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  "slug": "fault-sliding-history-criteria",
  "title": "Scalar history criteria for the first loss of full sliding under variable fluid injection",
  "shortTitle": "The injection point decides when a fault stops sliding forward",
  "url": "https://evidencepress.org/releases/fault-sliding-history-criteria/",
  "oneLine": "In the standard circular model of injection-driven slow slip, the slip rate at the injection point decides when the whole fault first stops sliding forward: under stated conditions the centre stops first, almost any abrupt cut ends full sliding, and for a point source no linear taper can halve the rate.",
  "abstract": "Fluid injected into a fault can drive slow, aseismic slip that spreads as an expanding crack. When the injection rate is reduced, part of the fault eventually stops slipping forward, and crack-based size and volume laws cease to apply. This candidate asks when this first happens, in the standard circular model with constant friction, zero fracture energy and zero Poisson ratio, and shows that one scalar quantity, the slip-rate history at the injection point, decides it. For a point source, a Gaussian source or any positive mixture of Gaussian widths and any injection rate that rises and then falls, the whole slipping disk moves forward exactly when the injection point does. For piecewise-smooth rates with any number of rises, falls and steps, the same holds over an interval exactly when the injection-point history has stayed nonnegative throughout it, under stated startup conditions; the crack radius then exists and grows automatically, and full sliding is lost first at the injection point. Explicit consequences include an abrupt-drop tolerance of roughly the square root of source width over stage duration (about 10⁻³ at wellbore scale), a two-term finite-radius criterion with a rigorous remainder, a closed-form deadline after shut-in by which full sliding must have ended, and, for a point source, the result that no linear taper can halve the rate without loss of full sliding. Annular sources can violate the centre-first property. The results concern the first loss of full sliding only, not the later slip pulse or seismic hazard. AI-assisted, unrefereed candidate; no external peer review, independent reproduction or formal verification is claimed.",
  "datePublished": "2026-10-31",
  "dateModified": "2026-10-31",
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  "doi": "10.5281/zenodo.23838529",
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    "detail": "Unrefereed AI-assisted applied-mathematics candidate. The theorems have written proofs; the constants s* and c_D are numerically verified upper bounds, not interval-certified; finite-radius taper thresholds are finite-window numerical estimates and formula (54) an approximation. Internal AI-assisted review in five roles, an adversarial correctness review, a verification re-review and two rounds of targeted proof audit; the last round found no fatal or major defect and its minor items were fixed by the editor without a further review round. External specialist review, independent reproduction and formal verification have not been established."
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      "note": "The versioned research package and manuscript are publicly archived on GitHub and Zenodo. Provider asset parity was checked against frozen local files; availability does not establish correctness or peer review."
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  "keywords": [
    "fluid injection",
    "aseismic slip",
    "fault mechanics",
    "induced seismicity",
    "slip front",
    "frictional rupture",
    "Dawson function",
    "Volterra positivity",
    "shut-in"
  ],
  "keyResults": [
    "Instantaneous criterion (Theorem 1, Proposition 3.3, proof): for a point source, a Gaussian source or any positive Gaussian mixture and a rate that rises then falls, the slip rate is nonnegative throughout the disk at a given time if and only if it is nonnegative at the injection point.",
    "Historical criteria (Theorems A, B, G and Proposition 4.1, proof): for piecewise-smooth or stepped rates with any number of rises and falls, under stated startup conditions, full sliding holds over an interval exactly when the centre history has stayed nonnegative; the crack radius exists and grows automatically, full sliding is lost first at the centre, and for a point source any downward jump ends it at once.",
    "Abrupt drops (equation 26, proof): after a constant-rate stage of duration T with a Gaussian source, the largest tolerated relative drop is below √(ε/(T+ε)), about 10⁻³ at wellbore scale for illustrative parameters.",
    "Inner limit (Theorem 3, proof): in the critically stressed limit the slip rate at radius r is the centre slip rate delayed by a random diffusive first-passage time.",
    "Finite radius (Propositions 7.2 and 7.3, proof with numerically verified constants): a uniform error bound and a two-term centre criterion A*Hq(t) − (2α/R)q(t−) with a rigorous remainder.",
    "Schedules (Proposition 8.2 and Corollary 8.4, proof): after shut-in no crack survives beyond t_s + f c_p V/τ_d − ε, so full sliding ends before then; for a point source no linear taper can halve the rate, the inner-limit threshold being ½√(L/(T+L)) and the finite-radius one strictly smaller."
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  "relatedWorks": [
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      "doi": "10.1126/sciadv.adq0662"
    },
    {
      "citation": "Sáez and Lecampion (2023). Post-injection aseismic slip as a mechanism for the delayed triggering of seismicity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Post-injection slip pulse and immediate locking of the injection point at point-source shut-in.",
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      "description": "For the circular constant-friction model of injection-driven aseismic slip with a point or Gaussian source, nonnegativity of the injection-point slip-rate history is equivalent to full sliding, under stated startup conditions; full sliding is first lost at the centre; explicit drop, shut-in and taper consequences.",
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                "reason": "Not instrumented; unknown is not zero."
              },
              {
                "field": "uncachedInputTokens",
                "reason": "Not instrumented; unknown is not zero."
              }
            ],
            "calibration": null
          }
        },
        "missingnessReason": null
      }
    ]
  }
}