We have developed a technique based on the move-out and stack of reflected seismic phases from local earthquake seismograms. For a given interface depth and a velocity model, the theoretical travel times of reflected/converted phases in a 1D medium are computed and used to align in time the vertical-component microearthquake records collected by a local seismic network. The locations and origin times of events are preliminarily estimated from P and S arrival times. Different seismic gathers are obtained for each considered reflected/converted phase at that interface, and the best interface depth is chosen as the one that maximizes the value of a semblance function computed on moved-out records. This method has been applied to seismic records of microearthquakes that occur at Mt. Vesuvius volcano. The analysis confirms the evidence for an 8 to 10-km-deep seismic discontinuity beneath the volcano, which was previously identified, by migration of active seismic data, as the roof of an extended magmatic sill.