Small and Large Earthquakes: The Effects of the Thickness of Seismogenic Layer and the Free Surface

Abstract

An examination of a set of well-determined source parameters for Japanese intraplate earthquakes shows that small earthquakes obey a scaling law different from large earthquakes: Mo ∝︁ L3 for small events but Mo ∝ L2 for large events where Mo is seismic moment and L is rupture length. Also an offset of a factor of 1.5–2.2 in the seismic moment is found at the transition between small and large earthquakes. Since a linear dimension of earthquakes at the transition is comparable to the thickness of the seismogenic layer, the difference in scaling strongly suggests that the fault width for small earthquakes is unbounded while that for large earthquakes is bounded by the thickness of the seismogenic layer. Namely, it implies that u ∝ L ∝ W for small earthquakes and that u ∝ L but W = constant for large earthquakes where u is slip and W is fault width. Thus we can classify earthquakes into large and small earthquakes according to whether or not an earthquake fault cuts across the entire thickness of the seismogenic layer. The offset in the seismic moment appears to be due to the difference in boundary conditions between buried and surface faults; in a certain idealized case, the amount of dislocation for surface fault is theoretically expected to be twice that of a buried fault if the stress drop is the same for both faults. The effect of the free surface has been overlooked probably because it tends to be masked by the difference in the slopes of the linear relationship between small and large earthquakes. A naive least-square fitting results in Mo ∝ L3 relationship for the whole data set. The maximum likelihood estimate of the parameters and the selection of a statistical model based on the Akaike Information Criterion show that the whole data set is not satisfactorily modeled by one regression line. But it is best modeled by two regression lines, one for large event and another for small event, with the threshold moment of 7.5×1025 dyne-cm.