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Relation between the earthquake statistics and fault patterns, and fractals and percolation

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  • Sahimi, Muhammad
  • Robertson, Michelle C.
  • Sammis, Charles G.

Abstract

Using computer simulations and analyzing experimental data, we investigate the structure of fault patterns in heterogeneous rock, and the distribution of earthquake hypocentral locations. At large length scales, the fracture networks of rock are fractal with a fractal dimension D⋍1.9 and 2.5, in 2D and 3D, respectively. We present a computer simulation model that explains these results in terms of percolation fractals. Three-dimensional fractal analysis of regional hypocentral locations yields a fractal dimension of about 1.8. This result can be explained if earthquakes are distributed on the backbone of the fractal network of fault structure with a fractal dimension equal to that of the percolation backbone. Thus, percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes.

Suggested Citation

  • Sahimi, Muhammad & Robertson, Michelle C. & Sammis, Charles G., 1992. "Relation between the earthquake statistics and fault patterns, and fractals and percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 57-68.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:57-68
    DOI: 10.1016/0378-4371(92)90506-L
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    Cited by:

    1. Carpinteri, Alberto & Paggi, Marco, 2009. "A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 540-546.
    2. P. Dimitriu & E. Scordilis & V. Karacostas, 2000. "Multifractal Analysis of the Arnea, Greece Seismicity with Potential Implications for Earthquake Prediction," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 21(2), pages 277-295, May.

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