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arxiv: 2606.11849 · v1 · pith:A2RVAJWDnew · submitted 2026-06-10 · ⚛️ physics.geo-ph · cond-mat.mtrl-sci· cond-mat.soft

Breakdown of the classical rupture theory and earthquake propagation in the "forbidden" super-Rayleigh range

Anna Pomyalov , Fabian Barras , Eran Bouchbinder This is my paper

Pith reviewed 2026-06-27 07:47 UTC · model grok-4.3

classification ⚛️ physics.geo-ph cond-mat.mtrl-scicond-mat.soft
keywords earthquake rupturesuper-Rayleigh rangesupershear propagationfrictional rate dependenceslip-rate nonlinearityclassical rupture theorytwo-dimensional solutions
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0 comments X

The pith

Frictional rate dependence lets earthquake ruptures propagate continuously through the super-Rayleigh range into the supershear regime without a sharp transition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Classical two-dimensional rupture theory treats speeds between the Rayleigh and shear wave speeds as forbidden and predicts a discontinuous jump from sub-Rayleigh to supershear propagation. The paper incorporates the dependence of frictional resistance on slip rate into the theory and finds quantitative agreement with simulations up to near the Rayleigh speed. Very close to that speed the nonlinear friction alters the character of the two-dimensional solutions. This change allows ruptures to cross the forbidden range continuously rather than jump. Rate-dependent friction is observed in experiments, so the result changes how fast earthquake propagation is modeled.

Core claim

When fault strength depends nonlinearly on slip rate, two-dimensional rupture solutions change their character very close to the Rayleigh wave-speed, enabling continuous propagation through the super-Rayleigh range into the super-shear regime without a sharp super-shear transition.

What carries the argument

Nonlinear dependence of frictional resistance on slip rate, which changes the character of two-dimensional rupture solutions near the Rayleigh wave-speed.

If this is right

  • Ruptures reach supershear speeds through continuous propagation rather than a discontinuous transition.
  • The classical theory ceases to apply near the Rayleigh wave-speed.
  • Two-dimensional solutions remain valid through the super-Rayleigh interval when rate dependence is included.
  • Quantitative agreement between theory and simulation holds nearly up to the Rayleigh speed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Three-dimensional rupture geometries may further smooth or alter the speed transition.
  • Laboratory friction experiments could directly test whether observed rate dependence produces continuous super-Rayleigh propagation.
  • Seismic records of rupture speed evolution could be re-examined for evidence of gradual rather than abrupt transitions.

Load-bearing premise

Frictional resistance follows a specific nonlinear function of slip rate that produces the change in rupture solution character near the Rayleigh wave-speed.

What would settle it

Numerical simulations or laboratory experiments with the same nonlinear friction law showing either a sharp discontinuous jump across the super-Rayleigh range or complete absence of propagation inside it.

Figures

Figures reproduced from arXiv: 2606.11849 by Anna Pomyalov, Eran Bouchbinder, Fabian Barras.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper claims that incorporating slip-rate dependence into fault strength revises classical 2D rupture theory, allowing quantitative agreement with simulations nearly up to the Rayleigh wave speed; very close to this speed, frictional rate nonlinearity changes the character of solutions so that rupture propagates continuously through the previously forbidden super-Rayleigh range into the super-shear regime without a sharp transition.

Significance. If the central result holds, the work would substantially revise understanding of rupture speed regimes in 2D, showing that rate-dependent friction (observed in experiments) can eliminate the classical forbidden zone and discontinuous super-shear transition, with direct implications for earthquake dynamics and ground-motion modeling.

major comments (1)
  1. [Abstract] Abstract and theory development: the claim that frictional rate nonlinearity enables continuous propagation through the super-Rayleigh range is load-bearing, yet the manuscript does not demonstrate whether this holds for generic rate-dependent laws (e.g., standard logarithmic rate-and-state friction) or only for the specific nonlinear functional form chosen; the skeptic concern that the effect may require a tuned nonlinearity is therefore unresolved and directly affects the generality asserted for earthquake propagation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review. The concern about generality across rate-dependent friction laws is substantive and we address it directly below, proposing revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and theory development: the claim that frictional rate nonlinearity enables continuous propagation through the super-Rayleigh range is load-bearing, yet the manuscript does not demonstrate whether this holds for generic rate-dependent laws (e.g., standard logarithmic rate-and-state friction) or only for the specific nonlinear functional form chosen; the skeptic concern that the effect may require a tuned nonlinearity is therefore unresolved and directly affects the generality asserted for earthquake propagation.

    Authors: We agree that the manuscript's numerical examples employ a specific nonlinear slip-rate dependence chosen to produce pronounced effects at high rates. The analytical theory is formulated for arbitrary slip-rate dependent strength, but the change in solution character near the Rayleigh speed arises from the nonlinear term. Standard logarithmic rate-and-state friction is only weakly nonlinear, so the continuous super-Rayleigh propagation may not occur for that law. In the revision we will add direct numerical simulations with a standard logarithmic rate-and-state law (velocity-weakening) to test the range of validity and clarify whether strong nonlinearity is required. revision: yes

Circularity Check

0 steps flagged

No circularity; theory validated against independent simulations

full rationale

The paper develops a rupture theory by incorporating slip-rate dependence of fault strength into the classical framework, then demonstrates quantitative agreement with separate numerical simulations up to near the Rayleigh speed, followed by a character change enabling continuous propagation. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work by the same authors. The frictional nonlinearity is an explicit modeling choice whose consequences are tested externally rather than assumed to produce the result. This is the most common honest non-finding.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on a particular nonlinear slip-rate friction law whose explicit form and parameters are not given in the abstract; this law is the main addition beyond classical theory.

free parameters (1)
  • parameters of the slip-rate friction law
    The functional dependence and any coefficients that produce the continuous transition are introduced to capture experimental behavior.
axioms (1)
  • domain assumption Frictional resistance depends nonlinearly on slip rate
    This is the key modeling choice added to the classical theory.

pith-pipeline@v0.9.1-grok · 5719 in / 1099 out tokens · 20957 ms · 2026-06-27T07:47:36.849989+00:00 · methodology

discussion (0)

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Reference graph

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