Borehole-consistent analysis (analogous to surface-consistent seismic refraction statics analysis) of compressional wave arrivals in full-waveform acoustic logs reveal arrival-time anomalies of tens of microseconds. These anomalies are correlated with lithology and are similar for logging sondes of different geometries. The magnitude of the anomalies makes it unlikely that they are caused by caliper errors or the presence of an altered annulus around the borehole. A possible explanation is given in terms of the Fourier phase spectrum of the first compressional arrivals. The theoretical delays depend on the formation elastic parameters, the borehole geometry and the properties of the borehole fluid; a sensitivity analysis of the relevant parameters is presented.