Size distributions for large and small earthquakes

Small and large earthquakes obey different scaling laws and inhabit distinct populations, both characterized by power laws with different exponents. When considering earthquakes on a single fault or fault segment, the one large earthquake that occurs during a seismic cycle is discontinuous with the population of small earthquakes. Here it is shown that these two observations, together with the scaling laws, are self-consistent when proper account is taken of the size distribution of faults.