Ductile deformation is typically associated with slow and steady-state deformation, yet the occurrence of deep earthquakes, which exhibit a rapid and transient behavior, challenges this view. One proposed mechanism to facilitate such behavior is thermal runaway. However, two-dimensional (2D) models that capture highly localized, transient ductile deformation, driven by thermal runaway, remain unexplored. This study presents 2D simple shear models using the pseudo-transient relaxation method optimized for graphics processing units. The models incorporate a Maxwell rheology including compressible elasticity, diffusion creep, dislocation creep, and low-temperature plasticity. Our models capture the nucleation and transient propagation of highly localized ductile ruptures driven by thermal runaway. Depending on rheological parameters, we observe a spectrum of behaviors: (a) broad shear zones which deform only slightly faster than the boundary conditions; (b) localized deformation which is orders of magnitude faster than far field deformation; and (c) highly localized ruptures reaching seismic slip velocities. Runaway intensity scales with nondimensional numbers derived from 1D studies, but its spatial and temporal evolution is more complex, traversing several stages. The rupture front perturbs the local stress field, generating opposing pressure anomalies of up to 1.5 GPa. For mantle transition zone conditions, thermal runaway-driven ductile ruptures can reach seismic slip velocities, confirming it as a viable mechanism for deep-focus earthquakes. Under brittle-ductile transition zone conditions, our models capture thermal runaway driving accelerated creep which disturbs the local pressure field sufficiently to facilitate brittle failure in an otherwise ductile host rock.
Spang et al. (Wed,) studied this question.