A model is presented which allows us to reexamine the interpretation of velocity anomalies observed before some earthquakes occur. This model extends the well-known dilatancy models by accounting for two scales of heterogeneities: the variations in pore/crack compressibility at a microscopic scale and the variations in the spatial fluid distribution for partially saturated rocks at a much larger scale. This model is relevant for cracked rocks which are partially saturated. Such a situation is likely to develop in impending earthquake source areas. Although previous models have considered cracked rocks and partially saturated rocks, none of the above heterogeneity-induced effects has been considered previously so that the previous predictions are in fact shown to be inappropriate. At earthquake or exploration seismic frequencies (1--100 Hz), saturation inhomogeneity can play a prominent role, and this results in velocity dispersion so that high-frequency predictions may not be valid and low-frequency velocities should be calculated. In order to do that, we assume that crustal rocks are described by a saturated matrix in which spherical undersaturated pockets are embedded. The matrix is itself made of a rock containing an isotropic distribution of cracks. Then, low- and high-frequency velocities are calculated coupling the Biot-Gassmann-Domenico theory with the effective medium approach (differential self-consistent method). If the diffusion-dilatancy model of Scholz et al. <1973> is superimposed on our theoretical velocity curves, it appears that the low-frequency predicted velocity anomaly is quite high when saturation heterogeneities are ignored. It is, however, quite small if this effect is taken into account. This result can explain the lack of observations of precursory changes of seismic velocities before many events. ¿ American Geophysical Union 1996