which seismic data can be represented parsimoniously, the recovery of the sequential-source data volumes is achieved using the sparsity-promoting program — SPGL1, a solver based on projected spectral gradients. The main outcome of this approach is a new technology where acquisition related costs are no longer determined by the stringent Nyquist sampling criteria.