Abstract
We consider expected relationships between apparent stresstau a and
static stress drop Deltataus using a standard energy balance and
findtau a = Deltataus(0.5 -xi ), wherexi is stress overshoot. A simple
implementation of this balance is to assume overshoot is constant;
then apparent stress should vary linearly with stress drop, consistent
with spectral theories (Brune, 1970) and dynamic crack models (Madariaga,
1976). Normalizing this expression by the static stress drop defines
an efficiencyeta sw =tau a/Deltataus as follows from Savage and Wood
(1971). We use this measure of efficiency to analyze data from one
of a number of observational studies that find apparent stress to
increase with seismic moment, namely earthquakes recorded in the
Cajon Pass borehole by Abercrombie (1995). Increases in apparent
stress with event size could reflect an increase in seismic efficiency;
however, eta sw for the Cajon earthquakes shows no such increase
and is approximately constant over the entire moment range. Thus,
apparent stress and stress drop co-vary, as expected from the energy
balance at constant overshoot. The median value ofeta sw for the
Cajon earthquakes is four times lower than eta sw for laboratory
events. Thus, these Cajon-recorded earthquakes have relatively low
and approximately constant efficiency. As the energy balance requireseta
sw = 0.5 -xi , overshoot can be estimated directly from the Savage-Wood
efficiency; overshoot is positive for Cajon Pass earthquakes. Variations
in apparent stress with seismic moment for these earthquakes result
primarily from systematic variations in static stress drop 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 efficiency, we
suggest the criterioneta sw > 0.3 as a test for dynamic weakening
in excess of that seen in the lab. 10.1785/0120020162
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