How to quantify earthquake predictability? Advances in earthquake forecasting and predictability limits

Jiancang Zhuang; Didier Sornette

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arXiv · 2607.26918

How to quantify earthquake predictability? Advances in earthquake forecasting and predictability limits

Jiancang Zhuang·Didier Sornette

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Abstract

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.

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Jiancang Zhuang, Didier Sornette. 2026-07-29. How to quantify earthquake predictability? Advances in earthquake forecasting and predictability limits. https://arxiv.org/abs/2607.26918

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