Observations of three‐dimensional ground motion at a single point on the surface of the Earth following an earthquake can be sufficient to determine the zeroth order moment tensor of the event. We adapt the centroid‐moment tensor (CMT) method [Dziewonski et al., 1981] of analysis to single station data and apply it to the September 19, 1985 Michoacan earthquake. The obtained mechanism indicates faulting on a shallow plane, consistent with the ongoing subduction of the Cocos plate. The scalar moment is 1.3 × 1028dyne‐cm. A direct deconvolution of the observed P‐wave train indicates that the moment release occurred in two subevents, each of 20 seconds duration with a peak‐to‐peak separation in time o