On relating apparent stress to the stress causing earthquake fault slip

Abstract

Apparent stress τ a is defined as , where is the average shear stress loading the fault plane to cause slip and η is the seismic efficiency, defined as E a / W , where E a 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 . 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 τ 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 τ a and η 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 η is always near 0.06, those for earthquakes tend to be less than this bounding value because E a for earthquakes is usually underestimated due to factors such as band‐limited recording. Thus upper bounds on 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 τ a for suites of earthquakes, using , are found to be comparable in magnitude to estimates of shear stress on the basis of extrapolating in situ stress data to seismogenic depths.