Relationship between size and waiting time distributions in the empirical data for natural hazards

Abstract

Using an analytic model relating the waiting time τ and magnitude S of hazard events, S ∝ σ₀exp(τ ), satisfactory fitting with empirical data for earthquake and landslides are obtained. The gamma distribution of return-time probabilities, p(τ ) result to a magnitude size distribution p(S) with systematic deviations from what would otherwise be a pure power-law. Taking all parameters from available data in literature, empirical earthquake waiting time distributions succesfully reproduces the trend in magnitude distributions. The model hints at the possible behavior of landslide waiting time distributions, in the absence of reliable high-resolution waiting time data survey for these events.