Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling

<jats:title>Abstract</jats:title> <jats:p> Small repeating earthquakes are thought to represent rupture of isolated asperities loaded by surrounding creep. The observed scaling between recurrence interval and seismic moment, <jats:italic>T</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> ∼ <jats:italic>M</jats:italic> <jats:sup>1/6</jats:sup> , contrasts with expectation assuming constant stress drop and no aseismic slip ( <jats:italic>T</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> ∼ <jats:italic>M</jats:italic> <jats:sup>1/3</jats:sup> ). Here we demonstrate that simple crack models of velocity‐weakening asperities in a velocity‐strengthening fault predict the <jats:italic>M</jats:italic> <jats:sup>1/6</jats:sup> scaling; however, the mechanism depends on asperity radius, <jats:italic>R</jats:italic> . For small asperities ( <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb53145-math-0001.png" xlink:title="urn:x-wiley:jgrb:media:jgrb53145:jgrb53145-math-0001"/> , where <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb53145-math-0002.png" xlink:title="urn:x-wiley:jgrb:media:jgrb53145:jgrb53145-math-0002"/> is the nucleation radius) numerical simulations with rate‐state friction show interseismic creep penetrating inward from the edge, and earthquakes nucleate in the center and rupture the entire asperity. Creep penetration accounts for ∼25% of the slip budget, the nucleation phase takes up a larger fraction of slip. Stress drop increases with increasing <jats:italic>R</jats:italic> ; the lack of self‐similarity being due to the finite nucleation dimension. For <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb53145-math-0003.png" xlink:title="urn:x-wiley:jgrb:media:jgrb53145:jgrb53145-math-0003"/> simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb53145-math-0004.png" xlink:title="urn:x-wiley:jgrb:media:jgrb53145:jgrb53145-math-0004"/> exhibit complex cycles of partial and full ruptures. Here <jats:italic>T</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> is explained by an energy criterion: full rupture requires that the energy release rate everywhere on the asperity at least equals the fracture energy, leading to the scaling <jats:italic>T</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> ∼ <jats:italic>M</jats:italic> <jats:sup>1/6</jats:sup> . Remarkably, in spite of the variability in behavior with source dimension, the scaling of <jats:italic>T</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> with stress drop Δ <jats:italic>τ</jats:italic> , nucleation length and creep rate <jats:italic>v</jats:italic> <jats:sub>pl</jats:sub> is the same across all regimes: <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb53145-math-0005.png" xlink:title="urn:x-wiley:jgrb:media:jgrb53145:jgrb53145-math-0005"/> . This supports the use of repeating earthquakes as creepmeters and provides a physical interpretation for the scaling observed in nature. </jats:p>