Fractal geometry and seismicity in the Mexican subduction zone

Main Article Content

F. Angulo-Brown
A. H. Ramírez-Guzmán
E. Yépez
A. Rudolf-Navarro
C. G. Pavía-Miller

Abstract

By means of the box counting method we calculate the fractal dimension D of the distribution of faults, fractures and lineaments in a region of the southern Mexican Pacific coast. The results suggest that in the spatial sense the b-value of the Gutenberg-Richter law and the fractal dimension are positively correlated. We also suggest that D depends on the depth of the seismogenic zone.

Article Details

How to Cite
Angulo-Brown, F., Ramírez-Guzmán, A. H., Yépez, E., Rudolf-Navarro, A., & Pavía-Miller, C. G. (1998). Fractal geometry and seismicity in the Mexican subduction zone. Geofisica Internacional, 37(1), 29–33. https://doi.org/10.22201/igeof.00167169p.1998.37.1.2157
Section
Article

References

AKI, K. 1981. A probabilistic synthesis of precursors phenomena. Earthquake Prediction. Maurice Ewing series, 4, (ed. Simson and Richards) (AGU, Washington D. C.) 566-575. DOI: https://doi.org/10.1029/ME004p0566

BAK, P., C. TANG and K. WIESENFELD, 1987. Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59, 381-384. DOI: https://doi.org/10.1103/PhysRevLett.59.381

BAK, P. and C. TANG, 1989. Earthquake as a self-organized critical phenomenon. J. Geophys. Res. 94. 15635-15637. DOI: https://doi.org/10.1029/JB094iB11p15635

BARRIERE, B. and D. L. TURCOTTE, 1994. Seismicity and self-organized criticality. Phys. Rev. E. 49, 1151-1160. DOI: https://doi.org/10.1103/PhysRevE.49.1151

GONZALEZ, M. E. 1992. Estudio geomorfológico comparativo con modelos magnetométricos del área del Cerro de Toro, Chilpancingo, Guerrero. M. Sc. Thesis ESIA-IPN Mexico.

GUO, Z. and Y. OGATA, 1995. Correlation between characteristic parameters of aftershock distributions in time space and magnitude. Geophys. Res. Lett. 22, 993-996. DOI: https://doi.org/10.1029/95GL00707

HIRATA, T. 1989a. A correlation between de b value and the fractal dimension of earthquakes. J. Geophys. Res. 94, 7507-7514. DOI: https://doi.org/10.1029/JB094iB06p07507

HIRATA, T. 1989b. Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales. Pageoh. 131, 157-170. DOI: https://doi.org/10.1007/978-3-0348-6389-6_9

INEGI. 1985. E-14-11 Hoja Acapulco, México.

INEGI. 1985. E-14-7 Hoja Zihuatanejo, México.

ITO, K. and M. MATSUZAKI, 1990. Earthquake as a self-organized critical phenomenon. J. Geophys. Res. 95, 6853-6860. DOI: https://doi.org/10.1029/JB095iB05p06853

KING, G. 1983. The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault systems: the geometrical origin of b-value. Pageoh. 121, 761-815. DOI: https://doi.org/10.1007/BF02590182

LOMNITZ-ADLER, J. 1992. Interplay of fault dynamics and fractal dimension in determining Gutenberg-Richter's b-value. Geophys. J. Int. 108, 941-944. DOI: https://doi.org/10.1111/j.1365-246X.1992.tb03482.x

MANDELBROT, B. B. 1982. The fractal geometry of nature. (Freeman, San Francisco).

OKUBO, P. G. and K. AKI, 1987. Fractal Geometry in the San Andreas Fault System. J. Geophys. Res. 92, 345-355. DOI: https://doi.org/10.1029/JB092iB01p00345

PACHECO, J. F., H. CHRISTOPHER SCHOLZ and R. LYNN SYKES, 1992. Change in frequency-size relationship from small to large earthquakes. Nature. 335, 71-73. DOI: https://doi.org/10.1038/355071a0

PARDO, M. and G. SUAREZ, 1993. Steep subduction geometry of the Rivera Plate beneath the Jalisco block in western Mexico. Geophys. Res. Lett. 20, 2391-2394. DOI: https://doi.org/10.1029/93GL02794

SANDER, E., L. M. SANDER and R. F. ZIFF, 1994. Fractals and fractal correlations. Comput. Phys. 8, 420-425. DOI: https://doi.org/10.1063/1.168501

SINGH, S. K., M. RODRIGUEZ and L. ESTEVA, 1983. Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone. Bull. Seism. Soc. Am., 73, 1779-1796.

SORNETTE, A. and D. SORNETTE, 1989. Self-organized criticality and earthquakes. Europhys. Lett. 9, 197-202. DOI: https://doi.org/10.1209/0295-5075/9/3/002

SORNETTE, D., C. VANNESTE and A. SORNETTE. 1991. Dispersion of b-values in Gutenberg-Richter law as a consequence of a proposed fractal nature of continental faulting. Geophys. Res. Lett. 18, 997-900. DOI: https://doi.org/10.1029/91GL01124

SUAREZ, G., T. MONFRET, G. WITTLINGER and C. DAVID, 1990. Geometry of subduction and depth of the seismogenic zone in the Guerrero gap, Mexico. Nature, 345, 336-338. DOI: https://doi.org/10.1038/345336a0

TURCOTTE, D. L. 1989. A fractal approach to probabilistic seismic hazard assessment. Tectonophysics 167, 171-177. DOI: https://doi.org/10.1016/0040-1951(89)90067-X

TURCOTTE, D. L., 1992. Fractals and chaos in geology and geophysics. (Cambridge University. Press. Cambridge).