Accurate and efficient seismic data interpolation in the principal frequency wavenumber domain

Seismic data irregularity caused by economic limitations, acquisition environmental constraints or bad trace elimination, can decrease the performance of the below multi-channel algorithms, such as surface-related multiple elimination (SRME), though some can overcome the irregularity defects. Therefore, accurate interpolation to provide the necessary complete data is a pre-requisite, but its wide applications are constrained because of its large computational burden for huge data volume, especially in 3D explorations. For accurate and efficient interpolation, the curvelet transform- (CT) based projection onto convex sets (POCS) method in the principal frequency wavenumber (PFK) domain is introduced. The complex-valued PF components can characterize their original signal with a high accuracy, but are at least half the size, which can help provide a reasonable efficiency improvement. The irregularity of the observed data is transformed into incoherent noise in the PFK domain, and curvelet coefficients may be sparser when CT is performed on the PFK domain data, enhancing the interpolation accuracy. The performance of the POCS-based algorithms using complex-valued CT in the time space (TX), principal frequency space, and PFK domains are compared. Numerical examples on synthetic and field data demonstrate the validity and effectiveness of the proposed method. With less computational burden, the proposed method can achieve a better interpolation result, and it can be easily extended into higher dimensions.

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