Micromorphic continuum, rotational wave and fractal properties of earthquakes and faults

Acta Geophysica Polonica

Volumn 46, Issue 3, 1998, Pages 289-294

  Nagahama, Hiroyuki ^a   Teisseyre, Roman ^b  

^a TOHOKU UNIVERSITY   (Japan)

^b INSTITUTE OF GEOPHYSICS   (Poland)

Author keywords

Earthquakes; Faults; Fractals; Micromorphic continuum; Rotational wave

Indexed keywords

EARTHQUAKE; FAULT; FRACTAL ANALYSIS;

EID: 0032456240     PISSN: 00015725     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (76)

1. Aki, K. A., 1981, Probabilistic synthesis of precursory phenomena. In: D.W. Simpson and P.G. Richards (eds.), "Earthquake Prediction: An International Review" Maurice Ewing Series, 4, 566-574, Am. Geophys. Union, Washington D.C.
2. Asada, T., Z. Suzuki and Y. Tomoda, 1950, On energy and frequency of earthquakes, J. Seism. Soc. Japan (ZISIN), 3, 11-15 (in Japanese with English abstract).
3. Bielski, W., 1995, Anisotropy in a micromorphic continuum. In: R. Teisseyre (ed.), "Theory of Earthquake Premonitory and Fracture Processes", 633-639, Polish Scientific Publ., Warszawa.
4. Chelidze, T., 1993, Fractal damage mechanics of geomaterials, Terra Nova, 5, 421-437.
5. Cobbold, P.R., 1977, Compatibility equations and the integration of finite strains in two dimensions, Tectonophysics, 39, T1-T6.
6. Droste, Z., and R. Teisseyre, 1976, Rotational and displacemental components of ground motion as deduced from data of the azimuth system of seismograph, Publs. Inst. Geophys. Pol. Acad. Sc., 97, 157-167 (in Polish with English abstract).
7. Dubolis, J., and L. Novali, 1989, Quantification of the fracturing of the slab using a fractal approach, Earth. Planet. Sci. Lett., 94, 97-108.
8. England, A.H., 1971, Complex Variable Methods in Elasticity, Wiley-Interscience, New York.
9. Enya, O., 1901, On aftershocks, Rep. Earthq. Invest. Comm., 35, 35-56 (in Japanese).
10. Eringen, A.C., 1968, Theory of micropolar elasticity. In: H. Liebowitz (ed.), "Fracture", vol. 2. 621-729, Academy Press, New York.
11. Eringen, A.C., and W.D. Claus (Jr.), 1970, A micromorphic approach to dislocation theory and its relation to several existing theories. In: J.A. Simmons, R. deWit and R. Bullough (eds.), "Fundamental Aspects of Dislocation Theory" 1023-1040, Nat. Bur. Stand. (U.S.), Spec. Publ. 317, II.
12. Eringen, A.C., and E.S. Suhubi, 1964, Nonlinear theory of micro-elastic solids, I, Int. J. Engn. Sci., 2, 189-203.
13. Feller, W., 1966, An Introduction to Probability Theory and its Applications, vol. 2, Wiley and Sons Inc., New York.
14. Fernandez, L., F. Guinea and E. Louis, 1988, Random and dendritic patterns in crack propagation, J. Phys. A: Math. Gen., 21, L301-L305.
15. Gutenberg, B., and C.F. Richter, 1954, Seismicity of the Earth and Associated Phenomena, 2nd edition, Princeton Univ. Press, Princeton.
16. Hanyga, A., and R. Teisseyre, 1973, The fundamental source solutions in the symmetric micromorphic continuum, Rivista Ital. di Geofis., 22, 336-340.
17. Hanyga, A., and R. Teisseyre, 1974, Point source models in the micromorphic continuum, Acta Geophys. Pol., 22, 1, 11-20.
18. Hanyga, A., and R. Teisseyre, 1975, Linear symmetric micromorphic thermoelasticity-source solution and wave propagation, Acta Geophys. Pol., 23, 2, 147-157.
19. Hirata, T., 1989, Fractal dimension of faults systems in Japan: Fractal structure in rock fracture geometry at various scales, Pageoph, 131, 157-170.
20. Iesan, D., 1981, Some applications of micropolar mechanics to earthquake problems, Int. J. Engng. Sci., 19, 855-864.
21. Inaoka, H., and H. Takayasu, 1996a, Universal fragment size distribution in a numerical model of impact fracture, Physica A, 229, 5-25.
22. Inaoka, H., and H. Takayasu, 1996b, Fractal analyses for a model of impact fragmentation, Fractals, 4, 393-399.
23. Ishimoto, M., and K. Iida, 1939, Observations of the seismic energy from the microseismograph, Bull. Earthq. Res. Inst., 17, Part 2, 443-478 (in Japanese with English abstract).
24. Ito, K., 1992, Towards a new view of earthquake phenomena, Pageoph, 138, 531-548.
25. Ito, K., and M. Matsuzaki, 1990, Earthquake as self-organized critical phenomena, J. Geophys. Res., 95, B5, 6853-6860.
26. Kanamori, H., and D.L. Anderson, 1975, Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Am., 65, 1073-1095.
27. King, G., 1983, The accomodation of large strains in the upper lithosphere of the Earth and the other solids by self-similar fault systems: The geometric origin of b-value, Pageoph, 121, 761-815.
28. Knopoff, L., 1958, Energy release in earthquakes, Geophys. J., 1, 44-52.
29. Lanczos, C., 1949, The Variation Principles of Mechanics, Univ. Toronto Press, Toronto.
30. Landau, L.D., and E.M. Lifshitz, 1959a, Theory of Elasticity, Pergamon Press, Oxford.
31. Landau, L.D., and E.M. Lifshitz, 1959b, Fluid Mechanics, Pergamon Press, Oxford.
32. Lehner, F.K., V.C. Li and J.R. Rice, 1981, Stress diffusion along rupturing plate boundaries, J. Geophys. Res., 86, B7, 6155-6169.
33. Louis, E., and F. Guinea, 1987, The fractal nature of fracture, Europhys. Lett., 3 (8), 871-877.
34. Louis, E., and F. Guinea, 1989, Fracture as a growth process, Physica D, 38, 235-241.
35. Louis, E., F. Guinea and F. Flores, 1986, The fractal nature of fracture. In: L. Pietronero and E. Tosati (eds.), "Fractal in Physics", 177-180, Elsevier Sci. Publ. Company, Amsterdam.
36. Main, I.G., 1991, A modified Griffith criterion for the evolution of damage with a fratal ditribution of crack lenghts: Application to seismic event rates and b-values, Geophys. J. Int., 107, 353-362.
37. Main, I.G., P.G. Meredith and C. Jones, 1989, A reinterpretation of the precursory seismic b-value anomaly from fracture mechanics, Geophys. J., 96, 131-138.
38. Main, I.G., S. Peacock and P.G. Meredith, 1990, Scattering attenuation and the fractal geometry of fracture systems, Pageoph, 133, 283-304.
39. Mandelbrot, B.B., 1982, The Fractal Geometry of Nature, Freeman, New York.
40. Meakin, P., 1991, Models formaterial failure and deformation, Science, 252, 226-233.
41. Meredith, P.G., and B.K. Atkinson, 1983, Stress corrosion and acoustic emission during tensile crack propagation in Whin Sill dolerite and other basic rocks, Geophys. J. R. astron. Soc., 75, 1-21.
42. Meredith, P.G., I.G. Main and C. Jones, 1990, Temporal variations in seimicity during quasi-static and dynamic rock failure, Tectonophysics, 175, 249-268.
43. Mogi, K., 1962, The influence of the dimensions of specimens on the fracture strength of rocks: comparison between the strength of rock specimens and that of the Earth's crust, Bull. Earthq. Res. Inst., 40, 175-185.
44. Nagahama, H., 1991, Fracturing in the solid earth, Sci. Repts. Tohoku Univ., 2nd sen (Geol.), 61, 103-126.
45. Nagahama, H., 1994, Self-affine growth pattern of earthquake rupture zones, Pageoph, 142, 263-271.
46. Nagahama, H., 1996, Non-Riemannian and fractal geometries of fracturing in geomaterials, Geol. Rund., 85, 96-102.
47. Nagahama, H., and K.Yoshii, 1993, Fractal dimension and fracture of brittle rocks, Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 30, 173-175.
48. Nagahama, H., and K. Yoshii, 1994, Scaling laws of fragmentation. In: J.H. Kruhl (ed.), "Fractal and Dynamical Systems in Geosciences", 25-36, Springer-Verlag, Berlin.
49. Nanjo, K., H. Nagahama and M. Satomura, 1998, Rates of aftershock decay and the fractal structure of active fault systems, Tectonophysics, 287, 173-186.
50. Shimbo, M., 1978, A geometrical foundation of the analysis of granular behaviour, 272-281, Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Sendai.
51. Sornette, A., P. Davy and D. Sornette, 1990, Growth of fractal fault patterns, Phys. Rev. Lett., 65, 2266-2269.
52. Sornette, D., and C. Vanneste, 1996, Fault self-organized by repeated earthquakes in a quasi-static antiplane, Nonlinear Proc. Geophys., 3, 1-12.
53. Sornette, D., P. Davy and A. Sornette, 1990, Structuration of the lithosphere in plate tectonics as a self-organized critical phenomenon, J. Geophys. Res., 95 (B 11), 17353-17361.
54. Stakhovsky, I.R., 1995, Fractal geometry of brittle failure at antiplanar shear, Phys. Solid Earth, 31, 268-275.
55. Stanley, H., and N. Ostrovsky, 1986, On Growth and Form, Nijhoff Publ., Amsterdam.
56. Suhubi, E.S., and A.C. Eringen, 1964, Nonlinear theory of micro-elastic solids (II), Int. J. Engng. Sci., 2, 389-404.
57. Suzuki, Z., 1953, A statistical study on the occurrence of small earthquake (I), Sci. Rep. Tohôku Univ., 5, 177-182.
58. Taguchi, Y., 1989, Fracture propagation governed by the Laplace equation, Phys. A., 156, 741-755.
59. Takayasu, H., 1985, A deterministic model of fracture, Prog. Theor. Phys., 74, 1343-1345.
60. Takayasu, H., 1986, Pattern formation of dendritic fractals in fracture and electric breakdown. In: L. Pietronero and E. Tosatti (eds.), "Fractals in Physics", 181-184, Elsevier Sci. Publ., Amsterdam.
61. Takeo, M., and H.M. Ito, 1997, What can be learned from rotational motions excited by earthquakes? Geophys. J. Int., 129, 319-329.
62. Teisseyre, R., 1973a, Earthquake processes in a micromorphic continuum, Pageoph, 102, 15-28.
63. Teisseyre, R., 1973b, Earthquake processes in a micromorphic continuum, Rev. Roum. Géol. Géophys. et Géogr., Sér. de Géophys., 17, 145-148.
64. Teisseyre, R., 1974, Symmetric micromorphic continuum wave propagation, point source solution and some application to earthquake processes. In: Thoft-Christensen (ed.), "Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics", 201-244, D. Riedel Publ., Holland.
65. Teisseyre, R., 1975, On the recent development of continuum mechanics and its application to seismology, Gerlands Beitr. Geophysik, Leipzig, 84 (6), 501-508.
66. Teisseyre, R., 1978, Relation between the defect distribution and stress. The glacier motion, Acta Geophys. Pol., 26 (4), 283-290.
67. Teisseyre, R., 1982, Some seismic phenomena in the light of the symmetric micromorphic theory, J. Techn. Phys., 38, 95-99.
68. Teisseyre, R., 1986, Some problems of mechanics of the continuum media and the application to earthquake studies. In: R. Teisseyre (ed.), "Physics and Evolution of the Earth's Interior", vol. 3 - "Continuum Theories in Solid Earth Physics", 256-309, Polish Scientific Publishers - Warszawa, Elsevier Scientific Publishing Company - Amsterdam.
69. Teisseyre, R., 1995a, Micromorphic model of a seismic source zone, 1. Introduction. In: R. Teisseyre (ed.), "Theory of Earthquake Premonitory and Fracture Processes", 613-615, Polish Scientific Publishers, Warszawa.
70. Teisseyre, R., 1995b, Symmetric micromorphic theory; application to seismology. In: R. Teisseyre (ed.), "Theory of Earthquake Premonitory and Fracture Processes", 616-627, Polish Scientific Publishers, Warszawa.
71. Turcotte, D.L., 1986a, Fractals and fragmentation, J. Geophys. Res., 91, 1921-1926.
72. Turcotte, D.L., 1986b, A fractal model for crustal deformation, Tectonophys., 132, 261-269.
73. Turcotte, D.L., 1986c, Fractals in geology and geophysics, Pageoph, 131, 171-196.
74. Turcotte, D.L., 1992, Fractals and Chaos in Geology and Geophysics, Cambridge Univ. Press, Cambridge.
75. Walgraef, D., 1988, Instabilities and patterns in reaction-diffusion dynamics, Solid State Phenom., 384, 77-96.
76. Wenousky, S.G., C.H. Scholz, K. Shimazaki and T. Matsuda, 1983, Earthquake frequency distribution and the mechanics of faulting, J. Geophys. Res., 88, 9331-9340.