An anti-aliasing POCS interpolation method for regularly undersampled seismic data using curvelet transform

Abstract

Seismic data interpolation are considered the key step in data pre-processing. Most current interpolation methods are just suitable for random undersampled cases. To deal with regular undersampled issue, we propose a novel anti-aliasing Projection Onto Convex Sets (POCS) interpolation method using the curvelet transform. First, we decompose the curvelet transform into two operators: a frequency-wavenumber (f-k) operator and a curvelet tiling operator. These two operators are used to respectively link time-space (t-x) domain to f-k domain, and f-k domain to the curvelet coefficients. In the f-k domain, the two boundaries for dominant dips can be identified by an angular searching within the whole frequency range. Second, we expand the two boundary dips to design a mask function that can eliminate the wraparound aliasing artefacts caused by regular undersampling. Finally, by incorporating the mask function into conventional POCS method, we are able to derive a robust anti-aliasing POCS interpolation method under the curvelet transform. With an exponential threshold model, the satisfactory interpolation result can be obtained by 10–12 iterations. The proposed interpolation method, which has no assumption for linear or quasi-linear events like a Fourier transform-based interpolation method, works for either regularly or randomly undersampled seismic data. Synthetic and real data examples are provided to illustrate the performance of the proposed method.