Seismic Data Regularization in the Presence of Aliased Energy

Many different techniques have been developed to produce a regularly sampled, unaliased data set from irregularly sampled, aliased data. Almost all techniques to correct for the aliased energy rely on the assumption that it wraps around in the frequency-wavenumber spectrum of the data, and that it can be easily removed or unwrapped. However, different sampling geometries have an effect on the way aliased energy is distributed in the spectrum of the data. In this paper we present a case study where synthetic data are produced for a number of different sampling geometries varying from regular to almost random sampling. For every data set the spatial appearance of aliased energy is analyzed. The results of this study clearly show that the sampling influences that appearance. The assumption that the aliased energy wraps around is only correct for regular or nearly regular sampling, but it does not hold for more irregular sampling geometries. Based on these findings we propose to carefully revise the de-aliasing techniques applied in current regularization methods and, where appropriate, replace them with an approach that handles the aliased energy in a sampling-dependent way.