Discrete Local Polynomial Basis Functions as an Alternative to Filter Seismic Data

Abstract

This paper represents an alternative to Fourier analysis for filtering seismic data by using discrete polynomial basis functions. The structure and theory of the matrix operators is presented as well as the choice of appropriate variables for wavelength selective filtering and their relationship to Savitzky-Golay filtering, as a seismic trace is not globally periodic, but locally periodic. As local polynomial approximation is applied in time domain, the introduced discrete polynomial filter is suitable for spatially highly undersampled data and performs well as a ground roll removing technique for land data – as an alternative to frequency-wavenumber filter techniques as quality improvement for quantitative seismic interpretation.