Application of Compressive Sensing to 3D-VSP Acquisition and Processing

From the viewpoint of classical sampling theory, 3D-VSP surveys are normally under-sampled over the shot and receiver axes. Because of this, strong acquisition footprints are commonly seen on migrated 3D depth slices in both pre- and post-stack domains. These image artefacts are usually considered to be acceptable, since they typically don’t prevent the asset team from deciding on further drilling objectives and mitigation via increased source effort is very costly. It has been recognized for some time that conventional offset VSP images can be improved by irregular depth sampling of borehole receivers. More recently, it was discovered that image improvements from randomized sampling can be understood through the theory of compressive sensing (CS) and that source-axis bandwidth can also be improved by irregular sampling of the surface shot locations. Survey spatial bandwidth is, in fact, optimized in the CS sense when shot sampling is chosen to have “minimum mutual coherence” Candes and Wakin (2008), Tang et al (2008). Improved bandwidth for equivalent source effort is one important use of compressive sampling. The big win for 3D-VSP, however, is that CS can also be used to separate or “de-blend” two or more independent sources acquired simultaneously in time. This technique is a particularly cost-effective application when source acquisition costs are dominated by rig time and can be extremely high.