T.-F. Wong S.H. Hickman N.M. Beeler 2003 <div class="margin-size-16-b margin-size-16-t"><div class="margin-size-4-t margin-size-16-b"><p class="typography serif indefinite-width"><span>We consider&nbsp;expected&nbsp;relationships&nbsp;between&nbsp;apparent&nbsp;stress&nbsp;τ_a&nbsp;and&nbsp;static&nbsp;stress&nbsp;drop&nbsp;Δτ_s&nbsp;using a standard&nbsp;energy&nbsp;balance and find τ_a&nbsp;= Δτ_s&nbsp;(0.5 - ξ), where ξ is&nbsp;stress&nbsp;overshoot. A simple implementation of this balance is to assume overshoot is constant; then&nbsp;apparent&nbsp;stress&nbsp;should vary linearly with&nbsp;stress&nbsp;drop, consistent with spectral theories (Brune, 1970) and dynamic crack models (Madariaga, 1976). Normalizing this expression by the&nbsp;static&nbsp;stress&nbsp;drop&nbsp;defines an&nbsp;efficiency&nbsp;η_sw&nbsp;= τ_sa/Δτ_s&nbsp;as follows from Savage and Wood (1971). We use this measure of&nbsp;efficiency&nbsp;to analyze data from one of a number of observational studies that find&nbsp;apparent&nbsp;stress&nbsp;to increase with seismic moment, namely earthquakes recorded in the Cajon Pass borehole by Abercrombie (1995). Increases in&nbsp;apparent&nbsp;stress&nbsp;with event size could reflect an increase in seismic&nbsp;efficiency; however, η_sw&nbsp;for the Cajon earthquakes shows no such increase and is approximately constant over the entire moment range. Thus,&nbsp;apparent&nbsp;stress&nbsp;and&nbsp;stress&nbsp;drop&nbsp;co-vary, as&nbsp;expected&nbsp;from the&nbsp;energy&nbsp;balance at constant overshoot. The median value of η_sw&nbsp;for the Cajon earthquakes is four times lower than η_sw&nbsp;for laboratory events. Thus, these Cajon-recorded earthquakes have relatively low and approximately constant&nbsp;efficiency. As the&nbsp;energy&nbsp;balance requires η_sw&nbsp;= 0.5 - ξ, overshoot can be estimated directly from the Savage-Wood&nbsp;efficiency; overshoot is positive for Cajon Pass earthquakes. Variations in&nbsp;apparent&nbsp;stress&nbsp;with seismic moment for these earthquakes result primarily from systematic variations in&nbsp;static&nbsp;stress&nbsp;drop&nbsp;with seismic moment and do not require a relative decrease in sliding resistance with increasing event size (dynamic weakening). Based on the comparison of field and lab determinations of the Savage-Wood&nbsp;efficiency, we suggest the criterion η_sw&nbsp;&gt; 0.3 as a test for dynamic weakening in excess of that seen in the lab.</span></p></div></div> application/pdf 10.1785/0120020162 en Seismological Society of America On the expected relationships among apparent stress, static stress drop, effective shear fracture energy, and efficiency article