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Blended acquisition improves the efficiency of seismic data acquisition sharply, and deblending algorithms are still open to prepare separated data. Most deblending methods are suitable for on-the-grid blended data. However, blended data in field cases are always at off-the-grid samples which pose great challenges in providing accurate deblended results. A binning strategy can assign an off-the-grid sample at its nearest on-the-grid sample approximately with the amplitude and phase bias caused by the existing distance between them. However, the subsequent deblending accuracy is low, especially when the amplitude and phase biases are large. With true off-the-grid data constraints, we introduce a Kaiser window tapered $\mathrm{sin}c$ interpolator to link off-the-grid samples and on-the-grid samples during the procedure of compressive sensing-based functional construction. Full expressions of the interpolator and its adjoint operator are provided to generate an iterative thresholding algorithm for off-the-grid blended data deblending. Separated on-the-grid data can be obtained accurately in an iterative manner. The deblending performance of artificially off-the-grid blended data demonstrates the validity of the proposed method quantitatively no matter whether the amplitude and phase biases are large or small. Field examples of off-the-grid blended data further prove the effectiveness of the proposed method to provide accurate on-the-grid separated data. [ABSTRACT FROM AUTHOR]

The blended acquisition can help improve the seismic data quality or enhance the acquisition efficiency. However, the blended seismic data should first be separated for subsequent traditional seismic data processing steps. The signal is coherent in the common receiver domain, and the blending noise shows randomness when the blending operator is constructed using a random time delay series. The seismic data can be characterized sparsely by the curvelet transform which can be used for deblending. However, it has a high computational cost, especially for large-volume seismic data. The spectrum of the seismic data is band-limited with the conjugate symmetry property, and thus the principal frequency components can characterize the signal accurately. The size of the principal frequency components is at least halved. Thus, we propose to implement the curvelet transform on the principal frequency wavenumber (PFK) domain data instead of the time-space (TX) domain data. The size of the PFK domain data is at least halved compared with the TX domain data, which can improve the deblending efficiency reasonably. The related formulae are fully derived and the efficiency enhancement analysis is provided in detail. One synthetic and two field artificially blended data are provided to demonstrate the validity and flexibility of the proposed method in the efficiency improvement and the deblending performance. The separated gathers can be beneficial for subsequent traditional seismic data processing procedures. [ABSTRACT FROM AUTHOR]