Quantifying the Earthquake Clustering that Independent Sources with Stationary Rates (as Included in Current Risk Models) Can Produce.

Abstract:

The recent Canterbury earthquake sequence (CES) renewed public and academic awareness concerning the clustered nature of seismicity. Multiple event occurrence in short time and space intervals is reminiscent of aftershock sequences, but aftershock is a statistical definition, not a label one can give an earthquake in real-time. Aftershocks are defined collectively as what creates the Omori event rate decay after a large event or are defined as what is taken away as “dependent events” using a declustering method. It is noteworthy that depending on the declustering method used on the Canterbury earthquake sequence, the number of independent events varies a lot. This lack of unambiguous definition of aftershocks leads to the need to investigate the amount of clustering inherent in “declustered” risk models. This is the task we concentrate on in this contribution. We start from a background source model for the Canterbury region, in which 1) centroids of events of given magnitude are distributed using a latin-hypercube lattice, 2) following the range of preferential orientations determined from stress maps and focal mechanism, 3) with length determined using the local scaling relationship and 4) rates from a and b values derived from the declustered pre-2010 catalog. We then proceed to create tens of thousands of realizations of 6 to 20 year periods, and we define criteria to identify which successions of events in the region would be perceived as a sequence. Note that the spatial clustering expected is a lower end compared to a fully uniform distribution of events. Then we perform the same exercise with rates and b-values determined from the catalog including the CES. If the pre-2010 catalog was long (or rich) enough, then the computed "stationary" rates calculated from it would include the CES declustered events (by construction, regardless of the physical meaning of or relationship between those events). In regions of low seismicity rate (e.g., Canterbury before 2010), it is hard to know how long is long enough. Using simulations, we can look at the apparent activity rate for the region over a few years (for example for events above M5.8), see how often it exceeds some level and also long those high activity rate periods last on average.