Robust POCS method for interpolation of seismic data

Abstract There always exist irregularly sampled traces along the spatial direction for the real seismic data. Projection onto convex sets (POCS) is a widely used method for interpolating missing traces. In general, the non-robust POCS method imposes the L2 norm minimization constraint on the reconstruction error. It can remove the Gaussian random noise effectively while conducting interpolation. However, the non-robust POCS method cannot remove the super-Gaussian noise of outliers. The outlier noise may negatively influence the interpolation accuracy. To better remove outliers and improve the interpolation accuracy, we propose the robust POCS method, which imposes the Huber norm minimization constraint on the reconstruction error. The Huber norm actually equals the L1 norm minimization constraint on the large reconstruction error (outlier noise) and the L2 norm minimization constraint on the small reconstruction error (random noise). Furthermore, we introduce a robust solving algorithm by using a theoretically-constructed pseudo data to transform the Huber norm minimization problem into the L2 norm minimization problem. In this way, the robust optimization problem of the robust POCS method can be solved effectively. The proposed robust POCS method can better remove the outliers and preserve signal than the non-robust POCS method. Synthetic and field data demonstrate that the proposed robust POCS method obtains better performance of data interpolation than the non-robust method in terms of recovered signal-to-noise ratio, F-K amplitude spectrum and visual view.