Seismic data reconstruction based on jittered sampling and curvelet transform

Traditional seismic data sampling must follow the Nyquist sampling theorem, while the field data acquisition can't meet the sampling theorem due to missing traces or exploration cost limit, so there exits data reconstruction problem. In this paper, based on the theory of compressed sensing, we render coherent aliases of regular under-sampling into harmless incoherent random noise using the random under-sampling, effectively turning the reconstruction problem into a much simpler de-noising problem. We introduce the Projections Onto Convex Sets (POCS) algorithm during the process of reconstruction, choosing the square root exponentially decreased threshold, constructing a curvelet-based recovery strategy of 3D seismic data. At the same time, aiming at the deficiency of simple random under-sampling, we introduce the jittered under-sampling, it shares the benefits of random sampling and controls the maximum gap size. Experiments show that reconstruction effect based on curvelet is better than FFT transform and jittered under-sampling is better than random under-sampling. At last, we apply this technology into practical seismic data and obtain a good application.