Explaining the seismic moment of large earthquakes by heavy and extremely heavy tailed models

Abstract

The search of physical laws that explain the energy released by the great magnitude earthquakes is a relevant question, since as a rule they cause heavy losses. Several statistical distributions have been considered in this process, namely heavy tailed laws, like the Pareto distribution with shape parameter α ≈ 0.6667. Yet, for the usually considered Californian region (where earthquakes with moment magnitude, MW, greater than 7.9 were never registered) the Pareto distribution with index near the above mentioned seems to have a “too heavy” tail for explaining the bigger earthquakes seismic moments. Usually an exponential tapper is applied to the distribution right tail (above the so called corner seismic moment), or another distribution is considered to explain these high seismic moment data (like another Pareto with different shape parameter). The situation is different for other regions where seisms of larger magnitudes do occur, leading to data sets for which heavy or even extremely heavy tailed models are appropriated. The purpose of this paper is to reduce the seismic moment, M0, of the very large earthquakes to particular heavy and extremely heavy tailed distributions. Using world seismic moment information, we apply Pareto, Log-Pareto and extended slash Pareto distributions to the data, truncated for M0 ≥ 1021 Nm and for M0 ≥ 1021.25 Nm. For these great seisms we conclude that extended slash Pareto is a promising alternative to the more traditional Pareto and Log-Pareto distributions as a candidate to the real model underlying the data.