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.

中文翻译：

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考虑低地震活动区内地震发生率的变异性：在 2022 年新西兰国家地震灾害模型中的应用

地震在时间和空间上的分布很少是固定的，这可能会阻碍稳健的统计分析，特别是在数据有限的低地震活动地区。这项工作根据可用的训练数据研究了平稳泊松和空间精确预测（例如平滑地震活动模型（SSM））的性能。进行目录引导实验的目的是：（1）确定 SSM 在空间上比信息最少的统一速率区域（URZ）模型表现更好所需的训练数据数量；(2) 描述了地震活动的过度分散和非平稳性的速率时间变化。形式上，传统预测中使用的严格平稳性假设被放松为局部和增量平稳性（即目录仅在给定时间点 t 附近是平稳的）以及幂律描述的自相似行为。结果显示，速率离散度比泊松模型预测的高出 10 倍，并强调了假设训练预测区间内平均速率恒定时非平稳性的影响。时间速率变异性通过 URZ 模型转化为空间精度的降低。首先，设计计数过程来捕获速率分布，将速率视为随机变量。其次，我们设计了一种基于大地应变率的数据驱动方法，在空间上界定 URZ 的精度，假设应变/应力率与地震相互作用的时间尺度相关。最后，根据每个 URZ 内的可用数据推断速率分布。我们提供新西兰国家地震灾害模型更新的预测，与 SSM 相比，该模型在低地震地区的预测率可能高出十倍。这项研究强调了在地震活动模型中考虑非平稳性的必要性，并强调了概率地震危险分析中对速率变异性进行适当统计描述的重要性。