SP 3.6 Equalization of irregular data by iterative inversion

Sampling irregularities in seismic data may introduce noise, cause am-plitude distortions and even structural distortions when wave equation processes such as dip moveout, azimuth moveout, and prestack migra-tion are applied. Data regularization before imaging becomes a pro-cessing requirement to preserve amplitude information and produce a good quality final image. We propose a new technique to invert for re-flectivity models while correcting for the effects of irregular sampling. The final reflectivity model is a two-step solution where the data is equalized in a first stage with an inverse filter and an imaging operator is then applied to the equalized data to invert for a model. Based on least-squares theory, the solution estimates an equalization filter that corrects the imaging operator for the interdependencies between data elements. Each element of the filter is a mapping between two data elements. It reconstructs a data trace with given input geometry at the geometry of the other data element. This mapping represents an AM