Two-step equalization of irregular data

Nizar Chemingui and Biondo Biondi

nizar@sep.stanford.edu, biondo@sep.stanford.edu

ABSTRACT

Sampling irregularities in seismic data may introduce noise, cause amplitude distortions and even structural distortions when wave equation processes such as dip moveout, azimuth moveout, and prestack migration are applied. Data regularization before imaging becomes a processing requirement to preserve amplitude information and produce a good quality final image. We propose a new technique to invert for reflectivity 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 AMO transformation. The filter is therefore a symmetric AMO matrix with diagonal elements being the identity and the off-diagonal elements being the trace-to-trace AMO transforms. We explore the effectivness of the method in the 2D case for the application of partial stacking by offset continuation. The equalization step followed by imaging has proved to correct and equalize the processing for the effects of fold variations.