Abstract
The generalized fractal dimension for epicentral distribution of earthquakes in west Taiwan is measured. The entire area is first divided into two zones, i.e., north and south zones, after which the two zones are further separated into three subzones for the former and two for the latter. The logC q (r) versus logr function, whereC q (r) is the generalized correlation integral andr is the distance between two epicenters, shows that a linear relation between logC q and logr exists in the range ofr smaller thanr c . The value ofr c is 25 km for the north zone, 40 km for the south and 12 km for the three north subzones. The valuesr c =25 and 40 km are almost the smallest ones of the width of epicentral distributions of the north and south zones, respectively. The value ofr c =12 km for the three north subzones is approximately the smallest size of the cluster of epicenters. For the plots of two south subzones, the pattern of data points does not bend in the range ofr in consideration, and, thus, there is not such a critical radius. TheD q −q relations forq=0, 1, 2,..., 15 are constructed for the two zones and five subzones. Results show significant multifractality and a spatial variation in multifractality for epicentral distributions of earthquakes in west Taiwan.
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References
Aki, K.,A probabilistic synthesis of precursory phenomena, InEarthquake Prediction: An International Review, Maurice Ewing Ser., vol. 4 (Simpson, D. W., and Richards, P. G., eds.) (AGU, Washington 1981) pp. 556–574.
An, Z.-W., Wang, L.-Y., Yao, D.-H. andZhu, C.-Z. (1993)The Chaotic Characteristics in Seismogenic Process, Acta Seism. Sinica6, 29–37.
Grassberger, P. (1983),Generalized Dimensions of Strange Attractors, Phys. Lett.97A, 227–230.
Gutenberg, B., andRichter, C. F. (1944),Frequency of Earthquakes in California, Bull. Seismol. Soc. Am.34, 185–188.
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., andShraiman, B. I. (1986),Fractal Measures and their Singularities: The Characterization of Strange Sets, Phys. Rev.A33, 1141–1151.
Hentschel, H. G. E., andProcaccia, I. (1983),The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors, Physica8D, 435–444.
Hirabayashi, T., Ito, K., andYoshii, T. (1992),Multifractal Analysis of Earthquakes, Pure and Appl. Geophys.138, 591–610.
Hirata, T. (1989),A Correlation between the b Value and the Fractal Dimension of Earthquakes, J. Geophys. Res.94, 7507–7514.
Hirata, T., andImoto, M. (1991),Multifractal Analysis of Spatial Distribution of Microearthquakes in the Kanto Region, Geophys. J. Int.107, 155–162.
Hirata, T., Satoh, T., andIto, K. (1987),Fractal Structure of Spatial Distribution of Microfracturing in Rock, Geophys. J. R. Astr. Soc.90, 369–374.
Ho, C. S. (1982),Tectonic Evolution of Taiwan, Explanatory Text of the Tectonic Map of Taiwan, The Ministry of Economic Affairs, ROC, 126 pp.
Kagan, Y. Y., andKnopoff, L. (1980),Spatial Distribution of Earthquakes: The Two-point Correlation Function, Geophys. J. R. Astr. Soc.62, 303–320.
Kurths, J., andHerzel, H. (1987),An Attractor in a Solar Time Series, Physica225, 165–172.
Lei, X., Nishizawa, O., andKusunose, K. (1993),Band-limited Heterogeneous Fractal Structure of Earthquakes and Acoustic-emission Events, Geophys. J. Int.115, 79–84.
Mandelbrot, B. B.,The Fractal Geometry of Nature (W. H. Freeman, New York 1983).
Mandelbrot, B. B. (1989),Multifractal Measures, Especially for the Geophysicst, Pure and Appl. Geophys.131, 5–42.
Sadovskiy, M. A., Golubeva, T. V., Pisarenko, V. F., andShnirman, M. G. (1984),Characteristic Dimension of Rock and Hierarchical Properties of Seismicity, Izv. Acad. Sci. USSR Phys. Solid Earth, Engl. Trans.20, 87–96.
Stach, L. W. (1957),Petroleum Potentialities and Exploration for Oil in Taiwan, Symp. Petrol. Geol. Taiwan, 15–34.
Takayasu, H. Fractals in the Physical Sciences (Manchester Univ. Press, Manchester 1990).
Tsai, Y. B., Teng, T. L., andChiu, J. M. (1977),Tectonic Implications of the Seismicity in the Taiwan Region, Mem. Geol. Soc. China2, 13–41.
Wang, J. H. (1988),b Values of Shallow Earthquakes in Taiwan, Bull. Seismol. Soc. Am.78, 1243–1254.
Wang, J. H. (1989),The Taiwan Telemetered Seismographic Network, Phys. Earth Planet. Inter.58, 9–18.
Wang, J. H., andLin, W. H. (1993),A Fractal Analysis of Earthquakes in West Taiwan, Terr. Atmo. Ocean4, 457–462.
Wang, J. H., Chen, K. C., andLee, T. Q. (1994),Depth Distribution of Shallow Earthquakes in Taiwan, J. Geol. Soc. China37, 125–142.
Yeh, Y. H., andTsai, Y. B. (1981),Crustal Structure of Central Taiwan from Inversion of P-wave Arrival Times, Bull. Inst. Earth Sci., Acad. Sin.1, 83–102.
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Wang, JH., Lee, CW. Multifractal measures of earthquakes in west Taiwan. PAGEOPH 146, 131–145 (1996). https://doi.org/10.1007/BF00876673
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DOI: https://doi.org/10.1007/BF00876673