5D dealiased seismic data interpolation using nonstationary prediction-error filter

The prediction-error filter (PEF) assumes that seismic data can be destructed to zero by applying a convolutional operation between the target data and the prediction filter in either the time-space or frequency-space domain. We have extended the commonly known PEF in 2D or 3D problems to its 5D version. To handle the nonstationary property of the seismic data, we formulate the PEF in a nonstationary way, which is called the nonstationary prediction-error filter (NPEF). In NPEF, the coefficients of a fixed-size PEF vary across the whole seismic data. In NPEF, we aim at solving a highly ill-posed inverse problem via the computationally efficient iterative shaping regularization. NPEF can be used to denoise multidimensional seismic data and, more importantly, to restore the highly incomplete aliased 5D seismic data. We compare our NPEF method with the state-of-the-art rank-reduction method for the 5D seismic data interpolation in cases of irregularly and regularly missing traces via several synthetic and real seismic data. The results show that although our NPEF method is less effective than the rank-reduction method in interpolating irregularly missing traces especially in the case of a low signal-to-noise ratio, it outperforms the rank-reduction method in interpolating an aliased 5D data set with regularly missing traces.