Seismic array theorem and rapid calculation of acquisition footprint noise

Abstract

The acquisition footprint noise in migrated sections partly consists of migration artifacts associated with a discrete recording geometry. Such noise can corrupt the interpretation of seismic sections for stratigraphic variations, AVO signatures, and enhanced oil recovery operations. We show that the point scatterer response of the far‐field Kirchhoff migration operator, which reveals acquisition footprint noise, is proportional to the stretched Fourier transform of the source and geophone sampling function. Using the array theorem developed by optical and electrical engineers, this Fourier transform for an orthogonal recording geometry can be calculated quickly by a product of 1‐D analytical functions. Thus, the acquisition footprint noise in migrated sections can be calculated efficiently for different recording arrays. By rapid trial and error or by an optimization method, the survey planner can use this theorem to help design a better recording geometry.