Irregularly Sampled Seismic Data Reconstruction Using Multiscale Multidirectional Adaptive Prediction-Error Filter

Abstract

The interpolation based on prediction-error filter (PEF) is one of the most effective approaches recently proposed for seismic data reconstruction. However, the number of effective regression equations for estimating the filter coefficients will be much less when missing many seismic traces, which makes the estimated filter coefficients inaccurate or even impossible to be estimated. To improve the accuracy of filter coefficients, in this paper, we design a multiscale and multidirectional PEF, in which the number of effective regression equations can be increased much more, and use it to seismic data reconstruction. First, we estimate the adaptive different directional PEFs using the known data in different scales. The known data can be regularly sampled with randomly or regularly missing, or even both of them. Then, we interpolate missing seismic traces using estimated PEF and the sparse known traces. The regularization in least-squares inversion controls the adaptivity of multiscale multidirectional PEF. The use of more effective regression equations in inversion makes the filter coefficients more accurate. In addition, the multiscale filter can conveniently deal with the case of the simultaneous existence of randomly and regularly missing, while the conventional methods have to be treated separately for randomly and regularly missing. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.