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## Rupture Synchronicity in Complex Fault Systems

Kevin R. Milner, & Thomas H. Jordan

Published September 2013, SCEC Contribution #1893

While most investigators would agree that the timing of large earthquakes within a fault system depends on stress-mediated interactions among its elements, much of the debate relevant to time-dependent forecasting has been centered on single-fault concepts, such as characteristic earthquake behavior. We propose to broaden this discussion by quantifying the multi-fault concept of rupture synchronicity. We consider a finite set of small, fault-spanning volumes {Vk} within a fault system of arbitrary (fractal) complexity. We let Ck be the catalog of length tmax comprising Nk discrete times {ti(k)} that mark when the kth volume participates in a rupture of magnitude > M. The main object of our analysis is the complete set of event time differences {τij(kk') = ti(k) - tj(k')}, which we take to be a random process with an expected density function ρkk'(t). When k = k', we call this function the auto-catalog density function (ACDF); when k ≠ k', we call it the cross-catalog density function (CCDF). The roles of the ACDF and CCDF in synchronicity theory are similar to those of autocorrelation and cross-correlation functions in time-series analysis. For a renewal process, the ACDF can be written in terms of convolutions of the interevent-time distribution, and many of its properties (e.g., large-t asymptote) can be derived analytically. The interesting information in the CCDF, like that in the ACDF, is concentrated near t = 0. If two catalogs are completely asynchronous, the CCDF collapses to an asymptote given by the harmonic mean of the ACDF asymptotes. Synchronicity can therefore be characterized by the variability of the CCDF about this asymptote. The brevity of instrumental catalogs makes the identification of synchronicity at large M difficult, but we will illustrate potentially interesting behaviors through the analysis of a million-year California catalog generated by the earthquake simulator, RSQSim (Deiterich & Richards-Dinger, 2010), which we sampled at a dozen fault-spanning volumes. At the magnitude threshold M = 7, the ACDF can be well fit by renewal models with fairly small aperiodicity parameters (α < 0.2) for all fault volumes but one (on the San Jacinto fault). At interseismic (Reid) time scales, we observe pairs of fault segments that are tightly locked, such as the Cholame and Carrizo sections of the San Andreas Fault (SAF), where the CCDF and two ACDFs are nearly equal; segments out of phase (Carrizo-SAF/Coachella-SAF and Coachella-SAF/San Jacinto), where the CCDF variation is an odd function of time; and segments where events are in phase with integer ratios of recurrence times (2:1 synchronicity of Coachella-SAF/Mojave-SAF and Carrizo-SAF/Mojave-SAF). At near-seismic (Omori) time scales, we observe various modes of clustering, triggering, and shadowing in RSQSim catalogs; e.g., events on Mojave-SAF trigger Garlock events, and events on Coachella-SAF shut down events on San Jacinto. Therefore, despite its geometrical complexity and multiplicity of time scales, the RSQSim model of the San Andreas fault system exhibits a variety of synchronous behaviors that increase the predictability of large ruptures within the system. A key question for earthquake forecasting is whether the real San Andreas system is equally, or much less, synchronous.

Citation
Milner, K. R., & Jordan, T. H. (2013, 9). Rupture Synchronicity in Complex Fault Systems. Poster Presentation at SCEC Annual Meeting 2013.