pure and applied geophysics

, Volume 138, Issue 4, pp 591–610 | Cite as

Multifractal analysis of earthquakes

  • Tadashi Hirabayashi
  • Keisuke Ito
  • Toshikatsu Yoshii


Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedDq-q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of theDq-q curve are also obtained for Californian and Japanese earthquakes. TheDq-q curve shows two distinctly different types in each region; the gentle type and the steep type. The steeptype corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur.Dq for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanDq forq≥2. We recommend use ofDq at smallq to detect the seismicity change in a local area.

Key words

Multifractal generalized dimension earthquakes epicenter and hypocenter distribution energy distribution 


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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Tadashi Hirabayashi
    • 1
  • Keisuke Ito
    • 2
  • Toshikatsu Yoshii
    • 3
  1. 1.Graduate School of Science and TechnologyKobe UniversityKobeJapan
  2. 2.Department of Earth ScienceKobe UniversityKobeJapan
  3. 3.Earthquake Research InstituteTokyo UniversityTokyoJapan

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