Research ArticleGEOPHYSICS

Induced seismicity provides insight into why earthquake ruptures stop

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Science Advances  20 Dec 2017:
Vol. 3, no. 12, eaap7528
DOI: 10.1126/sciadv.aap7528
  • Fig. 1 Arrested and runaway earthquake ruptures.

    The red line and the symbols delineate the rupture arrest area as a function of pore pressure inside the perturbation. The rupture extent is also illustrated by final slip maps. The sketch in the inset depicts the relative position of a fault and a reservoir.

  • Fig. 2 Influence of reservoir- and fault-related parameters on the evolution of rupture arrest area.

    (A) Varying reservoir-related parameters, (B) varying strength parameter S and reservoir radius re, and (C) varying fault-related parameters. The reference solution (bold blue line) is the same in all three panels. In each panel, the same color depicts the solutions for the same varying parameter. For (A) and (C), thin and bold lines indicate solutions for lower and greater value of the corresponding parameter compared to that of the reference solution. For stresses in (C), the thin and thick lines indicate lower and higher values of S, respectively. Transition to runaway ruptures is marked by the dashed lines. The horizontal gray lines indicate the area of the intersection of the reservoir and the fault; it also corresponds to the minimal arrested area. The horizontal dotted gray line in (A) indicates constant maximum arrested area (in other panels, maximum arrested area varies). Note that in (C), the lines for τ0 and σ are almost identical.

  • Fig. 3 Comparison of pore-pressure distribution inside sealed cylindrical reservoirs induced at time t = 100 days by steady-flux injection at its center, for varying compressibility ct, viscosity μv, porosity φ, and permeability k.

    Higher and lower values of parameters are depicted by thicker and thinner lines of the same color, respectively. The numbers indicate the values of the spatial integral of pressure in megapascals per square kilometer.

  • Fig. 4 Comparison of our estimate of magnitude of maximum arrested rupture, Embedded Image, for three values of γ with magnitudes of injection-induced earthquakes over a broad range of injected volumes.

    We find that our estimate is equivalent to that of magnitude of maximum possible earthquake by van der Elst et al. (12) for b = 1; therefore, we also indicate the corresponding values of seismogenic index Ap. For completeness, we also include the estimate of maximum possible induced earthquake by McGarr (9). Note that for the events induced during multistage hydrofracking in the Western Canada sedimentary basin (yellow circles), we consider the total volumes for all previous stages and all proximal well completions reported as “maximum volume” by Atkinson et al. (11).

  • Fig. 5 Fracture mechanics of rupture arrest under nonuniform stress.

    Sketch of (A) stress drop distributions Δτ(r) and (B) the corresponding static stress intensity factors K0(R) illustrating different crack behavior (although our approach supports Kc being a function of R, for illustration purposes, Kc is plotted as a constant).

  • Fig. 6 Verification of our theoretical estimates with numerical results.

    Comparison of estimated rupture arrest area Aarr and maximum rupture arrest area Amax with rupture arrest area from numerical simulations Embedded Image as functions of overstressed area for (A) a steplike distribution of stress drop and varying strength parameter S (B), a Gaussian distribution of stress drop, and varying minimal normal stress σmin. For a step-like stress drop distribution, we performed simulations with circular, square, and elliptical perturbations marked by circles, squares, and triangles. The transitions from solid to dashed lines indicate transition from arrested to runaway ruptures. The undulated double line indicates interrupted y axis; r.r. indicates runaway ruptures. Lfric = μ ⋅ Dc/(τs0 − τd0) is a characteristic length scale introduced by the slip-weakening process (39).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaap7528/DC1

    fig. S1. Comparison of dimensionless rupture arrest area calculated from numerical simulations with grid spacing h = 50 m (circles) and h = 100 m (squares) with our theoretical estimates (bold lines) for varying σmin (indicated by color).

    fig. S2. Comparison of stress drop distributions as functions of dimensionless crack radius at the time of Formula for situations from Fig. 6.

    fig. S3. Scaling of mean static and dynamic stress drops in results of numerical simulations.

    fig. S4. Comparison of various approaches to estimate Mw from ruptured area Aarr.

    fig. S5. Distributions of reservoir-fault parameters for all ~4250 configurations used for verification of Formula (point-load approximation) against Formula (finite-reservoir approach).

    fig. S6. Distributions of reservoir-fault parameters for all ~4250 configurations used for verification of Formula (point-load approximation) against Formula (finite-reservoir approach).

    fig. S7. Comparison of Formula (derived for a point-load approximation of a reservoir) with Formula (derived for a finite reservoir) and corresponding orthogonal residuals.

    fig. S8. Evaluation of the probability of occurrence rank of the largest event within a sequence.

    table S1. Reservoir and fault parameters used to prepare Fig. 2.

    References (40, 41)

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Comparison of dimensionless rupture arrest area calculated from numerical simulations with grid spacing h = 50 m (circles) and h = 100 m (squares) with our theoretical estimates (bold lines) for varying σmin (indicated by color).
    • fig. S2. Comparison of stress drop distributions as functions of dimensionless crack radius at the time of Amaxarr for situations from Fig. 6.
    • fig. S3. Scaling of mean static and dynamic stress drops in results of numerical simulations.
    • fig. S4. Comparison of various approaches to estimate Mw from ruptured area Aarr.
    • fig. S5. Distributions of reservoir-fault parameters for all ~4250 configurations used for verification of max w M (point-load approximation) against Mcritw (finite-reservoir
      approach).
    • fig. S6. Distributions of reservoir-fault parameters for all ~4250 configurations
      used for verification of Mmaxw (point-load approximation) against Mcritw (finite-reservoir approach).
    • fig. S7. Comparison of Mmax-arrw (derived for a point-load approximation of a reservoir) with Mcritw (derived for a finite reservoir) and corresponding orthogonal residuals.
    • fig. S8. Evaluation of the probability of occurrence rank of the largest event within a sequence.
    • table S1. Reservoir and fault parameters used to prepare Fig. 2.
    • References (40, 41)

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