Impact on Risk of Data-Constrained Inferences of the Variability of the Recurrence of Ground-Rupturing Earthquakes
Abstract:The concept of the time-dependence of the occurrence of large events on a given geologic structure emerged from the elastic rebound theory of Reid (1910). Models were developed or chosen to account for it. For the most part, those models need the long-term recurrence time, a measure of the allowed short-term variability of the recurrence time (e.g., the coefficient of variation CoV), and are applied in conjunction with the time since the last event whenever possible. Geologic estimates of the long-term have been used for a long time. CoV values, on the other hand, were first assigned usually through a logic-tree approach featuring a preferred value and one or two alternative values. Later-on a generic CoV value was determined on a global dataset (Elssworth et al 1999). It is only recently that earthquake timing data at a site have become numerous and high resolution enough to warrant data-constrained estimates of CoV.
Whereas a logic-tree approach, meant to formulate epistemic uncertainties, leads to different (weighted) estimates of risk metrics, an approach in which the model parameters (such as CoV) are constrained by earthquake data presents a different view of risk uncertainty.
Indeed, when the data are not informative, the resulting hazard rate curve vs. time since last event is flat. As information becomes integrated in the model, if the fault indeed exhibits a time-dependent behavior, the hazard rate curve shows variability with elapsed time. In terms of risk, a flat hazard rate translates into a time-independent view of risk whereas a time-varying hazard rate results in short-term variations in risk estimates.
In this view, the hazard rate at a given time does not have an uncertainty associated to it (in the same way that a probability density function does not have an uncertainty associated to it). Its value integrates all the uncertainties coming from model and data. This approach allows a seamless update of risk metrics as new earthquake data becomes available.
We show on the example of crustal faults in the Wellington region, New Zealand, how very impactful the choice on a model for CoV is in terms of capital reserve requirements and other risk metrics. To do this, we choose various individual values of CoV, and we compare the risk results with those obtained using data-constrained posterior distributions of CoV.