title: Accounting for earthquake rates’ temporal and spatial variability through least-information Uniform Rate Zone forecasts
Creators: name: Iturrieta, P.
name: Gerstenberger, Matt C.
name: Rollins, Chris
name: Van Dissen, Russ J.
name: Wang, T.
name: Schorlemmer, D.
Publisher: name: GNS Science
Year: 2022

description: The distribution of earthquakes in time and space is seldom stationary. In low-seismicity regions, non-stationarity and data scarcity may preclude a significant statistical analysis. We investigate the performance of traditional stationary Poisson forecasts (such as smoothed-seismicity models [SSM]), with applications in Probabilistic Seismic Hazard Assessment, in terms of the available training data. We design bootstrap experiments that use multiple pairs of consecutive training-forecast windows of a catalogue to: (i) analyse the lowest available training data in which SSM performs spatially better than the least-informative Uniform Rate Zone (URZ) and (ii) characterise the rate temporal variability in multiple training-forecast windows in terms of its over-dispersion and non-stationarity. The experiments rely on the assumption of fast-forward catalogues, i.e. the variability in catalogues from high-seismicity regions can be used as a proxy of long-term low-seismicity region catalogues. Formally, the strong stationarity assumption is relaxed into local and incremental stationarity, and self-similarity is described by a power law. Results show a rate variability up to 10 times higher, as predicted by Poisson models, and evidence the impact of non-stationarity in assuming a constant mean rate in training-forecast intervals. The description of rate variability is translated into a reduction of spatial precision, whose impact on seismic hazard is evaluated. First, counting processes (e.g. negative binomial) are devised to capture rate distributions, considering the rate as a random variable, which is now conditioned to the available information in a training period. Second, under the assumption that strain/stress rate is related to the timescale of earthquake interactions, we devise a data-driven method based on strain rate maps to delimit URZs. A rate distribution is inferred from the training earthquake counts within each URZ. We provide a set of forecasts for the New Zealand National Seismic Hazard Model update, which have mean rates up to four times higher in extensive low-seismicity regions compared to optimised smoothed-seismicity models. The forecasts’ impact in the hazard space is studied by implementing a negative binomial formulation in the OpenQuake hazard suite. For a 10% probability of exceedance in 50 years, forecasts that only reduce the spatial precision, i.e. stationary Poisson URZs, cause an increase of up to 0.1 g in low seismicity regions, compared to SSM. Furthermore, including the rate variability in URZ models increases the expected PGA up to 0.16 g in low-seismicity regions, whereas the effect on high-seismicity is minimal (~0.01–0.05 g). The hazard estimates presented here highlight the relevance, as well as the feasibility, of including analytical formulations of seismicity that extend beyond the inadequate stationary-Poisson description of seismicity. (The authors)