Multifractal analysis of earthquakes |
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| Authors: | Tadashi Hirabayashi Keisuke Ito Toshikatsu Yoshii |
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| Institution: | (1) Graduate School of Science and Technology, Kobe University, 657 Kobe, Japan;(2) Department of Earth Science, Kobe University, 657 Kobe, Japan;(3) Earthquake Research Institute, Tokyo University, 113 Tokyo, Japan |
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| Abstract: | Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedD
q-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 theD
q-q curve are also obtained for Californian and Japanese earthquakes. TheD
q-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.D
q for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanD
q forq 2. We recommend use ofD
q at smallq to detect the seismicity change in a local area. |
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| Keywords: | Multifractal generalized dimension earthquakes epicenter and hypocenter distribution energy distribution |
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