Summary
Observed seismic data is always irregular and seismic data interpolation is an essential procedure to provide accurate complete data for Surface Related Multiple Elimination (SRME) and wave equation based migration and inversion. While most interpolation methods belong to iterative method, how to define reconstruction error reasonably for terminating iterations duly is important for efficient seismic data interpolation. In this abstract, Projection Onto Convex Sets (POCS) method is achieved through the view of Iterative Hard Threshold (IHT) method and a novel reconstruction error definition is proposed with the information related with the observed seismic data. Tests on synthetic and real datasets demonstrate the validity of the proposed method.
Introduction
Acquired seismic data is always irregular sampled in spatial coordinates because of the presence of obstacles, forbidden areas, feathering and dead traces. Since multi-channel processing techniques, such as Surface Related Multiple Elimination (SRME), wave-equation based migration and inversion, require complete seismic data, seismic data interpolation technique, which can provide accurate complete seismic data for these multi-channel processing methods, is becoming an essential stage.
Interpolation methods can be divided into four categories (Gao et al., 2012; Wang et al., 2014): mathematical transform-based methods, prediction filtering-based methods, wave equation-based methods and rank reduction -based methods. While most interpolation methods belong to the category of iterative methods, the reconstruction error definition becomes essential for efficient seismic data interpolation. Gao et al. (2012) gave two reconstruction error definitions to monitor the convergence of the iterative interpolation methods: the first one uses the original complete seismic data and can only be used in theoretical research; the second one uses the adjacent iterative solutions and may trap in local minimum which leads to unsatisfactory interpolation results.
In this abstract, firstly, Projection Onto Convex Sets (POCS) method is achieved in the view of Iterative Hard Threshold (IHT) method; secondly, a novel reconstruction error definition is proposed with the information related with the observed seismic data. Tests on synthetic and real data prove the validity of the proposed method.
