[S-CG45] Science of slow-to-fast earthquakes

[SCG45-23] Depth-dependent Slow Earthquakes Controlled by Temperature Dependence of Brittle-ductile Transitional Rheology

*Ryosuke Ando¹, Kohtaro Ujiie², Naoki Nishiyama⁴, Yasushi Mori³ (1.Graduate School of Science, University of Tokyo, 2.Graduate School of Life and Environmental Sciences, University of Tsukuba, 3.Kitakyushu Museum of Natural History and Human History, 4.National Institute of Advanced Industrial Science and Technology)

Keywords:Rheology, Fault rocks, Physical model

The discovery of slow earthquakes illuminates the existence of a strange depth dependence of seismogenesis, which contradicts the common understanding of smooth brittle/seismic-ductile/aseismic transition as going deeper into the earth’s surface layers. However, within the transitional layer on plate interfaces, observations have clarified slip velocities of slow earthquakes changing from those slower to faster with increasing depth, as described by the “seismogenic inversion layer.” We propose a new mechanical model that can consistently explain the classic brittle-ductile transition and this inversion phenomenon by considering the heterogeneous fault zone composed of brittle blocks in the ductile matrix.
The key mechanism is the interplay between the volumetric fraction of brittle blocks and the viscosity of the surrounding plastically deformed matrix, where the former and the latter decrease with increasing temperature. We simplified the fault area with brittle patches embedded in an otherwise ductile background imposed in the one-degree-of-freedom model. We assume the fraction of the brittle patches over the fault area is described by a power law function of temperature T as Rb(T)=1-T-Tfb/Tfp-Tfbc, which decreases from one at the fully brittle temperature T_fb to zero at the fully ductile temperature T_fd. We can describe the amount of slip as the decreasing function of temperature:
maxΔu(T)∝Δfo[1-{(T-T_fb)/(T_fp-T_fb)}^c,
where Δfo is a constant corresponding to the amount of force drop at the fully brittle temperature. If we further incorporate the ductility governed by plastic flow mechanisms with the temperature-dependent viscosity given by the Arrhenius law (ηT=η_oexp(gT_m/T)), the maximum amount of slip rate at T is described by
max Δu(T)∝Δf_o[1-{(T-Tfb)/(Tfp-Tfb)^c}/η_o{(T-T_fb)/(T_fp-T_fb)}^cexp(gT_m/T).
This function exhibits a peak of the slip rate at an intermediate temperature Tsr satisfying Tfb<Tsr<Tfp. This peak of slip rate reproduces SIL as the result of the interplay between the brittle fraction Rb(T) and the viscosity ηT, which are both the decreasing function of temperature but, importantly, at a different speeds. This model is extended to shallow-slow earthquakes, where the origin of the ductility is shown to be different if SIL is absent. Our results open a new pathway to infer the deformation mechanisms underlying slow earthquakes.

Reference: Ando, Ujiie, Nishiyama and Mori, Geophys. Res. Letter, 2022GL101388, 2023 (in press).