AI 中文总结
本文构建统一信息论框架量化地震可预测性，推导点过程下相关熵率，明确时空震级可预测性的决定因素，提出高维震前观测可提升可预测性，为评估预测极限等提供基础。
AI 中文摘要
地震难以进行确定性预测，但其发生也并非完全随机。本文构建了一个统一的信息论框架以量化可预测性：通过梳理香农熵与Kullback-Leibler散度，将可预测性形式化为完全随机性与真实数据生成过程之间的熵差，并阐明这一绝对概念如何与前瞻性模型评估所用的相对技能增益相关联。在点过程框架下，推导了泊松过程及ETAS模型的熵率，将固有可预测性率定义为条件强度的信息增益泛函。基于此视角，总结了当前关于地震在时间、空间和震级维度可预测性的认知：时间与空间可预测性主要由聚类效应和异质背景速率主导，而震级可预测性需将边缘震级统计（如古登堡-里克特定律与截断定律）与多元震级分布编码的真实事件间依赖关系区分开。最后，证明整合高维震前观测可通过互信息提升可预测性，从而将预测进展重新表述为提取可用信息与未来地震活动性之间的结构化依赖关系。该视角为评估可预测性极限、比较模型及识别最可能带来实质性预测改进的额外信息与物理机制提供了连贯基础。
英文摘要
Earthquakes resist deterministic prediction, yet their occurrence is not fully random. This paper develops a unified information-theoretic framework to quantify predictability. By reviewing Shannon entropy and the Kullback-Leibler divergence, we formalize predictability as the entropy gap between complete randomness and the true data-generating process and clarify how this absolute notion relates to the relative skill gains used in prospective model evaluation. Within the point-process setting, we derive entropy rates for the Poisson process and for ETAS and identify the intrinsic predictability rate as an information gain functional of the conditional intensity. Using this lens, we summarize what is currently established about earthquake predictability in time, space, and magnitude: temporal and spatial predictability are dominated by clustering and heterogeneous background rates, while magnitude predictability requires separating marginal magnitude statistics (e.g., Gutenberg-Richter and tapered laws) from genuine inter-event dependence encoded by the multivariate magnitude distribution. Finally, we show how incorporating high-dimensional pre-event observations can increase predictability through mutual information, thereby reframing forecasting progress as the extraction of structured dependence between available information and future seismicity. This perspective provides a coherent basis for assessing predictability limits, comparing models, and identifying where additional information and physics that are most likely to yield substantive forecasting improvements.
Comments40 pages, 4 figures
