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Recurrent Large Earthquakes in a Fault Region: What Can Be Inferred from Small and Intermediate Events?

Interdisciplinary Center for the Dynamics of Complex Systems and Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany

S. Hainzl

GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany

M. Holschneider

Interdisciplinary Center for the Dynamics of Complex Systems and Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany

We present a renewal model for the recurrence of large earthquakes in a fault zone consisting of a major fault and surrounding smaller faults with Gutenberg–Richter-type seismicity represented by seismic moment release drawn from a truncated power-law distribution. The recurrence times of characteristic earthquakes for the major fault are explored. It is continuously loaded (plate motion) and undergoes positive and negative fluctuations due to adjacent smaller faults, with a large number N_eq of such changes between two major earthquakes. Because the distribution has a finite variance, in the limit N_eq the central limit theorem implies that the recurrence times follow a Brownian passage-time (BPT) distribution. This allows us to calculate individual recurrence-time distributions for specific fault zones without tuning free parameters: the mean recurrence time can be estimated from geological or paleoseismic data, and the standard deviation is determined from the frequency-size distribution, namely, the Richter b-value, of an earthquake catalog. The approach is demonstrated for the Parkfield segment of the San Andreas fault in California as well as for a long simulation of a numerical fault model. Assuming power-law distributed earthquake magnitudes up to the size of the recurrent Parkfield event (M 6), we find a coefficient of variation that is higher than the value obtained by a direct fit of the BPT distribution to seven large earthquakes. We argue that the BPT distribution is a reasonable choice for seismic hazard assessment because it governs not only Brownian motion with drift but also models with power-law statistics for the recurrence of large earthquakes in an asymptotic limit. Finally, we find that the condition b=1 separates two regimes: in the first (b<1) the failure rate after a long elapsed time is smaller than the mean failure rate whereas in the second (b>1) it is greater.