Scaling similarities of multiple fracturing of solid materials

Nonlinear Processes in Geophysics

Volumn 11, Issue 1, 2004, Pages 137-151

  Kapiris, P G ^a   Balasis, G T ^b   Kopanas, J A ^a   Antonopoulos, G N ^a   Peratzakis, A S ^a   Eftaxias, K A ^a  

^a UNIVERSITY OF ATHENS   (Greece)

^b GFZ GERMAN RESEARCH CENTRE FOR GEOSCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASTROPHYSICS; EARTHQUAKE PRECURSOR; EARTHQUAKE RUPTURE; ELECTROMAGNETIC RADIATION;

EID: 1842763743     PISSN: 10235809     EISSN: None     Source Type: Journal    
DOI: 10.5194/npg-11-137-2004     Document Type: Article

References (111)

1. Aki, K.: A probabilistic synthesis of precursory phenomena, in: Earthquake Prediction, Maurice Ewing Series 4, edited by Simpson, D. and Richards, P., AGU, Washington, D.C., 566-574, 1981.
2. Al-Kindy, F. and Main, I.: Testing self-organized criticality in the crust using entropy: A regionalized study of the CMT global earthquake catalog, J. Geophys. Res., 108, 5-1-5-9, 2003.
3. Anifrani, J.-C., Le Floc'h, C., Somette, D., and Souillard, B.: Universal log-periodic conection to renormalization group scaling for rupture stress prediction from acoustic emissions, J. Phys. I France. 5, 631-638, 1995.
4. Bahat, D., Frid, V., Rabinovitch, A., and Palchik, V.: Exploration via electromagnetic radiation and fractographic methods of fracture properties induced by compression in glass-ceramic, International Journal of Fracture, 116, 179-194, 2002.
5. Bak, P. and Tang, C.: Earthquakes as a self-organized critical phenomenon, J. Geophys. Res., 94, 15 635-15 637, 1989.
6. Barton, C. and Zoback, M.: Self-similar distribution and properties of macroscopic fractures at depth in crystalline rock in the Cajon Pass scientific borehole, J. Geophys. Res., 97, 5181-5200, 1992.
7. Boffetta, G., Carbone, V., Giuliani, P., Veltri, P., and Vulpiani, A.: Power laws in solar flares: Self-organized criticality or turbulence?, Phys. Rev. Lett., 83, 4662-4665, 1999.
8. Bowman, D., Ouillon, G., Sammis, C., Sornette, A., and Sornette, D.: An observational test of the critical earthquake concept. J. Geophys. Res., 103, 24 359-24 372, 1998.
9. Bufe, C. and Varnes, D.: Predictive modelling of the seismic cycle of the greater San Francisco Bay region. J. Geophys. Res., 98, 9871-9883, 1993.
10. Caldarelli, G., Di Tolla, F., and Petri, A.: Self-organization and annealed disorder in a fracturing process, Phys. Rev. Lett., 77, 2503-2505, 1996.
11. Cannelli, G., Cantelli, R., and Cordero, F.: Self-organized criticality of the fracture processes associated with hydrogen precipitation in niobium by acoustic emission, Phys. Rev. Lett., 70, 3923-3926, 1993.
12. Chelidze, T.: Percolation theory as a tool for imitation of fracture process in rocks, Pure Appl. Geophys., 124, 731, 1986.
13. Chen, K., Bak, P., and Obukhov, S.: Self-organized criticality in a crack-propagation model of earthquakes, Physics Review A. 43, 625, 1991.
14. Cheng, B., Epstein, R., Guyer, R., and Young, C.: Earthquake-like behaviour of soft γ-ray repeaters. Nature, 382, 518-520, 1996.
15. Contoyiannis, Y. and Diakonos, F.: Criticality and intermittency in the order parameter space, Phys. Lett. A, 268, 286-292, 2000.
16. Contoyiannis, Y., Diakonos, F., and Malakis, A.: Intermittent dynamics of critical fluctuations. Phys. Rev. Lett., 89, 35700/1-35 700/4, 2002.
17. Contoyiannis, Y., Diakonos, F., Kapiris, P., Peratzakis, A., and Eftaxias, K.: Intermittent dynamics of critical pre-seismic electromagnetic fluctuations, Phys. and Chem. of the Earth, accepted, 2004.
18. Cowie, A., Sornette, D., and Vanneste, C.: Multifractal scaling properties of a growing fault population, Geophys. J. Int., 122, 457-469, 1995.
19. Cowie, P., Vanneste, C., and Sornette, D.: Statistical physics model for spatio-temporal evolution of faults, J. Geophys. Res., 98, 21 809-21 821, 1993.
20. de Boer, J., Jackson, A., and Wettig, T.: Criticality in simple models of evolution. Phys. Rev. E., 51, 1059-1073, 1995.
21. Diodati, P., Marchesoni, F., and Piazza, S.: Acoustic emission from volcanic rocks: An example of self-organized criticality, Phys. Rev. Let., 67, 2239-2241, 1991.
22. Eftaxias, K., Kopanas, J., Bogris, N., Kapiris, P., Antonopoulos, G., and Varotsos, P.: Detection of electromagnetic earthquake precursory signals in Greece, Proc. Japan Acad., 76(B), 45-50, 2000.
23. Eftaxias, K., Kapiris, P., Polygiannakis, J., Bogris, N., Kopanas, J., Antonopoulos, G., Peratzakis, A., and Hadjicontis, V.: Signatures of pending earthquake from electromagnetic anomalies. Geophys. Res. Lett., 28, 3321-3324, 2001a.
24. Eftaxias, K., Kapiris, P., Polygiannakis, Y., Hadjicontis, V., Chelidze, Z., Zilpimiani, D., and Chelidze, T.: Seismogenic radio-emission as a signature of the earthquake preparation process. Journal of the Georgian Geophysical Society. 6, 3-16, 2001b.
25. Eftaxias, K., Kapiris, P., Dologlou, E., Kopanas, J., Bogris, N., Antonopoulos, G., Peratzakis, A., and Hadjicontis, V.: EM anomalies before the Kozani earthquake: A study of their behavior through laboratory experiments, Geophys. Res. Lett., 29, 69/1-69/4, 2002.
26. Eftaxias, K., Kapiris, P., Polygiannakis, J., Peratzakis, A., Kopanas, J., and Antonopoulos, G.: Experience of short term earthquake precursors with VLF-VHF electromagnetic emissions, Natural Hazards and Earth System Sciences, 3, 217-228, 2003.
27. Eftaxias, K., Frangos, P., Kapiris, P., Polygiannakis, J., Kopanas, J., Peratzakis, A., Skountzos, P., and Jaggard, D.: Review/ model of pre-seismic electromagnetic emissions in terms of fractal electrodynamics, Fractals, in press, 2004.
28. Elgazzar, A.: An inhomogeneous self-organized critical model for earthquakes, Physica A. 251, 303-308, 1998.
29. Fifolt, A., Petrenko, F., and Schulson, M.: Preliminary study of electromagnetic emissions from cracks in ice. Phil. Mag. B, 67, 289-299, 1993.
30. Filizzola, C., Pergola, N., Pietrapertosa, C., and Tramutoli, V.: Robust satellite techniques for seismically active areas monitoring: a sensitivity analysis on September 7th 1999 Athens earthquake, Physics and Chemistry of the Earth, accepted, 2004.
31. Frid, V., Rabinovitch, A., and Bahat, D.: Electromagnetic radiation associated with induced triaxial fracture in granite. Philos. Mag. Lett., 79, 79-86, 1999.
32. Gabrielov, A., Keilis-Borok, V., Zaliapin, I., and Newman, W.: Critical transitions in colliding cascades. Phys. Rev. E, 62, 237-249, 2000.
33. Garcimartin, A., Guarino, A., Bellon, L., and Ciliberto, S.: Statistical analysis of fracture precursors. Phys. Rev. Lett., 79, 3202-3205, 1997.
34. Geller, R., Jackson, D., Kagan, Y., and Mulargia, F.: Earthquakes cannot be predicted, Science, 275, 1616-1617, 1997.
35. Gluzman, S. and Sornette, D.: Log-periodic route to fractal functions, Phys. Rev. E, 65, 036 142-1-036 142-19, 2001.
36. Gokhberg, M., Morgunov, V., and Tomizawa, I.: Experimental measurements of electromagnetic emissions possibly related to earthquake in Japan, J. Geophys. Res., 87(B9), 7824-7828, 1982.
37. Grasso, J.-R. and Sornette, D.: Testing self-organized criticality by induced seismicity, J. Geophys. Res., 103, 1998.
38. Hainzl, S., Zoller, G., and Kurths, J.: Seismic quiescence as an indicator for large earthquakes in a system of self-orginized criticality, Geophys. Res. Let., 27, 597-600, 2000.
39. Hainzl, S., Zoller, G., and Scherbaum, F.: Earthquake clusters resulting from delayed rupture propagation in finite fault segments, J. Geophys. Res. Lett., 108, 2013, 2003.
40. Hayakawa, M.: Atmospheric and Ionospheric Electromagnetic Phenomena Associated with Earthquakes, Terrapub, Tokyo. 1999.
41. Hayakawa, M. and Fujinawa, Y.: Electromagnetic Phenomena Related to Earthquake Prediction, Terrapub, Tokyo, 1994.
42. Hayakawa, M. and Molchanov, O.: Seismo Electromagnetics, Terrapub, Tokyo, 2002.
43. Heffer, K. and Beven, T.: Scaling relationships in natural fractures-data theory and applications, Proc. Eur. Petrol. Conf., 2, 367-376, 1990.
44. Heimpel, M.: Critical behavior and the evolution of fault strength during earthquake cycles, Nature, 388, 865-868, 1997.
45. Houle, P. and Sethna, J.: Acoustic emission from crumpling paper, Phys. Rev. E, 54, 278-283, 1996.
46. Huang, Y., Ouillon, G., Saleur, H., and Sornette, D.: Spontaneous generation of discrete scale invariance in growth models. Phys. Rev. E, 55, 6433-6447, 1997.
47. Huang, Y., Saleur, H., Sammis, C., and Sornette, D.: Precursors, aftershocs, criticality and self-organized criticality, Europhys. Lett., 41, 43-48, 1998.
48. Johansen, A. and Sornette, D.: Critical ruptures, Eur. Phys. J. B. 18, 163-181, http://arXiv.org/abs/cond-mat/0003478, 2000.
49. Johansen, A., Sornette, D., Wakita, H., Tsunogai, U., Newman, W., and Saleur, H.: Discrete scaling in earthquake precursory phenomena: evidence in the Kobe earthquake, Japan, J. Phys., I France, 6, 1391-1402, 1996.
50. Kakimi, T.: Magnitude-frequency relation for displacement of minor faults and each significance in crustal deformation, Bull. Geol. Surv. Jap., 31, 467-487, 1980.
51. Kanamori, H. and Anderson, D.: Theoretical basis of some empirical relations on seismology, Bull. Seism. Soc. Am., 65, 1073-1095, 1975.
52. Kapiris, P., Polygiannakis, J., Nomicos, K., and Eftaxias, K.: VHF-electromagnetic evidence of the underlying pre-seismic critical stage. Earth Planets Space, 54, 1237-1246, 2002.
53. Kapiris, P., Eftaxias, K., Nomikos, K., Polygiannakis, J., Dologlou, E., Balasis, G., Bogris, N., Peratzakis, A., and Hadjicontis, V.: Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches. Nonlin. Proc. Geophys., 10, 511-524, 2003.
54. Kapiris, P., Eftaxias, K., and Chelidze, T.: The electromagnetic signature of prefracture criticality in heterogeneous media. Phys. Rev. Lett., in press, 2004.
55. Knopoff, L.: The magnitude distribution of declustered earthquakes in southern California, Proc. Natl. Acad. Sci. USA, 97, 11 880-11 884, 2000.
56. Kontoes, C., Elias, P., Sycioti, O., Briole, P., Remy, D., Sachpazi, M., Veis, G., and Kotsis, I.: Displacement field and fault model for the September 7, Athens earthquake inferred from the ERS2 satellite radar interferometry. Geophys. Res. Lett., 27, 3989-3992, 2000.
57. Kossobokov, V., Keillis-Borok, V., and Cheng, B.: Similarities of multiple fracturing on a neutron star and on Earth, Phys. Rev. E. 61, 3529-3533, 2000.
58. Lavrov, A.: The Kaizer effect in rocks: principle and stress estimation techniques, Int. J. Rock Mech. Mining Sciences, 40, 151-171, 2003.
59. Lei, X., Nishizawa, O., Kusunose, K., Cho, A., Satoh, T., and Nishizawa, O.: Compressive failure of mudstone samples containing quartz veins using rapid ae monitoring: the role of asperities, Tectonophysics, 328, 329-340, 2000.
60. Lei, X., Kusunose, K., Satoh, T., and Nishizawa, O.: The hierarchical rupture process of a fault: an experimental study, Phys. Earth Planet. Inter., 137, 213-20-8, 2003.
61. Maes, C., Moffaert, A., Frederix, H., and Strauven, H.: Criticality in creep experiments on cellular glass, Phys. Rev. B, 57, 4987-4990, 1998.
62. Main, I. and Al-Kindy, F.: Entropy, energy and proximity to criticality in global earthquake populations, Geophys. Res. Lett., 29, 25/1-25/4, 2002.
63. Mandelbrot, B.: The fractal geometry of nature, Freeman, New York, 1982.
64. Maslov, S., Paczuski, M., and Bak, P.: Avalanches and 1/f noise in evolution and growth models, Phys. Rev. Lett., 73, 2162, 1994.
65. Mavromatou, C. and Hadjicontis, V.: Laboratory investigation of the electric signals preceding the fracture of crystalline insulators, in: Earthquake thermodynamics and phase transformations in the earth's interior, edited by Teisseyre, R. and Majewski, E., 501-517, Academic Press, 2001.
66. Meredith, P.: Fracture and failure of brittle polycrystals: an overview, in Deformation Processes in Minerals, Ceramics and Rocks, edited by Barder, D. and Meredith, P. 5-41, Unwin Hyman, London, 1990.
67. Mogi, K.: Magnitude frequency relation for elastic shocks acc0ompanying fractures of various materials and some related problems in earthquakes, Bull. Earthquake Res. Instit., 40, 831-853, 1962.
68. Newman, W. and Turcotte, D.: A simple model for the erthquake cycle combining self-organized complexity with critical point behavior, Nonlin. Proc. Geophys., 9, 453-461, 2002.
69. Nolen-Hoeksema, R. and Gordon, R.: Optical detection of crack patterns in the opening-mode fracture of marble, Int. J. Rock Mech. Min. Sci., 98, 11935-11940, 1987.
70. Ogawa, T., Oike, K., and Miura, T.: Electromagnetic radiations from rocks. J. Geophys. Res., 90, 6245-6249, 1985.
71. Olami, Z., Feder, H., and Christensen, K.: Self organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Let., 68, 1244-1247, 1992.
72. Ouillon, G., Castaing, C., and Sornette, D.: Hierarchical geometry of faulting, J. Geophys. Res., 101, 5477-5487, 1996.
73. Petrenko, V. and Gluschenkov, O.: Crack velocities in freshwater and saline ice, J. Geophys. Res., 101(B5), 11 541-11 551, 1996.
74. Petri, A., Paparo, G., Vespignani, A., Alippi, A., and Constantini, M.: Experimental evidence for critical dynamics in microfracturing processes, Phys. Rev. Let, 73, 3423-3426, 1994.
75. Ponomarev, A., Zavyalov, A., Smirnov, V., and Lockner, D.: Physical modelling of the formation and evolution of seismically active fault zones. Tectonophysics, 277, 57-81, 1997.
76. Rabinovitch, A., Frid, V., and Bahat, D.: Gutenberg-Richter-type relation for laboratory fracture-induced electromagnetic radiation, Phys. Rev. E, 65, 11 401/1-11401/4, 2001.
77. Sahimi, M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys., 65, 1393-1534, 1993.
78. Sahimi, M. and Arbadi, S.: Scaling laws for fracture of heterogeneous materials and rock, Phys. Rev. Lett., 77, 3689-3692, 1996.
79. Sahimi, M., Robertson, M., and Sammis, C.: Fractal distribution of earthquakes hypocenters and its relation to fault patterns and percolation, Phys. Rev. Lett., 70, 2186-2189, 1993.
80. Saleur, H., Sammis, C., and Sornette, D.: Discrete scale invariance, complex fractal dimensions, and log-periodic fluctuations in seismicity, J. Geophys. Res., 101, 17 661-17 667, 1996a.
81. Saleur, H., Sammis, C., and Sornette, D.: Renormalization group theory of earthquakes, Nonlin. Proces. Geophys., 3, 102-109, 1996b.
82. Salminen, L., Tolvanen, A., and Alava, M.: Acoustic emission from paper fracture, Phys. Rev. Lett., 89, 185 503-1 1885 503-4, 2002.
83. Sammis, C. and Smith, S.: Seismic cycles and the evolution of stress correlation in cellular automaton models of finite fault networks, Pure Appl. Geophys., 155, 307-334, 1999.
84. Sammis, C. and Sornette, D.: Positive feedback, memory, and the predictability of earthquakes, PNAS, 99, 2501-2508, 2002.
85. Sammis, C., Sornette, D., and Saleur, H.: Complexity and earthquake forecasting, in Reduction and Predictability of Natural Disasters, SFI studies in the Sciences of complexity, edited by Rundle, J., Klein, W. and Turcotte, D., vol. XXV, 143-156, Addison-Wesley, Reading, Mass., 1996.
86. Sanchez, R., Newman, D., and Carreras, B.: Waiting-time statistics of self-organized-criticality systems. Phys. Rev. Lett., 88, 068 302/1-068 302/4, 2002.
87. Scholz, C.: The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes, Bull. Seism. Soc. Am., 58, 399-415, 1968.
88. Schuster, H.: Deterministic Chaos, VCH, Weinheim, 1998.
89. Sobolev, G., Chelidze, T., Zavyalov, A., and Slavina, L.: Maps of expected earthquakes based on a combination of parameters. Tectonophysics, 193, 255-265, 1991.
90. Sornette, A. and Sornette, D.: Self-organized criticality and earthquakes, Europhys. Lett., 9, 197-202, 1989.
91. Sornette, D.: Self-organized criticality in plate tectonics, in: Spontaneous Formation of Space-Time Structures and Criticality, edited by Riste, T. and Sherrington, D., 57-106, Kluwer Academic Publishers, 1991.
92. Sornette, D.: Critical Phenomena in Natural Sciences, Springer, 2000.
93. Sornette, D. and Helmstetter, A.: Occurrence of finite-time singularities in epidemic models of rupture, earthquakes and starquakes, Phys. Rev. Lett., 89(15), 158 501-1-158 501-4, 2002.
94. Sornette, D. and Le Floc'h, C.: Predictability of catastrophic events: a new approach for structural health monitoring. Structural Health Monitoring Review, in press, (http://arXiv.org/abs/condmat/0210418), 2003.
95. Sornette, D. and Sammis, C.: Complex critical exponents from renormalization group theory of earthquakes: Implications for earthquake predictions. J. Phys. I., 5, 607-619, 1995.
96. Sornette, D., Miltenberger, P., and Vanneste, C.: Statistical physics of fault patterns self-organized by repeated earthquakes, Pure and Applied Geophysics, 142, 491-527, 1994.
97. Stanley, H.: Scaling, universality, and renormalization: Three pillars of modern critical phenomena, Reviews of Modern Physics, 71, S358-S366, 1999.
98. Torrence, C. and Compo, P.: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79, 61-78, 1998.
99. Tramutoli, V., Di Bello, G., Pergola, N., and Piscitelli, S.: Robust satellite techniques for remote sensing of seismically active areas, Annali di Geofisica, 44, 295-312, 2001.
100. Turcotte, D.: Fractal in geology and geophysics, in: Fractal in Geophysics, edited by Scholz, C. and Mandelbrot, B., 171, Birkhäuser, 1989.
101. Turcotte, D.: Fractals and chaos in geology and geophysics. Cambridge University Press, 1992.
102. Turcotte, D.: Self-organized criticality: does it have anything to do with criticality and is it useful?. Nonlin. Proc. Geophys., 8, 193-196, 2001.
103. Tzanis, A. and Makropoulos, K.: Did the 7/9/ 1999 M5.9 Athens earthquake come with a warning?, Natural Hazard, 27, 85-103, 2002.
104. b=4.8 earthquake on 1980 February 14 near the Virgin Islands. Geophys. J. Int., 124, 149-158, 1996.
105. Velde, B., Moore, D., Badri, A., and Ledesert, B.: Fractal and length analysis of fractures during brittle to ductile changes, J. Geophys. Res., 98, 11935-11940, 1993.
106. Vespignani, A., Petri, A., Alippi, A., Paparo, G., and Costantini, M.: Long range correlation properties of aftershock relaxation signals, Fractals, 3, 839, 1995.
107. Warwick, J., Stoker, C., and Meyer, T.: Radio emission associated with rock fracture: possible application to the great Chilean earthquake of May 22, 1960, J. Geophys. Res., 87, 2851-2859, 1982.
108. Weiss, J.: Fracture and fragmentation of ice: A fractal analysis of scale invariance. Engineering Fracture Mechanics, 68, 1975-2012, 2001.
109. Yamada, I., Masuda, K., and Mizutani, H.: Electromagnetic and acoustic emission associated with rock fracture, Physics of the Earth and Planetary Interiors, 57, 157-168, 1989.
110. Zoller, G. and Hainzl, S.: A systematic spatiotemporal test of the critical point hypothesis for large earthquakes, Geophys. Res. Lett., 29, 53/1-53/4, 2002.
111. Zoller, G., Hainzl, S., and Kurths, J.: Observations of growing correlation length as an indicator for critical point behavior prior to large earthquakes, J. Geophys. Res., 106, 2167-2175, 2001.