Dynamic simulations of slip on a smooth fault in an elastic solid

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Abstract
We report on numerical simulations of slip evolution along a two dimensional (slip varies only with depth) vertical strike‐slip fault in an elastic half‐space, using a framework incorporating full inertial elastodynamics. The model is a follow‐up on earlier quasi‐static and quasi‐dynamic simulations of deformations along smooth fault systems in elastic continua. The fault is driven below a crustal depth of 24 km by a constant plate velocity of 35‐mm/yr. Deformation at each fault location in the crustal zone is the sum of slip rate contributions from rate‐ and state‐dependent friction and power law creep, where both processes have temperature‐dependent (and hence depth‐varying) coefficients and both take place locally under the same stress. The simulations employ two versions of rate‐ and state‐dependent friction: a “slip” law, which requires nonzero velocity for state evolution, and an ”ageing/slowness“ law, which incorporates state evolution and restrengthening in stationary contact. The assumed constitutive laws and distribution of frictional parameters are compatible with laboratory experiments. The elastodynamic calculations are based on spectral representations of variables and a new algorithm providing a unified computational framework for calculations of long deformational histories containing short periods of rapid instabilities. The simulations show dynamic rupture propagation and wave phenomena not accounted for in the previous quasi‐static and quasi‐dynamic works. However, the results are qualitatively similar to those obtained by corresponding quasi‐static and quasi‐dynamic calculations. Slip histories along a smooth fault, simulated here with full elastodynamics for various constitutive laws and model parameters, consist mostly of quasi‐periodic large events. This finding indicates that inertial dynamics does not provide a generic mechanism for generating spatio‐temporal complexities of slip. On the other hand, calculations done for cases representing, approximately, strongly disordered systems do show rich slip histories with a range of event sizes. This result is compatible with our previous conclusions that the origin of observed broad distributions of earthquake sizes is strong fault zone heterogeneities. The fully dynamic calculations illustrate the evolution of nucleation phases of instabilities associated with accelerating and expanding creep. Final slip values of model earthquakes in full elastodynamic calculations are larger than those of corresponding quasi‐static and quasi‐dynamic events. The dynamic overshoot in simulations with the slip version of friction is larger than in those employing the ageing/slowness law.

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