Rates of aftershock decay and the fractal structure of active fault systems

K. Nanjo, Hiroyuki Nagahama, M. Satomura

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65 Citations (Scopus)


Aftershock activity on frequency decay against time is characterized by a power law (the modified Omori formula) of an exponent p, which differs with each aftershock sequence. A theoretical study suggested that p, which is a rate constant of aftershock decay, is related to the fractal dimension of a pre-existing fault system. This has however never been checked. Aftershock activity on size distribution is also characterized by an exponential distribution against magnitude (the Gutenberg-Richter relation) with a slope b. Although p is expected to be related to b, which is related to the partitioning rate of earthquake energy, the relationship has never been established. Here the relation between the p-values and the fractal dimensions of the pre-existing fault systems, and that between the p-values and the b-values are explored, using natural seismicity data and data of the observable fault systems. The p- and b-values were estimated for fifteen aftershock sequences which occurred in Japan. In this paper aftershocks were identified on the basis of a phenomenological definition in the seismicity data. The fractal capacity dimensions D0 are estimated for the pre-existing active fault systems observed on the surface in the aftershock regions. In the present paper the standard box-counting method was adopted to get the D0. Negative correlations between (1) p and D0, and (2) p and b were observed with some scattering. Observation (1) shows that the rate of aftershock decay p decreases systematically with increasing occupancy rate of the pre-existing active fault system D0 and suggests that aftershock decay dynamics is constrained by the pre-existing fracture field. Observation (2) shows that p certainly has a relation with b. Moreover, we offer possible interpretation on these negative correlations and some scatters in both observations; the scatters are interpreted as the scatter of the difference of two fractal dimensions between 3-D fracture construction in the crust and 2-D cross-sectional surface (observed active fault system). Supported by further tests, this paper strongly suggests that the scaling for a natural fracture system is self-affine (with different fractal scalings in different directions) rather than self-similar, which would be a manifestation of regional anisotropy of the fracture system, and that the seismic parameters p and b depend on the 3-D construction of the fracture system in the crust.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
Issue number1-4
Publication statusPublished - 1998 Jan 1


  • Active fault system
  • Aftershock decay
  • Fractal dimension
  • Self-affine
  • b-value of the Gutenberg-Richter relation
  • p-value of the modified Omori formula

ASJC Scopus subject areas

  • Geophysics
  • Earth-Surface Processes


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