An Efficient POCS Interpolation Method in the Frequency-Space Domain

Abstract

Sampling irregularity in observed seismic data may cause a significant complexity increase in subsequent processing. Seismic data interpolation helps in removing this sampling irregularity, for which purpose complex-valued curvelet transform is used, but it is time-consuming because of the huge size of observed data. In order to improve efficiency as well as keep interpolation accuracy, I first extract principal frequency components using forward Fourier transform. The size of the principal frequency-space domain data is at least halved compared with that of the original time-space domain data because the complex-valued components of the representation of a real-valued signal (i.e., a complex-valued signal with zero as its imaginary component) exhibit conjugate symmetry in the frequency domain. Then, the projection onto convex projection (POCS) method is used to interpolate frequency-space data based on complex-valued curvelet transform. Finally, interpolated seismic data in the time-space domain can be obtained using inverse Fourier transform. Synthetic data and field data examples show that the efficiency can be improved more than two times and the performance is slightly better in the frequency-space domain compared with the POCS method directly performed in the time-space domain, which demonstrates the validity of the proposed method.