Diffuse earthquake rupture dynamics in nonlinear visco-elasto-plastic materials

Abstract:

Earthquake fault zones are more geometrically and rheologically complex than an idealised infinitely thin plane embedded in linear elastic material. Field and laboratory measurements reveal complex fault zone structure involving tensile and shear fractures spanning a wide spectrum of length scales (e.g., Mitchell & Faulkner, 2009), dense seismic and geodetic recording of small and large earthquakes show hierarchal volumetric faulting patterns (e.g., Cheng et al., 2018, Ross et al., 2019) and 2D numerical models explicitly accounting for off-fault fractures demonstrate important feedback with rupture dynamics and ground motions (e.g., Thomas & Bhat 2018, Okubo et al., 2019).

Here we adopt a diffuse crack representation to incorporate finite strain nonlinear material behaviour, natural complexities and multi-physics coupling into dynamic earthquake rupture modeling (Gabriel et al., 2020), using a first order hyperbolic and thermodynamically compatible mathematical model, namely the GPR model (Godunov & Romenski, 1972; Romenski, 1988). Pre-damaged faults as well as dynamically induced off-fault cracks are therein described via a scalar function indicating the local level of material damage (Tavelli et al., 2020); arbitrarily complex geometries are represented via a diffuse interface approach (Tavelli et al., 2019). High-order accuracy and adaptive Cartesian meshes are enabled in 2D and 3D by using the extreme scale hyperbolic PDE solver ExaHyPE (Reinarz et al., 2019).

We compare the new diffuse interface fault models of kinematic cracks, spontaneous dynamic rupture and dynamically generated off-fault shear cracks to sharp interface reference models. To this end, we calibrate the GPR model to resemble empirical tensile and shear crack formation and friction laws. We find that the continuum model can resemble and extend classical solutions, while introducing dynamic differences (i) on the scale of pre-damaged/low-rigidity fault zone, such as out-of- plane rupture rotation; and (ii) on the scale of the intact host rock, such as conjugate shear cracking in tensile lobes.

We next aim to combine tensile micro-fracture with mesoscopic shear failure off-fault, diffuse fault dynamic rupture and 3D seismic wave propagation with complex topography to span the entire scales of fault zone fracture dynamics.