We used intensity information from five calibration earthquakes to estimate an intensity attenuation model for the Rio Grande rift region (encompassing west Texas, New Mexico, and southern Colorado). The attenuation model lies between similar models developed for the Basin and Range Province and central and eastern North America. Analysis of two test earthquakes occurring in 1931 and 2014 validated that the intensity attenuation relation adequately predicted the events’ magnitudes and epicenters. We then analyzed intensity information for nine historical (1906–1960) earthquakes to determine their magnitudes and epicenters. Our results indicate that the largest earthquakes of the 1906 Socorro, New Mexico, sequence had intensity magnitudes (MI) 5.7–5.9 and may represent north‐to‐south migration of seismicity associated with the Socorro magma body. Moderate earthquakes in 1935 and 1960 also are associated with the magma body. The 1938 Arizona–New Mexico border earthquake sequence occurred about 50 km northeast of the ongoing 2014 Arizona–New Mexico border sequence. The 17 September earthquake of the 1938 sequence had an MI (4.1) that was about 1.0 units less than that of the 29 June 2014 Arizona–New Mexico event (MI 4.9).