We present results from the cross-correlations of seismic noise recordings among pairs of stations in the Parkfield network, California. When performed on many station pairs at short ranges, the noise correlation function (NCF) is the passive analog to a shot gather made with active sources. We demonstrate the presence of both a P-wave and a Rayleigh wave in the NCF. A time-frequency analysis allows us to separate the two wave packets that are further identified through their polarization. Arrival times were estimated from the NCF and they compared favorably with predictions using ray tracing in a regional velocity model and with the velocity gradient across the San Andreas Fault.