Statistical Modeling of the 1997-1998 Colfiorito Earthquake Sequence: Locating a Stationary Solution within Parameter Uncertainty

The Umbria-Marche region of Italy is a seismically active region that experienced a strong sequence of earthquakes during 1997-1998, with a cluster of magnitude M >= 5 events, during which the average event rate increased from the long-term level by several orders of magnitude. Using maximum-likelihood (ML) inversion of the epidemic-type aftershock sequences model to characterize the seismicity of this region over 22 years, we find, in agreement with previous studies, the event rate during the sequence is underpredicted, based on simulations with the large M >= 5 events fixed. However, by sampling the parameter space around the ML solution within the inversion uncertainty and comparing the simulated event rate with that of the real data, we are able to find near-maximum-likelihood parameters that provide a reasonable match to both the long-term average event rate and the rate during the sequence. We use the shape of the interevent time histogram to infer that the events in the sequence are probably mostly aftershocks of the large events, rather than an increased occurrence of background events. We suggest that event rate comparisons can be useful as an additional constraint on the selection of parameters from within the 95% confidence interval of the ML fit. Our results demonstrate the extra constraint can greatly improve the match between a stationary model and finite catalog data and that care is needed before adding further parameters to ascribe nonstationarity to time-dependent event rate changes.