3D seismic data reconstruction based on complex-valued curvelet transform in frequency domain

• A 3D seismic data reconstruction method based on the POCS and CCT has been proposed in the frequency domain.
• ESRD threshold is proposed to reduce iterations and improve reconstruction efficiency.
• A comparative analysis is reported between frequency domain and time domain using CCT-based POCS reconstruction method.
• Synthetic and real data examples demonstrate the effectiveness of our proposed method.

Traditional seismic data sampling must follow the Nyquist Sampling Theorem. However, the field data acquisition may not meet the sampling criteria due to missing traces or limits in exploration cost, causing a prestack data reconstruction problem. Recently researchers have proposed many useful methods to regularize the seismic data. In this paper, a 3D seismic data reconstruction method based on the Projections Onto Convex Sets (POCS) algorithm and a complex-valued curvelet transform (CCT) has been introduced in the frequency domain. In order to improve reconstruction efficiency and reduce the computation time, the seismic data are transformed from the t–x–y domain to the f–x–y domain and the data reconstruction is processed for every frequency slice during the reconstruction process. The selection threshold parameter is important for reconstruction efficiency for each iteration, therefore an exponential square root decreased (ESRD) threshold is proposed. The experimental results show that the ESRD threshold can greatly reduce iterations and improve reconstruction efficiency compared to the other thresholds for the same reconstruction result. We also analyze the antinoise ability of the CCT-based POCS reconstruction method. The example studies on synthetic and real marine seismic data showed that our proposed method is more efficient and applicable.