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Scaling laws of earthquakes derived by renormalization group method

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  • Iwashita, Yukinori
  • Nakanishi, Ichiro

Abstract

Size-frequency distribution of earthquakes (Gutenberg–Richter relation) is characterized by the b value, and its average is about 1 in observational works. The high-frequency asymptotes of displacement spectra of seismic waves provide another evidence of scale invariance of seismic faulting. The asymptotes of the observed spectra show ω−θ with θ≃2, which was first suggested by Aki [J Geophys Res 1967;72:1217–31]. Matsuba [Chaos, Solitons & Fractals 2002;13:1281–94] applied the renormalization group method to the three-dimensional Burridge–Knopoff (BK) model and obtained the relation between b and θ. b=0.880 was derived for θ=2. However, his result does not seem to explain the observed values of b.

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  • Iwashita, Yukinori & Nakanishi, Ichiro, 2005. "Scaling laws of earthquakes derived by renormalization group method," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 511-518.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:511-518
    DOI: 10.1016/j.chaos.2004.08.002
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    Cited by:

    1. Cun Chen & Shaokang Guan & Liying Zhang, 2018. "Complex Dynamical Behavior in the Shear-Displacement Model for Bulk Metallic Glasses during Plastic Deformation," Complexity, Hindawi, vol. 2018, pages 1-13, December.
    2. Harrouni, S. & Guessoum, A., 2009. "Using fractal dimension to quantify long-range persistence in global solar radiation," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1520-1530.
    3. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.

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