Exploring two different methods of seismic interpolating operators
Farzaneh Bayati, Daniel O. Trad
3D land data acquisitions are often undersampled along offset and azimuth directions because of large shot and receiver line intervals. In marine data acquisition, data are well sampled in the inline direction but coarsely sampled in the crossline direction. These issues can often be alleviated by seismic interpolation, which is an important step in data processing since many processing and migration tools require regularly sampled input data. We compare two methods of seismic amplitude reconstruction. The first one is Singular Spectrum Analysis (SSA) which is based on rank reduction methods. In this approach, we generate Hankel matrices from constant frequency data and reduce their rank by using Truncated Singular Value Decomposition (TSVD). Since missing traces and random noise increase the rank of the Hankel matrix, TSVD changes the data by removing noise and interpolating missing traces. By reducing the rank, the algorithm iteratively infills missing traces. The second method is Minimum Weighted Norm Interpolation (MWNI) which infills missing traces by transforming the data to the Fourier domain and removing sampling artifacts by enforcing wavenumber-domain sparsity. In this report, we test how these two methods perform on pre-stack and irregular sampled synthetic 2D data. For the case we tested, SSA seems more affected by curvature than MWNI but it seems better in preserving the amplitude for the hyperbola flanks. For SSA, we implement a multidimensional version and test it for 3D synthetic data.