Determinationof the OptimumFilterFunction for SPECTImaging

A system and method is provided for characterizing earth formations. In one embodiment, the method includes passing a logging tool through a borehole and repeatedly: (a) triggering an acoustic wave generator; (b) recording acoustic waveforms received by receivers in the logging tool; (c) determining a time semblance of the recorded acoustic waveforms; and (d) smoothing the time semblance. In a different embodiment, a phase semblance of the recorded acoustic waveforms is determined and smoothed. The smoothing may be performed using an adaptive wavelet denoising technique or an adaptive moving average filter technique. In each case the average time or frequency spacing between semblance peaks is preferably determined and used to adapt the smoothing operation in a manner that varies with the slowness value s.