Summary
Projection Onto Convex Sets (POCS) method is an efficient iterative method for seismic data interpolation. In each iteration, observed seismic data is inserted into the updated solution, therefore it has difficulty for interpolation in noisy situations. Weighted POCS method can weaken the noise effects because it uses a weight factor to scale the observed seismic data, then fewer noisy data is inserted into the updated solution, but it still inserts some random noise. In this abstract, a novel method is proposed by combining the advantages of the weighted POCS method and the Iterative Hard Threshold (IHT) method: the weighted POCS method used for interpolation and the IHT method used for random noise elimination. The novel method can be used for simultaneous interpolation and random noise removal of seismic data, and its validity is demonstrated on synthetic and real datasets.
Introduction
Spatial irregularity and random noise observed in seismic data can affect the performance of Surface-Related Multiple Elimination (SRME), wave-equation based migration and inversion. Therefore, interpolation and random noise elimination is pre-requisite for multi-channel processing techniques.
Interpolation methods can be divided into four categories (Gao et al., 2012; Wang et al., 2014): mathematical transform based methods, prediction filters based methods, wave-equation based methods and rank-reduction based methods. Among these methods, mathematical transform based methods are easy to implement and have drawn much attention. While the random noise in observed seismic data can affect the interpolation performance and the irregularity of observed data can also affect the results of random noise elimination. Therefore, simultaneous interpolation and random noise attenuation is developed (Naghizadeh, 2012; Oropeza and Sacchi, 2011), while it is suitable for linear or quasi-linear events and should be handled window by window for curved events.
