Discrete Local Basis Functions and Their Application to Seismic Data

This paper presents the concept of discrete local basis functions and their application to seismic data, together with the use of orthogonal projections to remove specific features from a data set. This method is demonstrated on ground-roll elimination. The structure and theory of the matrix operators is presented and their relationship to Savitzky-Golay filtering. A new implementation for anisotropic filtering is presented whereby a local polynomial basis is used for the $x$ direction and a local Fourier basis is used in the $y$ direction. It is shown that this new filtering technique can for example be used to filter the first break.