Role of Static Stress Diffusion in the Spatiotemporal Organization of Aftershocks

E. Lippiello, L. de Arcangelis, and C. Godano

Phys. Rev. Lett. 103, 038501 – Published 14 July 2009

Abstract

We investigate the spatial distribution of aftershocks, and we find that aftershock linear density exhibits a maximum that depends on the main shock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and the fractal dimensionality of epicenters clearly indicate triggering by static stress. The nonmonotonic behavior of the linear density and its dependence on the main shock magnitude can be interpreted in terms of diffusion of static stress. This is supported by the power law growth with exponent $H ≃ 0.5$ of the average main-aftershock distance. Implementing static stress diffusion within a stochastic model for aftershock occurrence, we are able to reproduce aftershock linear density spatial decay, its dependence on the main shock magnitude, and its evolution in time.

Received 13 January 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.038501

Authors & Affiliations

E. Lippiello¹, L. de Arcangelis², and C. Godano¹

¹Department of Environmental Sciences, Second University of Naples and CNISM, 81100 Caserta, Italy
²Institute for Building Materials, ETH Hönggerberg, 8093 Zürich, Switzerland and Department of Information Engineering, Second University of Naples and CNISM, 81031 Aversa (CE), Italy

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Vol. 103, Iss. 3 — 17 July 2009

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Images

Figure 1
The distribution of distances from the main shock (filled symbols) versus $Δ r$ for main shock magnitude $m \in [M, M + 1 [$ . Aftershocks are events occurring within $T = 30 \min $ from the main shock (678, 864, and 494 aftershocks for $M = 2$ , 3, and 4, respectively). Open symbols represent $ρ_{B} (Δ r)$ . For $M = 4$ , the power law fit in the range $[1 ∶ 100] km$ gives $μ = 1.88 \pm 0.05$ [dashed blue line in panel (c)]. Magenta curves are obtained by adding the experimental $ρ_{B} (Δ r)$ to the numerical $ρ (Δ r)$ . The orange line in panel (b) is the power law $x^{- 1.4}$ obtained by FB in the intermediate range $[0.2 ∶ 16] km$ .Reuse & Permissions
Figure 2
The distribution of distances from the main shock for $M = 2$ (circles), $M = 3$ (squares), $M = 4$ (diamonds), and $M = 5$ (triangles). Aftershocks are events occurring within $T = 5 h$ from the main shock. The aftershock (main shock) number is 1065 (12 746) for $M = 2$ , 1800 (3410) for $M = 3$ , 1425 (349) for $M = 4$ , and 1454 (52) for $M = 5$ . Continuous lines are the result of numerical simulations. In inset (a), the collapse of the curve is obtained by rescaling $Δ r$ by $10^{β M}$ according to Eq. (1), with $β = 0.42$ . The continuous magenta line is the theoretical master curve $F (x)$ , and the brown dashed line shows the asymptotic decay $F (x) \sim x^{- 2}$ . Inset (b) shows the comparison of experimental $ρ (Δ r)$ for $M = 2, 4$ (symbols) with the theoretical predictions $ρ_{th} (Δ r)$ (continuous magenta lines). Dashed lines (red $M = 2$ , blue $M = 4$ ) are the results of the stochastic model simulations.Reuse & Permissions
Figure 3
The maximum distance $R_{MAX} (Δ t)$ for $M = 2$ , 3, 4, and 5 (circles, squares, diamonds, and triangles, respectively) from bottom to top. $R_{MAX} (Δ t)$ grows until $Δ t_{M}$ ( $Δ t_{M} = 16 000$ , 2900, 690, and 190 sec for $M = 5$ , 4, 3, and 2, respectively). The dashed line is the power law fit $R_{MAX} (Δ t) \sim Δ t^{H}$ , with $H = 0.54 \pm 0.05$ obtained for $M = 5$ and $Δ t < Δ t_{M}$ . Continuous lines are the theoretical prediction for $L_{MAX} (Δ t)$ .Reuse & Permissions
Figure 4
The average spatial distance $R (Δ t)$ from the main shock (black circles) of aftershocks occurring in the time window $[Δ t, Δ t (1 + ϵ)]$ with $ϵ = 0.02$ versus $Δ t$ . The initial growth $R (Δ t) \sim Δ t^{0.47}$ (magenta line) is consistent with the diffusion behavior. The decay at larger times is related to the upper cutoff $L_{\sup}$ . Continuous red and dashed green curves are the theoretical prediction Eq. (2): Green curves correspond to $K = 1.8 \times 10^{0.42 (M - 5)} km$ fitted from Fig. 2. Red curves correspond to $K = 0.018 Δ t^{0.47} km$ , where $Δ t$ is measured in seconds, obtained from the numerical model.Reuse & Permissions

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