Low-cost time-lapse seismic with distributed compressive sensing - Part 2: Impact on repeatability

Irregular or off-the-grid spatial sampling of sources and receivers is inevitable in field seismic acquisitions. Consequently, time-lapse surveys become particularly expensive because current practices aim to replicate densely sampled surveys for monitoring changes occurring in the reservoir due to hydrocarbon production. We have determined that under certain circumstances, high-quality prestack data can be obtained from cheap randomized subsampled measurements that are observed from nonreplicated surveys. We extend our time-jittered marine acquisition to time-lapse surveys by designing acquisition on irregular spatial grids that render simultaneous, subsampled, and irregular measurements. Using the fact that different time-lapse data share information and that nonreplicated surveys add information when prestack data are recovered jointly, we recover periodic densely sampled and colocated prestack data by adapting the recovery method to incorporate a regularization operator that maps traces from an irregular spatial grid to a regular periodic grid. The recovery method is, therefore, a combined operation of regularization, interpolation (estimating missing fine-grid traces from subsampled coarse-grid data), and source separation (unraveling overlapping shot records). By relaxing the insistence on replicability between surveys, we find that recovery of the time-lapse difference shows little variability for realistic field scenarios of slightly nonreplicated surveys that suffer from unavoidable natural deviations in spatial sampling of shots (or receivers) and pragmatic compressed-sensing-based nonreplicated surveys when compared with the "ideal" scenario of exact replicability between surveys. Moreover, the recovered densely sampled prestack baseline and monitor data improve significantly when the acquisitions are not replicated, and hence they can serve as input to extract poststack attributes used to compute time-lapse differences. Our observations are based on experiments conducted for an ocean-bottom cable survey acquired with time-jittered continuous recording assuming source equalization (or the same source signature) for the time-lapse surveys and no changes in wave heights, water column velocities or temperature, and salinity profiles.