Statistical and probabilistic dependence between magnitude and time-interval for Mexico City earthquakes

This paper investigates the bivariate distribution of data consisting of earthquake magnitudes and the time-interval between earthquakes, to see whether the two variables are independent of each other. In searching for an association with magnitude, we consider time interval after an earthquake as well as the time interval before the earthquake. The characteristics of the interdependence between time interval Δt and earthquake magnitude M could be investigated using the statistical and probabilistic approaches. In the statistical approach the data for 250 successive earthquakes felt in Mexico City with magnitude 4.5 or greater, are used to compute the χ²-statistic to test the independence between the two variables. In the probabilistic approach we follow Suppes (1970) and as a measure of the probabilistic association we use an estimate of the earthquake conditional probabilities P(Δt/M) and P(M/ΔT) obtained through the application of bivariate distribution theory. The investigation revealed that there is some association between earthquake magnitude and the successive (after) time interval. There is no statistical evidence that the successive earthquake magnitude characteristics depend upon the preceding (before) time interval. However, from the probabilistic view point if the length of the preceding time interval increases, then, the probability of the occurrence of a successive large earthquake increases.