The large number of high-quality stations from global networks (e.g., IRIS, GEOSCOPE) allows for rapid and robust recovery of source parameters of large earthquakes. We present a self-consistent analysis of surface waves in terms of directivity parameters. The boxcar is often used to recover source parameters but is rarely a faithful representation of an event's time function. We demonstrate that more reliable estimates of directivity parameters can be obtained when we take into account the source time function (STF) of the event. A low-frequency STF is obtained from first (R1) and second (R2) orbit Rayleigh waves in the range 2 to 15 mHz, with a spectral synthesis and inversion method. We measure the differential amplitudes between data and 3D synthetics. We use the R1/R2 ratio of differential amplitudes to invert, in a single narrow-frequency band, for the event's apparent rupture azimuth and velocity. For the Mw 8.1 Chile 1995 event, data are consistent with unilateral southward propagation, with a velocity of about 2.4 km/sec. For the Mw 7.9 Mexico 1995 earthquake, the rupture propagated toward the NW at about 2.0 km/sec. Our low-frequency estimates agree with broadband studies of both events and can be retrieved rapidly on a routine basis after a large earthquake.