Interpolated Compressive Sensing for Seismic Data Reconstruction

Li, Chengbo (ConocoPhillips) | Mosher, Charles C. (ConocoPhillips) | Kaplan, Sam T. (ConocoPhillips)



Recent research indicates that compressive sensing (CS) can be successfully applied to seismic data reconstruction. It also provides a powerful tool that reduces the acquisition cost, and allows for the exploration of new seismic acquisition designs. Most seismic data reconstruction methods require a predefined nominal grid for reconstruction, and the seismic survey must contain observations that fall on the corresponding nominal grid points. However, the optimal nominal grid depends on many factors, such as bandwidth of the seismic data, geology of the survey area, and noise level of the acquired data. It is understandably difficult to design an optimal nominal grid when sufficient prior information is not available. In addition, it may be that the acquired data contain positioning errors with respect to the planned nominal grid. We propose an interpolated compressive sensing method which is capable of reconstructing the observed data on an irregular grid to any specified nominal grid, provided that the principles of CS are satisfied. We first describe the theory and implementation of this interpolated CS method. Then we illustrate this approach using synthetic and real data examples, and make comparisons to the traditional CS method. We show that the interpolated CS method provides an improved data reconstruction compared to results obtained from the traditional CS method.