## Earthquake Death Tolls

Leon Knopoff, & Didier Sornette

Published December 1995, SCEC Contribution #223

In the risk and insurance literature, the (one-point) distributions of losses in natural disasters have been proposed to be characterized by "fat tail" power laws, i.e. very large destruction may occur with a non-vanishing rate. A naive hypothesis of uncorrelated Poissonian occurrence would suggest that the losses are solely characterized by the properties of the underlying power law distributions, i.e. the longer we wait, the more dramatic will be the largest disaster, which could be as much as a finite fraction of the total population or the total wealth of a country. We find indeed that the numbers Z of deaths in the very largest earthquakes of this century can be described by a power law distribution $P(Z)\simeq Z^{-(1+\delta)}$ with $\delta=1.0\pm0.3$, implying an unbounded behavior for the most devastating earthquakes. However, the distribution of the number of deaths per capita in each country in this century has a well-defined maximum value, suggesting that the naive extrapolation of the power law distribution is incorrect and that the understanding of correlations is necessary to ascertain the level of risk from natural disasters. The one-point distributions only provide an upper bound of the expected risk. We propose a speculative model to explain the correlations between deaths in large earthquakes and their countries of occurrence: we suggest that large ancient civilizations that have matured into large present-day populations were the beneficiaries of isolation from marauders due to the relative geographic protection by tectonic processes largely of an orogenic nature.

Citation
Knopoff, L., & Sornette, D. (1995). Earthquake Death Tolls. Journal de Physique I, 5(12), 1681-1688. doi: 10.1051/jp1:1995223 .