Insights on a Key Parameter of Earthquake Forecasting, the Coefficient of Variation of the Recurrence Time, Using a Simple Earthquake Simulator

Abstract

NTRODUCTION Probabilistic fault-based and time-dependent seismic-hazard studies are commonly used to forecast the time between con- secutive earthquakes; however, the correct evaluation of key parameters is critical for obtaining accurate results. Probabilities of occurrence must be input to formulate seismic design maps and to develop national recommendations for building codes around the world (e.g., Field et al., 2009; Stucchi et al., 2011; Stirling et al., 2012). The basic require- ments for computing earthquake probabilities are the mean re- currence time and its variability. To understand the statistical behavior of earthquakes, data on long earthquake sequences is necessary. However, worldwide during the instrumental period (approximately the past century), no major active fault segment has entirely ruptured more than once. Additional information on the recurrence of such events can be found in historical documents and damaged archaeological structures. Surface rup- tures can also be preserved in sedimentary deposits, leading to paleoseismological records. In many cases, the compilation of these data sources for a given fault segment may yield catalogs of large earthquakes that include 3–4 events, with exceptional examples reaching 15 events (e.g., the San Andreas fault sys- tem, Working Group on California Earthquake Probabilities [WGCEP], 2007; the Jordan valley fault, Ferry et al., 2011). Therefore, considering that the period over which histori- cal and palaeohistorical earthquake records are available is relatively short compared to the recurrence time of major earthquakes, synthetic catalogs generated from numerical sim- ulation models are needed. Earthquake simulations model long earthquake histories using various approximations of what is known about the physics of stress transfer due to fault slip and the rheological proprieties of faults (Tullis, 2012a). Today, the scientific knowledge regarding earthquake dynamics is far from complete; moreover, a realistic simulation of a full earth- quake cycle over sufficient time to generate enough data is cur- rently computationally infeasible. Therefore, the purpose of the simulations is to learn more about the statistical behavior of earthquakes in the hope that the earthquake physics hypotheses are not wrong. Many models with varying degrees of simpli- fication have been developed for writing ad hoc code to study the objective parameters (e.g., Ellsworth et al., 1999; Zöller and Hainzl, 2007; Robinson et al., 2009; Tullis, 2012b). This study focuses on a fault system earthquake simulator that explores the variability in the coefficient of variation (CV) of the recurrence time by analyzing the effects of the tectonic loading stress, the slip-rate variability, and the fault system geometry. The simulations incorporate variability in the mag- nitude threshold and stress-dependent earthquake nucleation. The impact of fault interaction on the recurrence time distribution of large earthquakes is an important question. Although local interactions are known to lead to self-organized criticality in many systems (e.g., Hainzl et al., 1999; Zöller and Hainzl, 2007), these interactions, especially from nearby faults, can advance or delay the occurrence of an earthquake (Gom- berg et al., 2005). However, in many cases, earthquake inter- actions are neglected and the seismicity is modeled for isolated faults. Moreover, if a fault is close to a critical state, small trans- ferred stresses can trigger an event almost instantaneously (e.g., King et al., 1994; Harris, 1998; Stein, 1999). Therefore, the recurrence time distribution of large events on individual faults will be modified if the influence of stresses transferred from nearby faults is taken into account. The variability in earthquake recurrence intervals is typ- ically defined using the CV for a sequence of earthquakes, which is defined as the standard deviation of the recurrence times over their mean. Several studies acknowledge that the CV values for earthquake recurrence intervals are poorly con- strained (e.g., Ellsworth et al., 1999), and small differences in the CV can lead to order of magnitude differences in earth- quake probability forecasts.We analyze data from a synthetic seismicity catalog, in which geometry is based on an active normal fault system in central Italy, to obtain predictive CV equations.