Research On POCS Interpolation Method Based On Fourier Transform

Irregular seismic data causes problems with multi-trace processing algorithms and degrades processing quality. We introduce the Projection onto Convex Sets (POCS) based image restoration method into the seismic data reconstruction field to interpolate irregularly missing traces. A projection onto convex sets POCS algorithm using Fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high-quality results.The original2D image restoration method, the POCS algorithm, is extended easily to higher dimensions, and the3D version of the process used here produces much better interpolations than typical2D methods. For entire dead traces, we transfer the POCS iteration reconstruction process from the time to frequency domain to save computational cost because forward and reverse Fourier time transforms are not needed. The only parameter that makes a substantial difference in the results is the number of iterations used, and this number can be overestimated without degrading the quality of the results. This simplicity is a significant advantage because it relieves the user of extensive parameter testing.In each iteration, the selection threshold parameter is important for reconstruction efficiency. And, slow convergence of the POCS reconstruction method could jeopardize its computational appeal. For this reason, we designed four types of threshold models to reconstruct irregularly missing seismic data. The experimental results show that an exponential threshold and inverse threshold can greatly reduce iterations and improve reconstruction efficiency compared to a linear threshold and driven threshold for the same reconstruction result.In addition, we address an important issue with the classical implementations of POCS reconstruction in that they cannot interpolate regularly missing data. To solve this problem, we introduce a masking operator that is based on a dominant dip scanning method into the POCS iteration. First, an angular search in the f-k domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. Last, The mask function is utilized with POCS principle for optimal denoising or interpolation of data. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid.At the end, we present a variant of the POCS method that permits de-noising seismic volumes during the reconstruction stage. This is achieved by defining a weighted trace re-insertion strategy that alleviates the influence of noisy traces in the final reconstruction of the seismic volume.We show the effectiveness of the proposed method using synthetic and field data.