Art McGarr
1999
<p><span>Apparent stress τ</span><sub><i>a</i></sub><span> is defined as </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/c99e8535-ab71-4047-9e77-a095556771a3/jgrb11721-math-0001.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0001" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/c99e8535-ab71-4047-9e77-a095556771a3/jgrb11721-math-0001.gif"><span>, where </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0002" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif"><span> is the average shear stress loading the fault plane to cause slip and η is the seismic efficiency, defined as </span><i>E<sub>a</sub></i><span>/ </span><i>W</i><span>, where </span><i>E<sub>a</sub></i><span> is the energy radiated seismically and </span><i>W</i><span> 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 </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/1d6a5a68-60de-4d0d-85e7-e96af0d20ae3/jgrb11721-math-0003.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0003" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/1d6a5a68-60de-4d0d-85e7-e96af0d20ae3/jgrb11721-math-0003.gif"><span>. This hypothesis is tested here against a substantially augmented data set of earthquakes for which </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0002" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif"><span> can be estimated, mostly from in situ stress measurements, for comparison with τ</span><sub><i>a</i></sub><span>. 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</span><sub><i>a</i></sub><span> 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 </span><i>E<sub>a</sub></i><span> for earthquakes is usually underestimated due to factors such as band-limited recording. Thus upper bounds on </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/45bb1595-5de5-4b06-8e69-381c266a2e7e/jgrb11721-math-0004.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0004" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/45bb1595-5de5-4b06-8e69-381c266a2e7e/jgrb11721-math-0004.gif"><span> appear to be controlled by just a few fundamental aspects of frictional stick-slip behavior that are common to shallow earthquakes everywhere. Estimates of </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0002" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/faa02e65-a228-4ec8-a107-30fe058d033f/jgrb11721-math-0002.gif"><span> from measurements of τ</span><sub><i>a</i></sub><span> for suites of earthquakes, using </span><img class="section_image" src="https://agupubs.onlinelibrary.wiley.com/cms/asset/1d6a5a68-60de-4d0d-85e7-e96af0d20ae3/jgrb11721-math-0003.gif" alt="urn:x-wiley:01480227:media:jgrb11721:jgrb11721-math-0003" data-mce-src="https://agupubs.onlinelibrary.wiley.com/cms/asset/1d6a5a68-60de-4d0d-85e7-e96af0d20ae3/jgrb11721-math-0003.gif"><span>, are found to be comparable in magnitude to estimates of shear stress on the basis of extrapolating in situ stress data to seismogenic depths.</span></p>
application/pdf
10.1029/1998JB900083
en
American Geophysical Union
On relating apparent stress to the stress causing earthquake fault slip
article