Seismic moment ratio of aftershocks with respect to main shocks

Abstract

The empirical Båth's law indicates that the earthquake process is self‐similar and provides an opportunity to estimate the magnitude of the largest aftershock subsequent to a main shock. However, the analysis of this relation is limited to a small magnitude range and also depends on the aftershock selection rules. As an alternative, we analyze, in this paper, the cumulative seismic moment of aftershocks relative to the main shock moment, because (i) it is a physical quantity that does not only take the largest aftershock into account; (ii) background activity can be considered and as a result estimations are less affected by selection rules; and (iii) the effects of the catalog cut‐off magnitude can be corrected, what leads to larger magnitude range for the analysis. We analyze the global preliminary determination of epicenters U.S. Geological Society catalog (combined with centroid moment tensor focal mechanisms) and find that the seismic moment release of aftershocks is on average approximately 5% of the main shock seismic moment. We show that the results can be well fitted by simulations of the Epidemic Type Aftershock Sequence model. In particular, we test whether simulations constrained by predictions of the static stress‐triggering model, proposing a break of self‐similarity due to the finite seismogenic width, are in agreement with observations. Our analysis shows that the observed dependency on the main shock magnitude as well as systematic variations with the main shock fault plane solution can be both explained by the constraints based on the static stress triggering.