A method for estimating earthquake occurrence probability using first- and multiple-order Markov chain models

It is valuable in earthquake prediction to determine the occurrence probability of major earthquakes by making use of data obtained from precursory phenomena up to the time of the evaluation. In this study, the time evolution of the state determined by earthquakes and precursory phenomena was modelled using Markov chains. Various probabilities suitable for earthquake prediction were derived from the transition probability of the Markov chain with a chosen length of memory time. As an example, earthquake sequence records for northern China, which covered a period of about two thousand years, were examined and the results were also obtained from modern scientific observations of the radon anomaly which covered a period of about 10 years.Assuming moderate-sized earthquakes of two magnitude ranges 4 3/4 M 5 3/4, 6 M 6 3/4 as precursors to large earthquakes of a magnitude range, 7 M 8 1/2, transition probabilities were calculated for a time interval from 2 to 40 yr. The results showed that the precursory time of moderate-sized earthquakes is mainly distributed in a time span of around several years and that the earthquake occurrence probability is considerably large when the precursory earthquakes occur successively. Furthermore, it was shown that a larger moderate-sized earthquake (4 3/4 M 5 3/4) is a more effective precursor than an entire moderate-sized earthquake (4 3/4 M 6 3/4).Second, a multiple precursor case was tried by means of simulation based on the radon anomaly data obtained during a limited observation period. Simultaneous occurrence of two precursors makes the earthquake occurrence probability increase by 1.5–2.0 for a reasonable choice of a mean recurrence interval of the radon anomaly compared with the case where only a moderate-sized earthquake was treated as the precursor. However, the probability is much the same if the average recurrence interval of the radon anomaly is the same through time, including the preparatory period before the earthquake.