EARTHQUAKE TRIGGERING BY TRANSIENT AND STATIC DEFORMATIONS

Observational evidence for both static and transient near-field and fa r-field triggered seismicity are explained in terms of a frictional in stability model, based on a single degree of freedom spring-slider sys tem and rate- and state-dependent frictional constitutive equations. I n this study a triggered earthquake is one whose failure time has been advanced by Delta t (clock advance) due to a stress perturbation. Tri ggering stress perturbations considered include square-wave transients and step functions, analogous to seismic waves and coseismic static s tress changes, respectively. Perturbations are superimposed on a const ant background stressing rate which represents the tectonic stressing rate. The normal stress is assumed to be constant. Approximate, closed -form solutions of the rate-and-state equations are derived for these triggering and background loads, building on the work of Dieterich [19 92, 1994]. These solutions can be used to simulate the effects of stat ic and transient stresses as a function of amplitude, onset time t(0), and in the case of square waves, duration. The accuracies of the appr oximate closed-form solutions are also evaluated with respect to the f ull numerical solution and t(0). The approximate solutions underpredic t the full solutions, although the difference decreases as t(0) approa ches the end of the earthquake cycle. The relationship between Delta t and t(0) differs for transient and static loads: a static stress stop imposed late in the cycle causes less clock advance than an equal ste p imposed earlier, whereas a later applied transient causes greater cl ock advance than an equal one imposed earlier. For equal Delta t, tran sient amplitudes must be greater than static loads by factors of sever al tens to hundreds depending on t(0). We show that the rate-and-state model requires that the total slip at failure is a constant, regardle ss of the loading history. Thus a static load applied early in the cyc le, or a transient applied at any time, reduces the stress at the init iation of failure, whereas static loads that are applied sufficiently late raise it. Rate-and-state friction predictions differ markedly fro m those based on Coulomb failure stress changes (Delta CFS) in which D elta t equals the amplitude of the static stress change divided by the background stressing rate. The Delta CFS model assumes a stress failu re threshold, while the rate-and-state equations require a slip failur e threshold. The complete rate-and-state equations predict larger Delt a t than the Delta CFS model does for static stress steps at small t(0 ), and smaller Delta t than the Delta CFS model for stress steps at la rge t(0). The Delta CFS model predicts nonzero Delta t only for transi ent loads that raise the stress to failure stress levels during the tr ansient. In contrast, the rate-and-state model predicts nonzero Delta t for smaller loads, and triggered failure may occur well after the tr ansient is finished. We consider heuristically the effects of triggeri ng on a population of faults, as these effects might be evident in sei smicity data. Triggering is manifest as an initial increase in seismic ity rate that may be followed by a quiescence or by a return to the ba ckground rate. Available seismicity data are insufficient to discrimin ate whether triggered earthquakes are ''new'' or clock advanced. Howev er, if triggering indeed results from advancing the failure time of in evitable earthquakes, then our modeling suggests that a quiescence alw ays follows transient triggering and that the duration of increased se ismicity also cannot exceed the duration of a triggering transient loa d. Quiescence follows static triggering only if the population of avai lable faults is finite.