Velocity filtering of acoustic well logging waveforms

A velocity filter that is based on a particularly convenient and effective combination of an up/down filter and slanting (time-shift) operations is presented. The up/down filter is based on a cascade of spatial and temporal Hilbert transform filters. The Hilbert transform filters and the time-shift operators are finite-duration impulse response (FIR) filters designed according to the minimax criterion. The velocity filter is applied to acoustic well logging waveforms to isolate the initial P, S, and Stoneley waves from their reflected and converted waves at bed boundaries. To achieve this objective, the waveforms are time-shifted to align the primary wave of interest before the velocity filter is applied. Examples demonstrate the effectiveness of this procedure in separating the primary waves from their reflected and converted waves.<>