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Self-similar branching of aftershock sequences

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  • Holliday, James R.
  • Turcotte, Donald L.
  • Rundle, John B.

Abstract

In this paper we propose a branching aftershock sequence (BASS) model for seismicity. We suggest that the BASS model is a preferred alternative to the widely studied epidemic type aftershock sequence (ETAS) model. In the BASS model an initial, or seed, earthquake is specified. The subsequent earthquakes are obtained from the statistical distributions of magnitude, time, and location. The magnitude scaling is based on a combination of the Gutenberg–Richter scaling relation and the modified Båth’s law for the scaling relation of aftershocks relative to the magnitude of the seed earthquake. Omori’s law specifies the distribution of earthquake times, and a modified form of Omori’s law specifies the distribution of earthquake locations. Since the BASS model is specified by the four scaling relations, it is fully self-similar. This is not the case for ETAS. We also give a deterministic version of BASS and show that it satisfies Tokunaga side-branching statistics in a similar way to diffusion-limited aggregation (DLA).

Suggested Citation

  • Holliday, James R. & Turcotte, Donald L. & Rundle, John B., 2008. "Self-similar branching of aftershock sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 933-943.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:4:p:933-943
    DOI: 10.1016/j.physa.2007.09.045
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    References listed on IDEAS

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    1. K. R. Felzer & E. E. Brodsky, 2006. "Decay of aftershock density with distance indicates triggering by dynamic stress," Nature, Nature, vol. 441(7094), pages 735-738, June.
    2. A. Saichev & D. Sornette, 2006. "Power law distribution of seismic rates: theory and data analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(3), pages 377-401, February.
    3. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    4. A. Saichev & D. Sornette, 2006. "Renormalization of branching models of triggered seismicity from total to observable seismicity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(3), pages 443-459, June.
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    1. Gkarlaouni, Charikleia & Lasocki, Stanislaw & Papadimitriou, Eleftheria & George, Tsaklidis, 2017. "Hurst analysis of seismicity in Corinth rift and Mygdonia graben (Greece)," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 30-42.

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