Seismic data interpolation beyond aliasing using regularized nonstationary autoregression

Seismic data are often inadequately or irregularly sampled along spatial axes. Irregular sampling can produce artifacts in seismic imaging results. We have developed a new approach to interpolate aliased seismic data based on adaptive prediction-error filtering (PEF) and regularized nonstationary autoregression. Instead of cutting data into overlapping windows (patching), a popular method for handling nonstationarity, we obtain smoothly nonstationary PEF coefficients by solving a global regularized least-squares problem. We employ shaping regularization to control the smoothness of adaptive PEFs. Finding the interpolated traces can be treated as another linear least-squares problem, which solves for data values rather than filter coefficients. Compared with existing methods, the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence. The technique was tested on benchmark synthetic and field data to prove it can successfully reconstruct data with decimated or missing traces.