Relationships between fault geometry, slip rate variability and earthquake recurrence in extensional settings

Field observations and modelling indicate that elastic interaction between active faults can lead to variations in earthquake recurrence intervals measured on timescales of 102-104 yr. Fault geometry strongly influences the nature of the interaction between adjacent structures as it controls the spatial redistribution of stress when rupture occurs. In this paper, we use a previously published numerical model for elastic interaction between spontaneously growing faults to investigate the relationships between fault geometry, fault slip rate variations and the statistics of earthquake recurrence. These relationships develop and become systematic as a long-term consequence of stress redistribution in individual rupture events even though on short timescales earthquake activity appears to be stochastic. We characterize fault behaviour using the coefficient of variation (CV) of earthquake recurrence intervals and introduce a new measure, slip-rate variability (SRV) that takes into account the size and time ordering of slip events. CV generally increases when the strain is partitioned on more than one fault but the relationship between long-term fault slip rate (SRmean) and CV is poorly defined. In contrast, SRV increases systematically where faulting is more distributed and SRmean is lower. To first order, SRV is inversely proportional to SRmean. We also extract earthquake recurrence statistics and compare these to previously published probability density functions used in earthquake forecasting. The histograms of earthquake recurrence vary systematically as a function of fault geometry and are best characterized by a Weibull distribution with fitting parameters that vary from site to site along the fault array. We explain these phenomena in terms of a time-varying, geometrical control on stress loading of individual faults arising from the history of elastic interactions and compare our results with published data on SRV and earthquake recurrence along normal faults in New Zealand and in the Italian Apennines. Our results suggest that palaeoseismic data should be collected and analysed with structural geometry in mind and that information on SRV, CV and SRmean should be integrated with data from earthquake catalogues when evaluating seismic hazard.