Reconstruction of 3D non-uniformly sampled seismic data along two spatial coordinates using non-equispaced curvelet transform

Abstract

Seismic data acquisition often faces the challenge of non-uniformly sampled data with missing traces. Only a few existing multitrace reconstruction methods can natively handle non-uniformly sampled data with missing traces. In this paper, we propose the non-equispaced fast discrete curvelet transform (NFDCT)-based reconstruction method designed for 3D seismic data that are non-uniformly sampled along two spatial coordinates. By partitioning 3D seismic datasets into time slices along source-receiver coordinates, we introduce 2D non-equispaced fast Fourier transform in the conventional fast discrete curvelet transform and formulate a regularised inversion of operator that links the uniformly sampled curvelet coefficients to non-uniformly sampled data. Numerically, the uniform curvelet coefficients are calculated by solving the L1-norm problem via the spectral projected-gradient algorithm. With the uniform curvelet coefficients, the NFDCT is formed via the conventional inverse curvelet transform and is used to reconstruct 3D non-uniformly sampled seismic data along two spatial coordinates. At the hand of reconstructed results from synthetic and field data, we demonstrate that the proposed method shows significant improvement over the conventional anti-leakage Fourier transform-based reconstruction method. The method we propose, which has a strong anti-aliasing and anti-noise ability, can be used to reconstruct the subset of observed data to a specified uniform grid along two spatial coordinates.