Accounting for the Variability of Earthquake Rates within Low-Seismicity Regions: Application to the 2022 Aotearoa New Zealand National Seismic Hazard Model

The distribution of earthquakes in time and space is seldom stationary, which could hinder a robust statistical analysis, particularly in low -seismicity regions with limited data. This work investigates the performance of stationary Poisson and spatially precise forecasts, such as smoothed seismicity models (SSMs), in terms of the available training data. Catalog bootstrap experiments are conducted to: (1) identify the number of training data necessary for SSMs to perform spatially better than the least -informative Uniform Rate Zone (URZ) models; and (2) describe the rate temporal variability accounting for the overdispersion and nonstationarity of seismicity. Formally, the strict-stationarity assumption used in traditional forecasts is relaxed into local and incremental stationarity (i.e., a catalog is only stationary in the vicinity of a given time point t) along with self -similar behavior described by a power law. The results reveal rate dispersion up to 10 times higher than predicted by Poisson models and highlight the impact of nonstationarity in assuming a constant mean rate within training -forecast intervals. The temporal rate variability is translated into a reduction of spatial precision by means of URZ models. First, counting processes are devised to capture rate distributions, considering the rate as a random variable. Second, we devise a data -driven method based on geodetic strain rate to spatially delimit the precision of URZs, assuming that strain/stress rate is related to the timescales of earthquake interactions. Finally, rate distributions are inferred from the available data within each URZ. We provide forecasts for the New Zealand National Seismic Hazard Model update, which can exhibit rates up to ten times higher in low -seismicity regions compared with SSMs. This study highlights the need to consider nonstationarity in seismicity models and underscores the importance of appropriate statistical descriptions of rate variability in probabilistic seismic hazard analysis.