Earthquake magnitude probabilities and statistical independence for Mexico City earthquakes

Abstract

Abstract The absolute and the conditional earthquake magnitude probabilities are defined by direct enumeration of the successive earthquake magnitude observations. We make the assumption of independence of earthquake magnitude events in Mexico City earthquakes and then show by experimental data that the assumption of randomness, and consequently the model, is not a good one. Using the X2 statistic to check the statistical dependence, it is found that there is some statistical association between the magnitudes of 221 successive earthquakes felt in Mexico City with magnitude 4.5 or greater. In other words, the observed sequence of discrete earthquake magnitudes for the Mexico City area is nonrandom. Finally, the concept of energy is used to give a physical interpretation of the significance of the nonrandomness.