Evidence for Truncated Exponential Probability Distribution of Earthquake Slip

Abstract

Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation‐based seismic and tsunami‐hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture‐specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes. We show the parameters of the best‐fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale‐dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. Online Material: Figures showing scaling of slip area with seismic moment and Q – Q plots and tables listing earthquakes, rupture models, and fits of various distributions to the empirical probability distribution.