Apparent stress ??a is defined as ??a = ??????, where ???? is the average shear stress loading the fault plane to cause slip and ?? is the seismic efficiency, defined as Ea/W, where Ea is the energy radiated seismically and W is the total energy released by the earthquake. The results of a recent study in which apparent stresses of mining-induced earthquakes were compared to those measured for laboratory stick-slip friction events led to the hypothesis that ??a/???? ??? 0.06. This hypothesis is tested here against a substantially augmented data set of earthquakes for which ???? can be estimated, mostly from in situ stress measurements, for comparison with ??a. The expanded data set, which includes earthquakes artificially triggered at a depth of 9 km in the German Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland (KTB) borehole and natural tectonic earthquakes, covers a broad range of hypocentral depths, rock types, pore pressures, and tectonic settings. Nonetheless, over ???14 orders of magnitude in seismic moment, apparent stresses exhibit distinct upper bounds defined by a maximum seismic efficiency of ???0.06, consistent with the hypothesis proposed before. This behavior of ??a and ?? can be expressed in terms of two parameters measured for stick-slip friction events in the laboratory: the ratio of the static to the dynamic coefficient of friction and the fault slip overshoot. Typical values for these two parameters yield seismic efficiencies of ???0.06. In contrast to efficiencies for laboratory events for which ?? is always near 0.06, those for earthquakes tend to be less than this bounding value because Ea for earthquakes is usually underestimated due to factors such as band-limited recording. Thus upper bounds on ??a/???? appear to be controlled by just a few fundamental aspects of frictional stick-slip behavior that are common to shallow earthquakes everywhere. Estimates of ???? from measurements of ??a for suites of earthquakes, using ??a/???? ??? 0.06, are found to be comparable in magnitude to estimates of shear stress on the basis of extrapolating in situ stress data to seismogenic depths.
Additional publication details
On relating apparent stress to the stress causing earthquake fault slip