Trace interpolation for irregularly sampled seismic data using curvelet-transform-based projection onto convex sets algorithm in the frequency-wavenumber domain

In recent years, many studies have been performed to reconstruct traces missing from irregularly undersampled seismic data. In this paper, we introduce a new curvelet-transform-based projection onto convex sets (POCS) algorithm that applies the curvelet transform to 2D Fourier-transformed data in the f-k domain instead of data in the t-x domain for each iteration of the POCS algorithm. To verify the efficiency of the suggested method, it was applied to synthetic data generated using the Marmousi2 and Hess vertically transverse isotropy (VTI) models. The results clearly demonstrate that the presented algorithm, which applies the curvelet transform to data in the f-k domain, is superior to conventional POCS and curvelet-transform-based POCS in the t-x domain, especially for reconstructing events with diverse directions and various amplitudes. (C) 2015 Elsevier B.V. All rights reserved.