Probability of the occurrence of two significant earthquakes on the same date (of different years) striking the same site; the Mexico City case

On the afternoon of 19 September 2017, just a couple of hours after an earthquake drill, an intense M (sub w) 7.1, intermediate-depth, normal-fault earthquake struck Mexico City and neighboring states causing destruction and 369 deaths. This earthquake occurred on exactly the same date as the well-known 1985 M (sub w) 8.1 subduction earthquake that also struck Mexico City causing severe damage, structure collapses and more than 10,000 deaths. There was a difference of approximately 6 hrs between the hours of these historical seismic events; the 1985 event occurred at 7:17 (CST), and the 2017 event at 13:14 (CDT). Classic probability theory, probabilistic seismic hazard assessment (PSHA), and information on the correlation between deaths and seismic intensity are used to compute the probability of two significant earthquakes occurring on the same date and striking the same site. The probabilities of events associated with two significant earthquakes in these circumstances can be very low, lower than events of a different kind that are usually considered as highly improbable. This may not necessarily be expected for an earthquake-prone region such as Mexico City, where significant events occur relatively frequently (approximately a 9% probability in any given year); for any given day the probability decreases to about 0.026%, and for the referred event involving two earthquakes, the probability can be even smaller (on the order of 10 (super -5) to 10 (super -8) ), unless periods of observation of over a century are employed. Although this is expected, such probability is rarely (if at all) rigorously computed and not typically presented in an engaging way for students and the general public.