Changes in Frequency-Size Relationship from Small to Large Earthquakes

THE constant 'b value' observed in frequency-magnitude distributions of earthquakes has been taken as an indication of self-similarity at all magnitudes. Hence, earthquake properties should scale uniformly in the same way from small to large earthquakes. It has often been observed, however, that the seismic moment released in small earthquakes scales differently with rupture length than it does for large events 1,2, where the crossover between small and large events is defined at a rupture dimension equal to the down-dip width of the seismogenic zone. A possible explanation for this contradiction is that frequency-size distributions are biased by small earthquakes. Small events dominate most global earthquake catalogues because of the short time-period covered. Another source of bias in size distributions is the saturation of earthquake magnitudes for large events. Here we correct biases in calculations of b values and present evidence for a change in b value in frequency-size distributions. We find that a break in self-similarity, from small to large earthquakes, occurs at a point where the dimension of the event equals the down-dip width of the seismogenic layer.