Universal scaling between precursory duration and event size across mechanically driven geohazards

Lei, Qinghua; Sornette, Didier

doi:10.48550/arXiv.2601.07404

Preprints

https://doi.org/10.48550/arXiv.2601.07404

© Author(s) 2026. This work is licensed under
the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

https://doi.org/10.48550/arXiv.2601.07404

© Author(s) 2026. This work is licensed under
the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Preprints

07 Apr 2026

| 07 Apr 2026

Status: this preprint is open for discussion and under review for Natural Hazards and Earth System Sciences (NHESS).

Universal scaling between precursory duration and event size across mechanically driven geohazards

Qinghua Lei and Didier Sornette

Abstract. Many catastrophic events, including landslides, rockbursts, glacier breakoffs, and volcanic eruptions, are preceded by an observable acceleration phase that offers a critical window for early warning and hazard mitigation; however, the duration of this precursory phase remains poorly constrained across sites, scales, and hazard types. This limitation arises because the onset of acceleration is often identified using heuristic thresholds or empirical criteria. Here, we introduce a physics-based framework that objectively constrains the precursory duration from accelerating dynamics, without prescribing the onset a priori or being tied to any specific observable. We analyze a global dataset of 109 geohazard events across seven continents over the past century, quantifying their precursory durations in a consistent manner. For mechanically driven instabilities, we identify a robust scaling between precursory duration and failure volume spanning more than ten orders of magnitude. When expressed in terms of a characteristic system size, this relationship is close to linear, consistent with finite-size scaling near a dynamical critical point. This behavior indicates that precursory duration reflects the progressive growth of correlated deformation up to system-spanning scales, rather than local rupture kinetics. The resulting universality points to common organizing mechanisms governing the approach to catastrophic failure across mechanically driven geohazards.

Received: 06 Mar 2026 – Discussion started: 07 Apr 2026

Qinghua Lei and Didier Sornette

Status: open (until 22 May 2026)

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RC1:
'Comment on egusphere-2026-1271', Anonymous Referee #1, 11 May 2026 reply
The paper proposes an empirical relationship between the duration of early-stage creep, and the time to failure. The reported near-linear correlation over five orders of magnitude is potentially important and, if robust, could contribute to time-of-failure forecasting. However, in its present form, I find the result too empirical and somewhat underconstrained from a methodological and physical point of view.
Major comments:
The criteria used to select the failure cases should be described more precisely. The analysis of the selected datasets appears careful, but it is unclear how the cases were chosen besides their availability. Specifically, any case excluded? This is important because the reported relationship is very strong and may be affected by selection bias. Many failures, especially in natural systems, might not show a clear transition from primary creep to a minimum or quasi-stationary deformation rate. The manuscript should clarify whether cases without a clear creep transition were considered, excluded, or unavailable, and how this affects the generality of the proposed scaling.

The reported regularity is surprising. I do not dispute that it appears in the cases shown, but the manuscript does not establish how common this behaviour is among failure events more generally. If the scaling applies only to events with a well-defined deceleration to minimum to acceleration sequence, then this domain of validity should be stated explicitly (or other).

The identification of t_m is easier retrospectively than prospectively. In real-time forecasting, an apparent minimum may reflect noise, smoothing, external forcing, or a temporary reset rather than the actual transition toward failure. The authors should distinguish more clearly between retrospective identification and prospective detection of t_m, especially for natural systems where multiple candidate minima may occur.

The forecasting implications should be tested more directly. Can t_f be estimated using only data available up to, or shortly after, the identification of t_m? A pseudo-prospective test, in which the time series are progressively truncated before failure, would make the forecasting claim stronger.

Also, the associated dataset appears to include 52 failure cases, but the manuscript seems to imply a different number of analysed cases/time series. The authors should clarify the exact number of events and data series used, and provide a complete table of the cases included in Fig. 2.

Minors:
The manuscript currently does not seem fully adapted to the format and expectations of NHESS. In particular, the data and methods should be described in substantially more detail. The section structure and level of methodological detail also appear closer to a short-format submission than to a typical NHESS article. Also, the manuscript still states: “This manuscript has been submitted to Geology and has not yet been peer reviewed by the Geological Society of America.” The previous submission history is not an issue, but the manuscript should be reframed and updated to match the journal to which it is now being submitted.

A version of the manuscript with line numbers would be appreciated, as this would make the review process and specific commenting much easier.

Reply
Citation: https://doi.org/10.5194/egusphere-2026-1271-RC1
- RC2:
  'Reply on RC1', Anonymous Referee #1, 18 May 2026 reply
  Please disregard my previous comments, which were submitted in error and referred to a different manuscript. My comments on the present manuscript are provided below.
  
  I find the manuscript interesting and potentially important. The dataset is broad, and the LPPLS-based procedure appears internally coherent for systems that exhibit accelerating, intermittent precursory dynamics. However, in my view, the current evidence supports a suggestive empirical pattern more strongly than a universal physical law. My main concern is that the central scaling may depend on model-derived onset times extracted from a retrospective compilation that may be conditionally selected toward events with analysable precursory acceleration. The manuscript would be substantially strengthened by clearer inclusion/exclusion criteria, sensitivity tests to onset definition and model assumptions, comparisons with simpler null models, and a more cautious interpretation of the finite-size criticality claim.
  More specific comments:
  The main concern is that the applicability of LPPLS procedure is conditional. The method can be expected to work primarily for events that already display sufficiently clear accelerating and intermittent precursory dynamics. The manuscript should therefore clarify whether the proposed scaling applies to mechanically driven geohazards in general, or only to monitored events showing well-developed LPPLS-like behaviour. This requires explicit inclusion/exclusion criteria and a transparent accounting of candidate events or time series that were considered but rejected.
  
  The key variable, precursory duration, is not independently observed. It is inferred by optimizing the LPPLS fit over variable calibration windows. Therefore, the reported scaling depends directly on a model-derived quantity. The claim that the onset is “objective” should be softened: it is objective only conditional on the LPPLS model class, parameter bounds, regularization scheme, and preprocessing choices. The authors should test whether the scaling persists under onset definitions independent of LPPLS.
  
  A related concern is possible model imprinting. The same model family is used to define the precursory duration and to support the physical interpretation of accelerating, oscillatory critical behaviour. This could make heterogeneous systems appear more comparable than they actually are. The authors should compare LPPLS-derived onset times with other onset criteria.
  
  The universality claim appears stronger than warranted. Volcanic eruptions are included in the broad framing of the manuscript, but they do not show a comparable scaling and are excluded from the main mechanically driven relationship. The rockburst subset also appears statistically weak or inconclusive. These points should temper the cross-hazard generalization.
  
  It is surprising that a single-parameter scaling with volume works as well as reported, given that precursory duration should also depend on material properties, geometry, boundary conditions, monitoring resolution and others. The authors should probably examine residuals by hazard type, material class, monitoring method, temporal resolution, and data source, and test whether volume remains significant in a multivariate or hierarchical model where possible.
  
  The interpretation in terms of finite-size criticality is plausible, but the data primarily show an empirical association between duration and size. The abstract currently moves quickly from an empirical -association to a mechanistic interpretation in terms of system-spanning correlated deformation and universality. I think this should be toned down. The data may be consistent with finite-size scaling, but they do not uniquely demonstrate it.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2026-1271-RC2

Qinghua Lei and Didier Sornette

Data sets

Landslide dataset Qinghua Lei and Didier Sornette https://zenodo.org/records/16400500

Model code and software

LPPLS code Qinghua Lei and Didier Sornette https://zenodo.org/records/15362582

Qinghua Lei and Didier Sornette

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Short summary

Natural hazards such as mountain collapses, mine bursts, glacier breakoffs, and volcanic eruptions are often preceded by a period of accelerating activity before final failure. Understanding how long this preparatory phase lasts is crucial for forecasting. By analyzing 109 events worldwide, we discover a simple relationship between precursory duration and event size. The results suggest that precursory duration is controlled by the time required for correlated damage to grow to system scale.


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