Deblending of Off-the-Grid Blended Data via an Interpolator Based on Compressive Sensing

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.