Contributions of Grain Damage, Thermal Weakening, and Necking to Slab Detachment

Abstract

We investigate the impact of three coupled weakening mechanisms on the viscous detachment of a stalled lithospheric slab: structural weakening due to necking, material weakening due to grain size reduction, using a two-phase grain damage model, and thermal weakening due to shear heating (thermal damage). We consider a combined flow law of dislocation and diffusion creep. To understand and quantify the coupling of these three nonlinear weakening processes, we derive a mathematical model, which consists of three coupled nonlinear ordinary differential equations describing the evolution of slab thickness, grain size, and temperature. With dimensional analysis, we determine the dimensionless parameters which control the relative importance of the three weakening processes and the two creep mechanisms. We derive several analytical solutions for end-member scenarios that predict the detachment time, that is the duration of slab detachment until slab thickness becomes zero. These analytical solutions are then tested against numerical solutions for intermediate cases. The analytical solutions are accurate for end-member scenarios where one of the weakening mechanisms and one of the creep mechanisms is dominant. Furthermore, we use numerical solutions of the system of equations to systematically explore the parameter space with a Monte Carlo approach. The numerical approach shows that the analytical solutions typically never deviate by more than 50% from the numerical ones, even for scenarios where all three weakening and both creep mechanisms are important. When both grain and thermal damage are important, the two damage processes generate a positive feedback loop resulting in the fastest detachment times. For Earth conditions, we find that the onset of slab detachment is controlled by grain damage and that during later stages of slab detachment thermal weakening becomes increasingly important and can become the dominating weakening process. We argue that both grain and thermal damage are important for slab detachment and that both damage processes could also be important for lithosphere necking during continental rifting leading to break-up and ocean formation.

Impact of upper mantle convection on lithosphere hyperextension and subsequent horizontally forced subduction initiation

“…B1) in M1 is ca. 9.95 × 10 6 (see Table 1), which is close to estimated values for upper mantle convection (Torrance and Turcotte, 1971;Schubert et al, 2001). Potential lateral asymmetry caused by the convecting cells in the upper mantle is inherited from the cooling period.…”

“…9 × 10 7 in M6. Compared to estimates for present-day Earth's upper mantle convection (Torrance and Turcotte, 1971;Schubert et al, 2001) this Rayleigh number is an order of magnitude higher. The lithosphere is recycled rapidly and the resulting values for density directly below the lithosphere are ca.…”

“…In nature, more softening mechanisms act in concert with thermal softening, such as grain damage (e.g. Bercovici and Ricard, 2012;Thielmann and Schmalholz, 2020), fabric and anisotropy evolution (e.g. Montési, 2013), and reactioninduced softening (e.g.…”

Timescale of Short‐Term Subduction Episodicity in Convection Models With Grain Damage: Applications to Archean Tectonics

“…Any slab in tension, in this case due to the viscous resistance to sinking applied to the top of the slab by the lithosphere, will stretch and, with a non‐linear rheology, can undergo necking (e.g., Bercovici et al, 2015; Schmalholz, 2011; Thielmann & Schmalholz, 2020). However, whether necking occurs in practice depends on the timescale for necking and detachment.…”

“…Moyen and van Hunen (2012) argued that short‐term subduction episodicty could explain sequences of “arc” and “non‐arc” rocks that alternate on timescales of ∼1–10 Myr, seen in some Archean cratons. Likewise, the dynamics of slab necking has also been studied in both simple analytical models, and full two‐ and three‐dimensional numerical models with Newtonian and non‐Newtonian rheologies (e.g., Davies & von Blanckenburg, 1995; Duretz et al, 2012; Duretz et al, 2011; Gerya et al, 2004; Ribe & Xu, 2019; Schmalholz, 2011; van Hunen & Allen, 2011), and with a damage formulation (Bercovici et al, 2015; Bellas et al, 2018; Bercovici et al, 2019; Thielmann & Schmalholz, 2020).…”