Evolution of a Subducted Slab with Viscosity Controlled by Damage and Healing Processes

Abstract:

The rheology and viscosity in the lithosphere and mantle are fundamental to understanding mantle and lithospheric dynamics including the emergence and evolution of plate tectonics on Earth and other planets. The viscosity is controlled by temperature, stress, and grain size, and particularly, the grain size leads to history-dependence in viscosity through damaging and healing processes at grain scales. Motivated by studies by Bercovici, Schubert and Ricard, [2015] and Schmalholz [2011], in this study, we investigate the rheology and viscosity in the vicinity of a subducted slab which hangs from the overlying lithosphere. We calculate both numerically and analytically the timescale on which viscosity diminishes to a minimum as a result of grain size reduction caused by buoyancy induced deformation and damage. The evolution equation for grain size (or fineness as the inverse grain size) is solved with a second order Runge-Kutta scheme, together with a tracer method, and the mantle dynamics is solved with Citcom which has been modified to include grain size dependent viscosity. We initially do not allow the slab’s buoyancy to evolve. The analytical solution for viscosity evolution and its timescale is derived under the assumption that stress is constant. We find that the analytical and numerical solutions of viscosity reduction with time are in good agreement with each other. In all cases, when Dσ² > H, where D is damage parameter, σ stress, and H healing parameter, which ensures damage dominates over healing, the timescale of the viscosity reduction is inversely proportional to D, and is on the order of 1 Myr for an Earth-like planet. Our work implies that the evolution of rheology in a damage-dominated regime around a subducted slab is a rapid process. We will extend the models to allow slab buoyancy to co-evolve with grain size and viscosity to examine the effect on this characteristic timescale and slab dynamics.