A Burgers-Brittle model for the seismic-aseismic, brittle-ductile transition within the Earth crust
Authors: Dansereau Véronique , Shapiro Nikolai , Campillo Michel , Weiss Jérôme 
Published: March 2021

&lt;p&gt;&lt;span&gt;&lt;span&gt;The rheological stratification of &lt;/span&gt;&lt;span&gt;the subducting &lt;/span&gt;&lt;span&gt;frontiers of plate tectonics &lt;/span&gt;&lt;span&gt;is nowadays &lt;/span&gt;&lt;span&gt;recognized&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;So is &lt;/span&gt;&lt;span&gt;the spatial correlation&lt;/span&gt; &lt;span&gt;between&lt;/span&gt;&lt;span&gt; t&lt;/span&gt;&lt;span&gt;he transient Episodic Tremor and Slip (ETS) processes &lt;/span&gt;&lt;span&gt;and&lt;/span&gt;&lt;span&gt; the&lt;/span&gt; &lt;span&gt;brittle-ductile transition&lt;/span&gt; &lt;span&gt;that sits between &lt;/span&gt;&lt;span&gt;the &lt;/span&gt;&lt;span&gt;seismic zone at the surface and &lt;/span&gt;&lt;span&gt;the&lt;/span&gt;&lt;span&gt; aseismic zone at depth.&lt;/span&gt; &lt;span&gt;However, the mechanical processes &lt;/span&gt;&lt;span&gt;underlying ETS&lt;/span&gt;&lt;span&gt;, their relation to a mixed brittle-ductile rheology &lt;/span&gt;&lt;span&gt;and&lt;/span&gt;&lt;span&gt; the feedbacks between &lt;/span&gt;&lt;span&gt;highly&lt;/span&gt; &lt;span&gt;localized and &lt;/span&gt;&lt;span&gt;distributed&lt;/span&gt;&lt;span&gt; deformations and between &lt;/span&gt;&lt;span&gt;ETS and major earthquakes are still not well established. One &lt;/span&gt;&lt;span&gt;of the&lt;/span&gt;&lt;span&gt; main reason is the lack of direct models that can represent &lt;/span&gt;&lt;span&gt;the deformation of subduction zone&lt;/span&gt;&lt;span&gt;s&lt;/span&gt;&lt;span&gt; as a whole (the continental and oceanic plate&lt;/span&gt;&lt;span&gt;s&lt;/span&gt;&lt;span&gt;, their interface and the upper mantle)&lt;/span&gt; &lt;span&gt;and that can be compared to seismic and geode&lt;/span&gt;&lt;span&gt;t&lt;/span&gt;&lt;span&gt;ic observations of ETS. In this context, we propose a new continuum, Finite Elements-based model that can &lt;/span&gt;&lt;span&gt;serve as a&lt;/span&gt;&lt;span&gt; tool to improve the current understanding of &lt;/span&gt;&lt;span&gt;the seismic-aseismic, brittle-ductile transition within the Earth crust. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;span&gt;The framework is based on the visco-elastic Burgers &lt;/span&gt;&lt;span&gt;rheology&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;Here, t&lt;/span&gt;&lt;span&gt;he Maxwell &lt;/span&gt;&lt;span&gt;element&lt;/span&gt;&lt;span&gt; accounts for the permanent &lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;span&gt;transient and steady state&lt;/span&gt;&lt;span&gt;)&lt;/span&gt;&lt;span&gt; deformation&lt;/span&gt;&lt;span&gt;s&lt;/span&gt; &lt;span&gt;within&lt;/span&gt;&lt;span&gt; the shearing zone and &lt;/span&gt;&lt;span&gt;both &lt;/span&gt;&lt;span&gt;plates&lt;/span&gt;&lt;span&gt; and the Kelvin-&lt;/span&gt;&lt;span&gt;Voigt&lt;/span&gt; &lt;span&gt;element&lt;/span&gt;&lt;span&gt; accounts for the visco-elastic adjustment of the upper mantle. &lt;/span&gt;&lt;span&gt;A unique constitutive equation is applied to the entire system, &lt;/span&gt;&lt;span&gt;but the mechanical behavior &lt;/span&gt;&lt;span&gt;of&lt;/span&gt;&lt;span&gt; each of its parts is differentiated by allowing t&lt;/span&gt;&lt;span&gt;he elastic modulus and effective viscosity associated with the Maxwell &lt;/span&gt;&lt;span&gt;element&lt;/span&gt; &lt;span&gt;to &lt;/span&gt;&lt;span&gt;evolve in both space and time according to the level of fracturing at the sub-grid scale. &lt;/span&gt;&lt;span&gt;This is&lt;/span&gt;&lt;span&gt; represented by a scalar damage variable, &lt;/span&gt;&lt;span&gt;which&lt;/span&gt;&lt;span&gt; increases locally when the state of stress becomes overcritical with respect to a Mohr-Coulomb criterion and decreases logarithmically due to sealing &lt;/span&gt;&lt;span&gt;at the &lt;/span&gt;&lt;span&gt;sub-grid scale. The coupling is such that &lt;/span&gt;&lt;span&gt;within&lt;/span&gt;&lt;span&gt; undamaged zones,&lt;/span&gt;&lt;span&gt; the relaxation of the stresses is stable and set by the bulk viscosity of the bedrock &lt;/span&gt;&lt;span&gt;while&lt;/span&gt; &lt;span&gt;within&lt;/span&gt;&lt;span&gt; damaged zones, &lt;/span&gt;&lt;span&gt;such &lt;/span&gt;&lt;span&gt;as the shearing interface of the plates, the deformation is accomodated by a combination of seismic, brittle fracturing and aseismic, transient stress relaxation processes. &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;span&gt;The idealized 2-dimensional simulations of the brittle-ductile transition in a subduction zone that will be presented shows that the model represents a damaged shearing zone between the continental and oceanic plates. This zone, which concentrates the deformation, is maintained in time and space through a competition between brittle fracturing events, stress redistribution and healing processes. In between large damage events, associated with major earthquakes, the damage activity is correlated over a wide range of time scales.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;