[Paper Review] A probabilistic view on rupture predictability: all earthquakes evolve similarly

Jannes Münchmeyer, Ulf Leser+1 more|arXiv (Cornell University)|Mar 16, 2022

Seismology and Earthquake Studies34 references13 citations

TL;DR

This paper introduces a probabilistic framework to assess when earthquake ruptures become predictable by modeling the time-evolving distribution of magnitude given real-time observations. Using moment rate functions and teleseismic P-wave arrivals, it demonstrates that rupture size cannot be reliably predicted before half the rupture duration, as differentiation between small and large events only emerges after peak moment release—supporting a universal rupture initiation model and challenging early predictability theories.

ABSTRACT

Ruptures of the largest earthquakes can last between a few seconds and several minutes. An early assessment of the final earthquake size is essential for early warning systems. However, it is still unclear when in the rupture history this final size can be predicted. Here we introduce a probabilistic view of rupture evolution - how likely is the event to become large - allowing for a clear and well-founded answer with implications for earthquake physics and early warning. We apply our approach to real time magnitude estimation based on either moment rate functions or broadband teleseismic P arrivals. In both cases, we find strong and principled evidence against early rupture predictability because differentiation between differently sized ruptures only occurs once half of the rupture has been observed. Even then, it is impossible to foresee future asperities. Our results hint towards a universal initiation behavior for small and large ruptures.

Motivation & Objective

• To resolve the long-standing debate on whether large earthquakes can be predicted early in their rupture.
• To develop a rigorous probabilistic framework that models the time-evolving uncertainty in earthquake magnitude.
• To test the hypothesis of early predictability against the cascade model of rupture evolution.
• To evaluate predictability using real-time observables like moment rate functions and broadband teleseismic P-wave arrivals.
• To provide a principled, non-point-estimator approach that captures the full predictive distribution, avoiding oversimplification of non-Gaussian uncertainty.

Proposed method

• Proposes a probabilistic model P(M|Ot) to represent the time-evolving distribution of earthquake magnitude M given observables Ot up to time t.
• Uses variational inference with Gaussian mixture models to approximate P(M|Ot), enabling differentiable and scalable training.
• Employs the Continuous Ranked Probability Score (CRPS) as a differentiable loss function for training, allowing closed-form computation for mixture models.
• Trains and evaluates models on three datasets: SCARDEC, USGS, and Ye et al. moment rate functions, and a teleseismic P-wave dataset.
• Applies the framework to both moment rate functions and early P-wave arrivals to test consistency across data types.
• Uses a neural network architecture to map observables Ot to parameters of the Gaussian mixture approximation of P(M|Ot).

Experimental results

Research questions

• RQ1 At what point in the rupture process can the final magnitude of an earthquake be reliably predicted?
• RQ2 Do small and large earthquakes exhibit fundamentally different initiation behaviors, or is rupture evolution universal until mid-rupture?
• RQ3 Can early seismic observables such as moment rate functions or P-wave amplitudes provide principled, probabilistic constraints on final magnitude?
• RQ4 How does the predictive distribution P(M|Ot) evolve over time, and what does this imply for early warning systems?
• RQ5 To what extent do non-Gaussian uncertainty distributions obscure predictability in traditional point-estimator approaches?

Key findings

• Differentiation between small and large ruptures only becomes statistically significant after approximately half of the rupture duration has been observed.
• The predictive distribution P(M|Ot) remains close to a Gutenberg-Richter distribution before peak moment release, indicating no early predictability.
• After peak moment release, the distribution becomes Gaussian with a decreasing GR tail, reflecting uncertainty about future asperities.
• The framework shows strong consistency across two distinct data types: moment rate functions and teleseismic P-wave arrivals, both yielding similar predictability thresholds.
• The results provide principled, probabilistic evidence against early rupture predictability, supporting the cascade model over self-healing pulse or preslip models.
• The study reveals that traditional point-estimator methods may obscure non-Gaussian uncertainty, leading to misleading conclusions about predictability.