Accounting for earthquake rates’ variability through Uniform Rate Zone forecasts in the 2022 Aotearoa New Zealand Seismic Hazard Model

The distribution of earthquakes in time and space is clustered and may exhibit a non-stationary behaviour. The impacts of non-stationarity are further amplified when the observation window is short compared to the timescales of the underlying tectonic process, such as in regions of low-seismicity. This can preclude a robust statistical analysis for PSHA models, which commonly assume stationary Poisson models. We investigate the performance of forecasts for PSHA, such as smoothed-seismicity models (SSM), with respect to the available training data. We design bootstrap experiments for multiple pairs of consecutive training/forecast windows of a catalogue to: (i) analyse the lowest available amount of training data for which SSM performs spatially better than the least-informative Uniform Rate Zone (URZ) model; (ii) characterise the temporal variability of rates in terms of their over-dispersion and non-stationarity. The results show rate variability up to 10 times higher than predicted by Poisson forecasts, and demonstrate the impact of non-stationarity when assuming a constant mean rate derived during a training period for forecasting purposes. Analytical distributions are used to describe rate variability, which are conditioned on the information available from a training period. Furthermore, we devise a data-driven method based on strain-rate maps to spatially delineate URZs, under the assumption that the strain-rates field is related to the time scales of earthquake occurrence and interaction. For each URZ, a rate temporal distribution is inferred from the training events within it. We provide forecasts for the update of the New Zealand Seismic Hazard Model that have increased rates by up to 10 times higher in extensive low-seismicity regions compared to optimised SSMs. The new forecasts are implemented as negative-binomial distributions in the hazard integral. For a 10% exceedance probability in 50 years, the use of URZ with rate variability descriptions increases the expected PGA by up to 0.16 g in low seismicity regions (e.g. Auckland, Dunedin) compared to SSM. Our results highlight the relevance, as well as the feasibility, of incorporating analytical formulations of seismicity that go beyond the inadequate stationary Poisson description of seismicity.