arxiv: 2604.07630 · v1 · submitted 2026-04-08 · ⚛️ physics.geo-ph · stat.AP

Recognition: unknown

Diffusional earthquakes and their slip-distance scaling

Dye SK Sato , Keisuke Yoshida

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:54 UTC · model grok-4.3

classification ⚛️ physics.geo-ph stat.AP

keywords diffusional earthquakesseismic moment scalingconstant-slip modelearthquake swarmsslow earthquakesinjection-induced seismicitydiffusive migrationseismicity area

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The pith

Earthquakes with diffusively expanding active areas follow a constant-slip scaling that unifies swarms, induced seismicity, and slow earthquakes.

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

The paper tracks the growth of active areas and cumulative seismic moments during prolonged swarms in Northeast Japan. These trajectories match the final states of global swarms and injection-induced events at many scales. When seismic moment is plotted against seismicity area, the paths of swarms and induced sequences fall onto the same relation as slow earthquakes. A single diffusional model with constant slip per unit area accounts for the shared pattern. If this holds, it separates earthquake growth into two modes: one where final size remains bounded and predictable from area expansion, and the ordinary mode where size stays unpredictable from early radiation.

Core claim

Tracking prolonged earthquake swarms in Northeast Japan shows that their moment-duration trajectories coincide with the final states of global swarms and induced seismicity. Plotting seismic moment against seismicity area causes the trajectories of swarms and injection-induced events to collapse onto those documented for slow earthquakes. This common scaling is explained by a diffusional constant-slip model in which slip remains fixed while the active area migrates outward.

What carries the argument

The diffusional constant-slip model, which produces seismic moment scaling as the square of the diffusion distance under uniform slip.

If this is right

Final sizes of diffusional earthquakes remain bounded and can be estimated from early measurements of their expanding active area.
Ordinary earthquakes scale under constant stress drop while diffusional earthquakes scale under constant slip, producing two distinct predictability regimes.
Bimodal predictability in seismogenesis follows directly from whether an event migrates diffusively or follows standard rupture.
Seismicity area functions as a usable stand-in for slipped area specifically in these diffusional cases.

Where Pith is reading between the lines

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

Real-time tracking of area expansion could supply early bounds on maximum moment release during ongoing swarms or injection sequences.
The diffusive migration points to a shared role for fluid or pressure diffusion in driving both natural swarms and human-induced events.
Applying the same moment-area test to other regions could show how widely the constant-slip regime extends beyond the studied cases.
Trajectory shapes alone might help separate natural swarms from induced sequences in seismic monitoring.

Load-bearing premise

The observed seismicity area serves as a direct proxy for the actual slipped fault area, with slip remaining roughly constant across that area.

What would settle it

Direct observations from a well-monitored swarm or injection sequence in which the true slipped area differs substantially from the recorded seismicity area, or in which slip varies strongly inside the active region.

read the original abstract

The final size of an earthquake typically cannot be predicted from its ongoing seismic radiation. Expanding observations reveal distinct exceptions, such as slow earthquakes, injection-induced seismicity, and earthquake swarms, where fault slip has an upper bound. A common thread among these anomalies is the diffusive migration of their active areas. Here, we report a unified scaling relation for these diffusional earthquakes. By tracking prolonged earthquake swarms in Northeast Japan, we constrained the time evolution of their active seismicity areas and cumulative seismic moments. Their moment-duration trajectories coincide with the final states documented for global swarms and induced seismicity across various scales. When plotted as seismic moment versus seismicity area, the trajectories of swarms and injection-induced seismicity collapse onto those of slow earthquakes, uniformly explained by a diffusional constant-slip model. The constant-slip scaling of diffusional earthquakes and the constant-stress-drop scaling of ordinary earthquakes mark a bimodal predictability in seismogenesis.

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.

Desk Editor's Note private letter to a colleague

The paper unifies swarms, induced seismicity, and slow earthquakes under a diffusional constant-slip scaling via moment-area trajectories, but the claim hinges on seismicity area as a direct proxy for slipped area without clear independent validation.

read the letter

The central point is that these event classes show moment-duration paths that collapse onto a single line when plotted against seismicity area, consistent with constant slip and diffusive area growth rather than the constant stress-drop scaling of ordinary earthquakes. They back this with time-resolved tracking of swarms in Northeast Japan plus comparisons to published global catalogs for induced sequences and slow events. That framing is new in how it ties the classes together through the diffusive model and the bimodal predictability contrast at the end of the abstract. The observational collapse itself is the strongest part; if the area measurements are done consistently across datasets, it gives a clean empirical pattern worth testing further. The soft spot is exactly the one flagged in the stress-test note. Seismicity area from catalogs is not guaranteed to equal the region that actually slipped at constant slip, especially in swarms and injection cases where detection thresholds, aseismic slip, and network coverage can leave parts of the fault unmapped. Without direct cross-checks against geodetic or deformation data showing that the slipped area matches the catalog footprint, the scaling could partly reflect how events are detected rather than a uniform physical process. The paper derives the scaling from matching trajectories to the diffusive model instead of fitting it by construction, which helps, but the proxy assumption still carries the load. This is the kind of work that belongs in a reading group for people working on induced seismicity or slow-slip mechanics; it gives a concrete relation to check against new datasets. It deserves peer review because the unification is observationally grounded enough to be worth referee scrutiny and possible revision on the area-proxy question, even if the final interpretation needs tightening.

Referee Report

3 major / 2 minor

Summary. The paper claims that swarms, injection-induced seismicity, and slow earthquakes form a class of 'diffusional earthquakes' whose moment-duration trajectories collapse onto a common trend when plotted as seismic moment versus seismicity area; this collapse is uniformly explained by a constant-slip diffusional model (with a single diffusional constant) and stands in contrast to the constant-stress-drop scaling of ordinary earthquakes, implying a bimodal predictability in seismogenesis.

Significance. If the central scaling holds after addressing the proxy validation, the result would unify several classes of non-standard earthquakes under a simple diffusive constant-slip framework, offering a concrete alternative to stress-drop scaling and highlighting limits to predictability in diffusional regimes. The use of prolonged Northeast Japan swarms to track time-evolving areas and moments, together with global comparisons, provides an observational basis that could be strengthened by independent slip-area constraints.

major comments (3)

[Abstract] Abstract: the reported collapse of trajectories onto the slow-earthquake trend relies on seismicity area as a direct proxy for the slipped fault area under the constant-slip assumption, yet the manuscript provides no explicit cross-validation against geodetic, InSAR, or deformation data that would confirm whether undetected aseismic slip or sub-threshold events occupy additional area.
[Scaling relation and model section] The diffusional constant-slip model is presented as explaining the M0-area scaling, but the definition of 'active seismicity area' (including how event detection thresholds, network geometry, and magnitude of completeness affect the footprint) is not shown to be independent of the scaling fit itself; if the area is post-hoc adjusted to match the model, the collapse becomes partly tautological.
[Discussion] The claim of uniform applicability across swarms, induced sequences, and slow earthquakes requires that spatial slip variations remain negligible; without quantitative bounds on slip heterogeneity (e.g., via comparison to tremor or geodetic moment release), the constant-slip assumption remains an untested simplification that directly supports the reported linear scaling.

minor comments (2)

[Introduction] The symbol for the diffusional constant is introduced without an early equation reference or units, which could be clarified for readers unfamiliar with the diffusive migration framework.
[Figure captions] Figure captions for the moment-area plots should explicitly state the number of events, time windows, and error bars used in each trajectory to allow independent assessment of the collapse quality.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which have helped us strengthen the clarity and rigor of our analysis. We address each major comment point by point below, with revisions made to the manuscript where appropriate to clarify assumptions, definitions, and limitations.

read point-by-point responses

Referee: [Abstract] Abstract: the reported collapse of trajectories onto the slow-earthquake trend relies on seismicity area as a direct proxy for the slipped fault area under the constant-slip assumption, yet the manuscript provides no explicit cross-validation against geodetic, InSAR, or deformation data that would confirm whether undetected aseismic slip or sub-threshold events occupy additional area.

Authors: We agree that geodetic or InSAR cross-validation would provide stronger confirmation of the seismicity-area proxy. Our study is based on seismic catalogs, and the collapse of independent datasets onto a common trend offers empirical consistency with the constant-slip model. In the revised manuscript we have added a paragraph in the Discussion explicitly acknowledging this limitation, citing supporting geodetic studies on slow earthquakes and swarms where seismic and geodetic areas align within a factor of ~2, and stating that undetected aseismic contributions remain possible but do not alter the reported scaling. revision: partial
Referee: [Scaling relation and model section] The diffusional constant-slip model is presented as explaining the M0-area scaling, but the definition of 'active seismicity area' (including how event detection thresholds, network geometry, and magnitude of completeness affect the footprint) is not shown to be independent of the scaling fit itself; if the area is post-hoc adjusted to match the model, the collapse becomes partly tautological.

Authors: The active seismicity area is computed from hypocenter locations via a density-based clustering algorithm applied before any moment-area fitting. We have revised the Scaling relation and model section to detail this procedure, including explicit tests of robustness to magnitude-of-completeness thresholds and network geometry. These tests confirm that the linear scaling persists across reasonable parameter variations, demonstrating that the area definition is independent of the subsequent fit and that the collapse is not tautological. revision: yes
Referee: [Discussion] The claim of uniform applicability across swarms, induced sequences, and slow earthquakes requires that spatial slip variations remain negligible; without quantitative bounds on slip heterogeneity (e.g., via comparison to tremor or geodetic moment release), the constant-slip assumption remains an untested simplification that directly supports the reported linear scaling.

Authors: The constant-slip model is a first-order simplification, yet the data collapse across multiple independent catalogs supports its average validity. We have expanded the Discussion to incorporate quantitative bounds from the literature on slip heterogeneity in slow earthquakes and swarms, including comparisons with geodetic moment release and tremor observations that show variations typically remain within a factor that preserves the linear M0-area relation. We also note this assumption as a target for future work with denser geodetic coverage. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scaling derived from independent observations and physical model

full rationale

The paper's central claim rests on tracking observed seismicity areas and cumulative moments from Northeast Japan swarms, then showing their trajectories coincide with global datasets for swarms, induced seismicity, and slow earthquakes. The diffusional constant-slip model is invoked as an explanatory framework for the observed collapse in moment-area space, not as a fitted parameter whose output is renamed a prediction. No equations reduce the result to its inputs by construction, no self-citation chain is load-bearing for the scaling, and the proxy assumption (seismicity area ≈ slipped area) is stated explicitly as an interpretation rather than smuggled in via prior self-work. Global data provide external grounding, making the derivation self-contained against benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that seismicity area tracks slipped area and on a simple diffusive model whose constant is calibrated to observations.

free parameters (1)

diffusional constant
Governs the rate of area expansion in the constant-slip model; calibrated to match observed trajectories.

axioms (1)

domain assumption Active seismicity area is a faithful proxy for the slipped fault area
Invoked to convert observed seismicity metrics into slip-distance scaling.

pith-pipeline@v0.9.0 · 5450 in / 1087 out tokens · 49119 ms · 2026-05-10T16:54:00.417182+00:00 · methodology

discussion (0)

Reference graph

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