5D de-aliased seismic data interpolation using non-stationary prediction error filter
The prediction error filter (PEF) assumes that the seismic data can be destructed to zero by applying a convolutional operation between the target data and prediction filter in either time-space or frequency-space domain. Here, we extend the commonly known PEF in 2D or 3D problems to its 5D version. To handle the non-stationary property of the seismic data, we formulate the PEF in a non-stationary way, which is called the non-stationary prediction error filter (NPEF). In the 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. The NPEF can be used to denoise multi-dimensional seismic data, and more importantly, to restore the highly incomplete aliased 5D seismic data. We compare the proposed 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. Results show that although the proposed NPEF method is less effective than the rank-reduction method in interpolating irregularly missing traces especially in the case of low signal to noise ratio (S/N), it outperforms the rank-reduction method in interpolating aliased 5D dataset with regularly missing traces.