Conditional Probability Approaches for the Occurrence of Earthquake Generated Tsunamis

The problem of probabilistic tsunami hazard assessment is not an easy task because usually the number of events contained in a tsunami time series of a particular tsunamigenic zone is low and, therefore, do not allow for statistical significance of the results. On the contrary, the earthquake data set contains more events which is due to that not all of the earthquakes are tsunamigenic. As a consequence, should the problem of tsunami probabilistic hazard assessment is considered in association to approaches for earthquake probabilistic occurrence then more reliable tsunami probabilities may be obtained. We develop alternative approaches for the determination of conditional probabilities of tsunami occurrence by combining two interrelated time series, one for the earthquake events, and another for the tsunami events. The approaches allow to calculate the probability for a future earthquake to be tsunamigenic or non-tsunamigenic, within a given time interval, under the conditions that (1) the last earthquake took place at time t before the calculation date, (2) the last tsunamigenic earthquake occurred at time T before time t, and (3) the ratio of tsunami generating earthquakes is known. The approaches were applied in earthquake and tsunami data sets from the Pacific and the Mediterranean Sea and the efficiency in calculating conditional probabilities was successfully tested. The alternative approaches are discussed as for the superiority of one against the other.