It was found that the initial rise of the far-field P-wave velocity pulse generated by microearthquakes does not act as a ramp but gradually increases according to the function tn(2<n<4), where t is the time measured from the onset. This slow rise of the P-wave velocity pulse was termed the slow initial phase. The slow initial phase can not be explained by theoretical source models which assume a constant kinematic friction and a constant rupture velocity but by models which predict slow slip velocities and/or rupture velocities immediately after the rupture is initiated, such as the slip-weakening crack model. ¿ American Geophysical Union 1992