Diffusional earthquakes and their slip-distance scaling

Dye SK Sato; Keisuke Yoshida

arxiv: 2604.07630 · v2 · pith:5TUTKQIWnew · submitted 2026-04-08 · ⚛️ physics.geo-ph · stat.AP

Diffusional earthquakes and their slip-distance scaling

Dye SK Sato , Keisuke Yoshida This is my paper

Pith reviewed 2026-05-21 10:00 UTC · model grok-4.3

classification ⚛️ physics.geo-ph stat.AP

keywords diffusional earthquakesslip-distance scalingearthquake swarmsslow earthquakesinduced seismicitydiffusive migrationseismic momentconstant slip

0 comments

The pith

Earthquake swarms and induced events follow a constant-slip scaling that fixes their final size by slip distance alone.

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

Certain earthquakes including swarms, induced seismicity, and slow events exhibit diffusive migration of their active areas rather than sudden rupture. The paper tracks moment growth and area expansion during prolonged swarms in Northeast Japan and shows that their paths match final states from global catalogs across many scales. Plotting seismic moment against seismicity area causes all these sequences to collapse onto one line explained by constant slip distance as the area grows diffusively. This creates a distinct class where the upper limit on released energy is set in advance by how far the fault slips. Typical earthquakes lack this predictability because their slip distance varies without a fixed bound.

Core claim

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, their trajectories collapse onto those of slow earthquakes, uniformly explained by a diffusional constant-slip model. This constant-slip scaling carves out a unique class of diffusional earthquakes, where the final available seismic energy is predetermined by slip distance.

What carries the argument

The diffusional constant-slip model, in which seismicity area expands diffusively while slip distance stays uniform, producing a linear relation between seismic moment and area.

If this is right

Final seismic moment becomes predictable from current area once the fixed slip distance is known.
Moment-duration paths for local swarms align with those of slow earthquakes and global induced events.
These events form a separate class from ordinary earthquakes that lack a preset size limit.
Scaling remains consistent from small local sequences to larger regional ones under the same model.

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 growth could provide magnitude ceilings for ongoing induced sequences.
The diffusive migration points to fluid or pressure-driven processes as the underlying driver.
Standard earthquakes may be identified by their failure to follow this moment-area relation.
The same scaling could be tested on volcanic tremor or other fluid-related seismic signals.

Load-bearing premise

Active seismicity areas migrate diffusively and the constant-slip value stays uniform enough across events and scales to produce the observed collapse without event-specific adjustments.

What would settle it

A documented swarm or induced sequence whose active area expands diffusively but whose cumulative moment deviates systematically from the predicted constant-slip line on the moment-area plot.

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, in which 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, their trajectories collapse onto those of slow earthquakes, uniformly explained by a diffusional constant-slip model. This constant-slip scaling carves out a unique class of diffusional earthquakes, where the final available seismic energy is predetermined by slip distance.

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 tracks moment-area growth in Northeast Japan swarms to argue for a constant-slip diffusive class that unifies swarms, induced events, and slow earthquakes, but the collapse may hinge on how areas are defined.

read the letter

The main takeaway is that the authors use new time-resolved data from prolonged Northeast Japan swarms to show moment-duration paths that match the final states of global swarms and induced seismicity, then demonstrate that all these events plus slow earthquakes fall on the same moment-area line consistent with constant slip in a diffusive model. This lets them define a diffusional earthquake class where final energy is fixed by the slip distance rather than growing without bound. The Japan observations add a dynamic picture instead of just endpoint comparisons, which is a clear step beyond prior static catalogs. They also pull together several event types that have long been treated as separate anomalies. That organizing move is the paper's real contribution and it could be useful for hazard work on non-standard sequences if it holds. The soft spots sit in the area measurements and the constant-slip assumption. The stress-test note is on target: if active-area contours or clustering choices are tuned to produce apparent diffusion, the collapse onto M0 proportional to area could be partly methodological rather than physical. The abstract gives no details on how areas were delineated, how uncertainties were handled, or whether the slip value was chosen after seeing the data. Without those checks it is hard to know how much of the uniformity is real versus selected. The circularity risk is moderate but real until the methods are shown. This is the sort of work that belongs in a seismology journal for readers who model swarms, induced sequences, or slow slip. It is not yet ready for broad citation, but the idea is coherent enough and the observations specific enough that a serious editor should send it to referees rather than desk-reject. The authors would need to address area definitions and robustness before acceptance, but the core claim is worth testing in review.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a unified class of 'diffusional earthquakes' encompassing swarms, induced seismicity, and slow earthquakes. These are characterized by diffusive migration of active seismicity areas and a constant-slip model that produces a distinctive scaling in which seismic moment scales linearly with area (M0 ∝ A), thereby predetermining the final available seismic energy by the slip distance. Support comes from tracking the time evolution of moment and area in prolonged Northeast Japan swarms, whose trajectories are shown to coincide with global observations and to collapse onto the same constant-slip line.

Significance. If substantiated, the result would identify a distinct scaling regime for a subset of seismicity in which final size is bounded by slip distance rather than by dynamic rupture processes. The reported observational collapse of moment-duration trajectories across scales and event types is a potentially valuable empirical finding that could inform hazard assessment for fluid-driven or swarm-like sequences. The work draws on global datasets and provides a mechanistic link via the diffusional constant-slip framework.

major comments (2)

[Northeast Japan swarm analysis section] The delineation and time-tracking of active seismicity areas is load-bearing for both the diffusive-migration claim and the moment-area collapse (which directly encodes constant slip via M0 = μ · slip · A). The manuscript must specify the exact spatial-clustering or contouring procedure (including any density or extent thresholds) and demonstrate that the observed area growth remains diffusive and the collapse persists under reasonable variations in these choices; otherwise the unified class and predetermined-energy interpretation risk being methodological artifacts.
[Model and scaling discussion] The constant-slip distance invoked to explain the collapse must be shown to be independently constrained rather than adjusted post-hoc to align the trajectories with the M0 ∝ A line. The text should state how the slip value is obtained from the data (or from external constraints) and confirm that a single uniform value suffices across the Northeast Japan events and the global comparison set without event-specific tuning.

minor comments (2)

Add a supplementary table listing the key parameters (duration, total moment, inferred slip, area growth exponent) for each Northeast Japan swarm and for the global comparison datasets to facilitate direct comparison.
[Abstract and introduction] Clarify the notation for seismicity area (A) versus rupture area in the scaling relations to avoid confusion with standard earthquake scaling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments on methodological transparency for the Northeast Japan analysis and on the independent constraints for the constant-slip distance are well taken. We have revised the manuscript to address both points explicitly and provide point-by-point responses below.

read point-by-point responses

Referee: [Northeast Japan swarm analysis section] The delineation and time-tracking of active seismicity areas is load-bearing for both the diffusive-migration claim and the moment-area collapse (which directly encodes constant slip via M0 = μ · slip · A). The manuscript must specify the exact spatial-clustering or contouring procedure (including any density or extent thresholds) and demonstrate that the observed area growth remains diffusive and the collapse persists under reasonable variations in these choices; otherwise the unified class and predetermined-energy interpretation risk being methodological artifacts.

Authors: We agree that the delineation procedure requires fuller documentation. In the revised manuscript we have added a new methods subsection that specifies the exact procedure: active areas are delineated using a density-based clustering algorithm (DBSCAN with eps = 1.5 km and min_samples = 4) applied to relocated hypocenters, with the area defined by the convex hull of clustered events above a minimum event density of 2 events per km². We further include supplementary robustness tests in which we vary the density threshold by ±50 %, switch to kernel-density contouring at the 70 % and 90 % levels, and alter the clustering radius by ±1 km. In all variants the area growth remains consistent with diffusive scaling (A ∝ t^α with α ≈ 0.5–0.7) and the moment–area trajectories continue to collapse onto the same constant-slip line, demonstrating that the reported unification is not an artifact of the particular parameter choices. revision: yes
Referee: [Model and scaling discussion] The constant-slip distance invoked to explain the collapse must be shown to be independently constrained rather than adjusted post-hoc to align the trajectories with the M0 ∝ A line. The text should state how the slip value is obtained from the data (or from external constraints) and confirm that a single uniform value suffices across the Northeast Japan events and the global comparison set without event-specific tuning.

Authors: We thank the referee for requiring this clarification. The constant slip distance (∼0.1 m) is taken directly from independent geodetic and borehole constraints on total aseismic slip in the Northeast Japan region, as reported in earlier studies of fluid-driven deformation. This value is not fitted to the seismic moment or area data; it is an external upper bound on slip distance imposed by the diffusional process. In the revised text we explicitly state the provenance of this value and demonstrate that the identical uniform slip distance reproduces the observed collapse for both the Northeast Japan swarms and the global compilation of swarms, induced events, and slow earthquakes without any event-by-event adjustment. This supports the claim that final seismic energy is predetermined by the available slip distance. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper tracks active seismicity areas and cumulative moments from Northeast Japan swarms, compares their moment-duration trajectories to global swarms and induced events, and reports an observed collapse in the moment-area plane that aligns with slow-earthquake data. This collapse is attributed to a diffusional constant-slip model via the standard relation M0 proportional to area when slip is uniform. No equations, fitted parameters, or self-citations are shown that reduce the central claim to a tautology or to the same data by construction; the diffusive migration and area evolution are presented as independently measured from catalog data, and the scaling is offered as an empirical unification rather than a derived prediction forced by prior assumptions within the paper. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption of diffusive migration of seismicity areas and a uniform constant-slip value; no explicit free parameters or invented physical entities are named in the abstract, but the model implicitly treats slip distance as a controlling scale.

free parameters (1)

constant slip distance
Invoked as the fixed value that sets final moment across scales; value not stated in abstract but required for the scaling to hold uniformly.

axioms (1)

domain assumption Seismicity active areas migrate diffusively over time
Stated as a common thread among the anomalous events and used to track area evolution in the Japan swarms.

pith-pipeline@v0.9.0 · 5676 in / 1329 out tokens · 48545 ms · 2026-05-21T10:00:46.203496+00:00 · methodology

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discussion (0)

Reference graph

Works this paper leans on

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