Zhaojun Liu, University of Utah
The acquisition footprint noise in migrated sections consists of migration artifacts associated with a discrete recording geometry. Such noise can corrupt the interpretation of seismic sections for Amplitude Variation with Offset (AVO) studies and enhanced oil recovery operations. I show that the point scatterer response of the farfield Kirchhoff migration operator, which reveals the acquisition footprint noise, is proportional to the stretched Fourier transform of the source and geophone sampling function. Using the Array theorem developed by Optical/Electrical Engineers, the Fourier transform for an orthogonal recording geometry can be quickly calculated by a concatenation of 1-D analytical functions. I use the so-called Seismic Array theorem to rapidly calculate the acquisition footprint noise for different seismic surveys. The results of numerical tests for monochronic and transient sources show that the Seismic Array theorem image is a good approximation to the Kirchhoff migration image. By a rapid trial and error procedure, I use this theorem to determine the best shooting geometries from a variety of seismic survey geometries. Because of the high computing efficiency of the Seismic Array theorem, I also present a constrained optimization method that seeks to identify the optimal survey design. In this procedure, the aperture size and number of traces are constrained and the optimization algorithm searches for the receiver and source spacings that minimize the alias energy of the acquisition footprint. Examples with actual field data geometries show a rapid convergence to the optimal survey geometry, and this geometry results in a significantly reduced acquisition footprint relative to that for the starting geometry.