Characterization of tail distribution of earthquake magnitudes via generalized Pareto distribution

Extreme value theory in seismic risk analysis has important application, and the excess of earthquake magnitude distribution over a threshold can be approximated by generalized Pareto distribution. Based on the generalized Pareto distribution, we developed several estimation formulas of seismic activity parameters, including strong earthquake magnitude distribution, earthquake recurrence period and return level, expected recurrence magnitude, probability of seismic risk and maximum earthquake magnitude; then, based on historical seismic data in Yunnan region, we discussed how to choose the threshold value, model fitting diagnosis and parameter estimation. Finally we calculated seismicity parameters in the region. The results show that generalized Pareto distribution characterized strong earthquake magnitude distribution quite satisfactorily, the recurrence periods by POT (peaks over threshold method) model agree with the actual recurrence interval statistics, and the high quantile is stable within a specific threshold range. So the generalized Pareto distribution is a possible approach to determining the potential upper limit earthquake magnitude in engineering seismology.