Deconvolution of the Recording Footprint Noise in Migration Images

A data processing scheme is proposed to deconvolve the recording footprint noise in the migration image. For computational convenience, we assume a far eld approximation and shift invariance in the Greens function. Preliminary results with synthetic data show that the footprint signature can be partially suppressed by deconvolution with the migration Greens function. However, much work needs to be done before we prove the feasibility of this method on eld data. INTRODUCTION One of the major goals of seismic explorationists is to obtain high resolution images of subsurface structures. Towards this goal, di erent survey methods and data processing techniques have been developed in the past decade. Due to economic reasons, the survey designer 1 has to deal with both the geophysical problem and the cost, which can result in a compromised survey design. Such compromises can take the form of coarse geophone or source intervals, which can introduce artifacts into the migration image. In a 3-D survey, these artifacts are sometimes known as the recording footprint noise. Obviously, a dense survey con guration is an e ective but expensive solution to this footprint noise problem. An alternative to minimizing the footprint noise is use the Greens function for migration to deconvolve the footprint. In this paper, I report my results for deconvolving the footprint noise from synthetic data by using the inverse to the Greens function for migration. THE PRINCIPLE OF FOOTPRINT ELIMINATION The migrated image associated with primary re ection data can be represented (Schuster, 1996) by m(r ~ ) = Z G(r ~ j r ~ o)R(r ~ o)dr ~ o; (1) where m(r ~ ) is the migrated image at r ~ , G(r ~ j r ~ o) is the migration Greens function, R(r ~ o) is the re ectivity strength at r ~ o, and is the volume associated with a half space. The goal is to reconstruct R(r ~ o), which is free of migration artifacts, by the following equation: R(r ~ o) Z G>(r ~ o j r ~ )R(r ~ )dr ~ (2) where G>(r ~ o j r ~ ) is an inversion kernel. Equation 1 says that the migrated image at r ~ is coupled to all of the scatterers in the half