Abstract
Some strain steps which are often observed by the JMA strainmeters seem to occur prior to earthquakes. Therefore the strain steps have been considered to be a possible index of an earthquake occurrence. However, many other strain steps can occur unrelated to any earthquakes. It is statistically investigated whether these associations of strain steps with earthquake occurrences are causally related. The statistical method applied is based on Bayes' theorem which is useful when we have no prior information about the distribution of the parameters included in the study. There are two parameters in this study: one is π and the other is πH. The former is the probability of an earthquake or earthquakes occurring within an arbitary time interval of 48 hours, and the latter is the probability of an earthquake or earthquakes occurring within 48 hours after the occurrence of a strain step. The distributions of π and πH are given as posterior distributions in Bayes' theorem and the equality or the inequality of π and πH gives the statistical relationship between strain steps and earthquakes.
The expectation of πH, i.e., E (πH) is larger than that of π, i.e., E (π) for M≥4 earthquakes. On the contrary, the former is less than the latter for M≥3 and M≥2 earthquakes. Besides the probability of πH≥π is estimated to be over 80% for M≥4 earthquakes but less than 20% for M≥3 and M≥2 earthquakes. These results show the possibility that the strain steps are the precursors of earthquake occurrence, especially for larger earthquakes, although those larger than M5 did not occur during the period of the data collection in this study.
