Transformation shear instability and the seismogenic zone for deep earthquakes

We use a numerical model for olivine-spinel transformation to study deep earthquake nucleation and to delineate the seismogenic region within a subducting slab. The model includes laboratory-derived flow laws, latent heat release, and phase transformation kinetics. We calculate deformation, transformation state, grain growth, and rheology for several paths within a subducting slab. Strain rate perturbations are imposed to define the necessary conditions for instability. Strain rate perturbations decay for ξ < a critical value ξ_c, and thus the coldest, interior portion of the metastable wedge deforms stably. For ξ≥ξ_c, strain rate perturbations grow, shear strength decreases with strain, and the system is potentially unstable. The instability condition is mapped to delineate the seismogenic zone within a subducting slab. The model seismogenic zone is bounded by ξ_c, and, at larger percent transformations, by coarsening of spinel grains and saturation of the transformation weakening effect. The model predicts a narrow seismogenic region along the outer edges of the metastable wedge and thus a "double seismic" zone, consistent with some seismic observations. Several simplifying assumptions are required due to lack of thermo-kinetic data and incomplete knowledge of constituent mineralogy and rheology. However, the model provides a quantitative definition of the instability condition and a framework for testing the hypothesis of transformation-induced instability.