地震序列的有限时域触发核心
Finite-Horizon Triggering Cores of Earthquake Sequences
- Institute of Risk Analysis, Prediction and Management (Risks-X), Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology（南方科技大学前沿交叉学科研究院风险分析、预测与管理研究所）
- CNRS, ENS de Lyon, LPENSL, UMR 5672（法国国家科学研究中心里昂高等师范学院物理实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出有限时域触发核心大小，以量化地震序列中少数主导事件与长期多事件对预测的贡献差异，并推导其理论性质，揭示不同记忆核下的增长规律。
AI中文摘要：
触发地震模型通常将所有过去地震的贡献汇总为总预测速率。这种汇总无法区分由一次近期地震主导的预测与由分布在更长历史中的多次事件支持的等速率预测，尽管这些配置可能具有不同的持久性以及对目录和参数不确定性的敏感性。我们引入了有限时域触发核心大小 \(N_{p,T}(t)\)，定义为在过去地震中，其预期贡献在未来区间 \([t,t+T]\) 内占总触发潜力的比例为 \(p\) 的最小数量。该定义适用于任何在指定未来窗口内分配非负事件特定预期贡献的触发模型。我们为其在标记霍克斯和流行病型余震序列过程中的理论进行了发展，其中权重是单个过去地震产生的直接子事件的预期数量。有限时域使得该可观测量对于每个归一化奥莫里核（指数 \(\ heta>0\)）都有明确定义，包括对应的无限时域量发散的长记忆区域。我们推导了连续体和标记泊松基准、标记泊松分布的精确表示以及高 \(p\) 的分布律。对于有限时域奥莫里记忆，触发核心随 \((1-p)^{-1/\ heta}\) 增长，其幅度由总触发权重控制且依赖于实现；对于指数记忆，增长是对数形式的。
英文摘要：
Models of triggered seismicity commonly aggregate the contributions of all past earthquakes into a total predicted rate. This aggregation does not distinguish a forecast dominated by one recent earthquake from an equal-rate forecast supported by many events distributed across a longer history, even though these configurations can have different persistence and sensitivity to catalog and parameter uncertainties. We introduce the \emph{finite-horizon triggering core size} \(N_{p,T}(t)\), defined as the minimum number of past earthquakes whose expected contributions account for a fraction \(p\) of the total triggering potential over the future interval \([t,t+T]\). The definition applies to any triggering model that assigns nonnegative event-specific expected contributions over a specified future window. We develop its theory for marked Hawkes and epidemic-type aftershock sequence processes, where the weights are the expected numbers of direct offspring produced by individual past earthquakes. The finite horizon makes the observable well defined for every normalized Omori kernel with exponent \(θ>0\), including the long-memory regime in which the corresponding infinite-horizon quantity diverges. We derive continuum and marked-Poisson benchmarks, an exact representation of the marked-Poisson distribution, and high-\(p\) distributional laws. For finite-horizon Omori memory, the triggering core grows as \((1-p)^{-1/θ}\) with a realization-dependent amplitude controlled by the total triggering weight; for exponential memory, the growth is logarithmic.[...]
