A POCS algorithm for spectral extrapolation

Kristopher A. Innanen

Projection-onto-convex-sets or POCS algorithms are used to infill missing seismic data. Applications have generally been on multidimensional interpolation problems. We consider a different type of missing data: the low end of the frequency spectrum. We infill this spectral gap using a POCS algorithm, under the assumption that data events are lagged delta functions. A trace-by-trace implementation, tested on synthetics, confirms the applicability of the idea, and its resiliency to reduced data bandwidth, reasonable clustering-density of events, and uncorrelated noise. Testing on field data with well control is the next logical step. If successful, POCS spectral extrapolation could be a valuable preprocessing tool prior to seismic inversion.