Multistep autoregressive reconstruction of seismic records

Abstract

Linear prediction filters in the [Formula: see text] domain are widely used to interpolate regularly sampled data. We study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters. We propose a two-stage algorithm. First, we reconstruct the unaliased part of the data spectrum using a Fourier method (minimum-weighted norm interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter is implemented via a multistep autoregressive (MSAR) algorithm. Finally, these prediction filters are used to reconstruct the complete data in the [Formula: see text] domain. The applicability of the proposed method is examined using synthetic and field data examples.