Shear instability in a viscoelastic material as the cause of deep focus earthquakes

<jats:p>The mechanism of deep focus earthquakes has been examined by numerical and linear analysis of shear instability in subducting slabs. We assume subducting slabs deform such that the spatially averaged strain rate <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> becomes time independent. Furthermore, we assume that rheology depends on temperature in the manner of an activation process. Using this model, we investigate quantitatively the conditions under which shear instability takes place, i.e., the deformation in the material concentrates in a thin layer whose temperature increases explosively until melting occurs. First, we study instability in a material whose rheological properties are spatially homogeneous. Shear instability takes place in a homogeneous material when <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> exceeds a certain critical level <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="urn:x-wiley:01480227:media:jgrb6379:jgrb6379-math-0001"/>, which depends strongly on the stress in the slabs but does not depend on the detail of the creep law (the value of the activation energy). Next, we study instability in a material that contains shear zones similar to those often observed by field geologists, i.e., a thin layer made of material with lower vicosity than the surrounding region. We find that shear zones trigger shear instability even for the case of <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> provided that G, the ratio of characteristic time of thermal diffusion to that of shear heating in shear zones, exceeds 1, and that f, the ratio of stiffness of elastic deformation in the surrounding region to that of ductile deformation in shear zones, becomes lower than 1. Applying this condition to subducting slabs with shear zones, we find that shear zones trigger shear instability even when the average strain rate <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> is lower than <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> by an order of magnitude. From these results, and from an estimate of <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgrb6379-math-0001.gif" xlink:title="equation image"/> in subducting slabs, we conclude that shear instability is a mechanism likely to induce deep focus earthquakes.</jats:p>