We have determined the asperity distribution in the segment of the Ecuador-Columbia subduction zone that was ruptured by the 1979 (Mw=8.2) and 1958(MW=7.7) earthquake, we are able to document directivity in the P-wave source time functions and consequently, have spatially located the moment release. By combining results from both P-wave and surface wave directivity, we have defined three regions: (1) from 0 to 56 km northeast of the epicenter, with low moment release and a small seismic displacement, (2) the asperity, from 56 to 116 km northeast of the epicenter, with most of the moment release and a displacement of ~6 m, and (3) a small-displacement region from 116 to 180-240 km northeast of the epicenter. Thus the 1979 rupture zone is composed of an asperity 60 km in length, bounded by two weak (small displacement) regions. The displacement at the asperity is equal to the cumulative tectonic displacement between 1979 and 1906 (the year of the previous earthquake in this segment). The 1958 earthquake is characterized by the rupture of a small asperity (length scale approximately 25 km) in the epicentral region. The 1958 event continued to rupture past this small epicentral asperity and stopped near the epicenter of the following 1979 event. This detailed study of the spatial variation in moment release offers strong support for the asperity model of large earthquake occurrence.