Seismic data reconstruction using multidimensional prediction filters

In this paper we discuss a beyond-alias multidimensional implementation of the multi-step autoregressive reconstruction algorithm for data with missing spatial samples. The multi-step autoregressive method is summarized as follows: vital low-frequency information is first regularized adopting a Fourier based method (minimum weighted norm interpolation); the reconstructed data are then used to estimate prediction filters that are used to interpolate higher frequencies. This article discusses the implementation of the multi-step autoregressive method to data with more than one spatial dimension. Synthetic and real data examples are used to examine the performance of the proposed method. Field data are used to illustrate the applicability of multidimensional multi-step autoregressive operators for regularization of seismic data.