Comments on a Pure Phase Shift Filter to Improve Vibroseis Correlation

Based on the definition of the upsweep for the case where the instantaneous frequency varies linearly with time, Li et al. (1995) suggested a deterministical pure phase shift filter (PPSF) to eliminate harmonic distortions in vibroseis data. It is therefore possible to improve the desired correlation between the harmonically distorted ground force signal (HDS) and the harmonically distorted vibrogram. The PPSF has been successfully applied to real data. In this paper we first numerically compute the phase spectra of the HDS and its components, then compare them with the corresponding instantaneous phases. Finally we present the mathematical aspects of the elimination process using the PPSF.