Seismic Data Up-sampling beyond Aliasing Using Polynomial Phase Signals

This paper proposes a new trace up-sampling method for seismic data. The method is based on building a local time-space model of the seismic data following some physical assumptions about its structure. The model simplifies to a superposition of second order polynomial phase signals, which are estimated using a matching pursuit algorithm. The estimated model is then used to generate traces at the desired locations. The proposed method performs up-sampling beyond aliasing thanks to the ability of its matching pursuit basis to model aliasing. It differs from Fourier-based matching methods in the inclusion of a curvature term in the matching basis. The method does not rely on priors from un-aliased part of the data to build the aliasing protection. A good signal to noise ratio is the only condition needed instead. The method is tested on real data and compared to conventional up-sampling solutions. Its performance is remarkably good particularly when it comes to up-sampling highly aliased data.