Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state-dependent friction

We present an efficient and rigorous numerical procedure for calculating th e elastodynamic response of a fault subjected to slow tectonic Boding proce sses of long duration within which there are episodes of rapid earthquake f ailure. This is done for a general class of rate- and state-dependent frict ion laws with positive direct velocity effect. The algorithm allows us to t reat accurately, within a single computational procedure, loading intervals of thousands of years and to calculate, for each earthquake episode, initi ally aseismic accelerating slip prior to dynamic rupture, the rupture propa gation itself, rapid post seismic deformation which follows, and also ongoi ng creep slippage throughout the loading period in velocity-strengthening f ault regions. The methodology is presented using the two-dimensional (2-D) antiplane spectral formulation and can be readily extended to the 2-D in-pl ane and 3-D spectral formulations and, with certain modifications, to the s pace-time boundary integral formulations as well as to their discretized de velopment using finite difference or finite element methods. The methodolog y can be used to address a number of important issues, such as fault operat ion under low overall stress, interaction of dynamic rupture propagation wi th pore pressure development, patterns of rapture propagation in events nuc leated naturally as a part of a sequence, the earthquake nucleation process , earthquake sequences on faults with heterogeneous frictional properties a nd/or normal stress, and others. The procedure is illustrated for a 2-D cru stal strike-slip fault model with depth-variable properties. For lower valu es of the state-evolution distance of the friction law, small events appear . The nucleation phases of the small and large events are very similar, sug gesting that the size of an event is determined by the conditions on the fa ult segments the event is propagating into rather than by the nucleation pr ocess itself. We demonstrate the importance of incorporating slow tectonic loading with elastodynamics by evaluating two simplified approaches, one wi th the slow tectonic loading but no wave effects and the other with all dyn amic effects included but much higher loading rate.