Oscillatory regime of aftershocks of the 1984 Ddzhirgatal earthquake: Implications for the internal dynamics of an unstable geological system
Tóm tắt
On the basis of seismological and geological evidence, the aftereffect region of the strong Dzhirgatal earthquake is localized as a real physical object. The time dependence of the number of aftershocks of this earthquake is best described by a simple hyperbolic law (p = 1, or the Omori law), which is well consistent with the ideas of self-similarity of the material fracture and the development of the seismotectonic process. Features characteristic of the evolution of self-similar systems are recognizable in the dynamics of the aftershock flow and parameters of seismotectonic deformation (STD) calculated from focal mechanisms of aftershocks. The evidence for this is the Feigenbaum inverse cascade in predominant frequencies of variations in the numbers of aftershocks and “catastrophes” in the form of an increase in the variability of STD parameters at the time moments when the corresponding predominant periods abruptly change. In this way, the term “catastrophe,” speculative with respect to the geophysical medium, acquires real meaning as a set of observable changes in the dynamics of STD parameters and the flow of aftershocks that occur over a fairly short time compared to the entire duration of the aftershock series.
Tài liệu tham khảo
C. J. Allegre et al., “Scaling Rules in Rock Fracture and Possible Implications for Earthquake Prediction,” Nature 297, 47–49 (1982).
T. P. Belousov, A. A. Lukk, A. B. Maksimov, et al., “The Dzhirgatal Earthquake of October 26, 1984,” in Earthquakes in Central Asia and Kazakhstan in 1984 (Donish, Dushanbe, 1988), pp. 152–168 [in Russian].
T. P. Belousov and I. R. Stakhovsky, “Multifractal Analysis of Fault Clusters in the Junction Zone of the Pamirs and Tien Shan,” in Geophysical Processes in a Discrete Medium (OIFZ RAN, Moscow, 1993), pp. 49–61 [in Russian].
E. A. Boyarsky, V. A. Volkov, and L. V. Afanas’eva, “Advantages of Using a Residual Curve for the Treatment of Earth Tide Observations,” Fiz. Zemli, No. 11, 68–73 (1995).
S. R. Brown and C. H. Scholz, “Broad Bandwidth Study of the Topography of Natural Rock Surfaces,” J. Geophys. Res. 90, 12 575–12 582 (1985).
A. V. Deshcherevsky and A. A. Lukk, “Extraction of Regular Components from Time Realizations of Geophysical Parameters by the Method of Decomposition into Nonharmonic Components,” in Investigations of the Origin of Variations in Geophysical Fields (OIFZ RAN, Moscow, 1994), pp. 18–36 [in Russian].
A. V. Deshcherevsky and V. I. Zhuravlev, Analysis of Time Series Using the ABD Software (OIFZ RAN, Moscow, 1997) [in Russian].
J. H. Dieterich, “Time Dependent Friction and the Mechanics of Stick Slip,” Pure Appl. Geophys. 116, 790–806 (1978).
J. H. Dieterich, “Modeling of Rock Friction: 1. Experimental Results and Constitutive Equations,” J. Geophys. Res. 84, 2161–2168 (1979).
J. H. Dieterich, “Constitutive Properties of Faults with Simulated Gouge,” in Mechanical Behavior of Crustal Rocks. AGU Geophys. Mono. 24 (AGU, Washington, DC, 1981), pp. 103–120.
J. H. Dieterich, “Foreshocks, Aftershocks and Earthquake Recurrence,” in International Program of the National Science Foundation, Japan Society for the Promoting of Science (U.S. Geological Survey (Open-File Report 90-98) Menlo Park, 1990), pp. 251–257.
G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, Merrifield, 1968; Mir, Moscow, 1972).
M. J. Feigenbaum, “Quantitative Universality for a Class of Nonlinear Transformations,” J. Stat. Phys. 19 (1978).
G. S. Golitsyn, “Earthquakes: Implications of the Similarity Theory,” Dokl. Akad. Nauk 346 (4), 536–539 (1996).
T. Hirata, “Omori’s Power Law Aftershock Sequences of Microfracturing in Rock Fracture Experiment,” J. Geophys. Res. 92 (87), 6215–6221 (1987).
Y. Y. Kagan and L. Knopoff, “Statistical Study of the Occurrence of Shallow Earthquakes,” Geophys. J. R. Astron. Soc. 55, 67–86 (1978).
Y. Y. Kagan and L. Knopoff, “Spatial Distribution of Earthquakes: The Two-Point Correlation Function,” Geophys. J. R. Astron. Soc. 62, 303–320 (1980a).
Y. Y. Kagan and L. Knopoff, “Dependence of Seismicity on Depth,” Bull. Seismol. Soc. Am. 70, 1811–1822 (1980b).
Y. Y. Kagan and L. Knopoff, “Stochastic Synthesis of Earthquake Catalogs,” J. Geophys. Res. 86, 2853–2862 (1981).
G. King, “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,” Pure Appl. Geophys. 121, 761–815 (1983).
A. A. Lukk, “Space-Time Sequences of Weak Earthquakes,” Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No. 2, 25–37 (1978).
A. A. Lukk and S. L. Yunga, “Stress-Strain State of the Crust in the Garm Area: I. General Problems and Methods,” Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No. 6, 14–26 (1988).
A. A. Lukk and A. V. Deshcherevsky, Time Succession of Aftershocks of the Dzhirgatal Earthquake (OIFZ RAN, Moscow, 1998) [in Russian].
T. R. Madden, “Microcrack Connectivity in Rocks: A Renormalization Group Approach to the Critical Phenomena of Conduction and Failure in Crystalline Rocks,” J. Geophys. Res. 88, 585–592 (1983).
T. Mikumo and T. Miyatake, “Earthquake Sequences on a Frictional Fault Model with Non-Uniform Strengths and Relaxation Times,” Geophys. J. R. Astron. Soc. 59, 497–522 (1979).
K. Mogi, “Study of Elastic Shocks Caused by the Fracture of Heterogeneous Materials and Its Relations to Earthquake Phenomena,” Bull. Earthq. Res. Inst. Univ. Tokyo 40 125–171 (1962).
H. Nakanishi, “Earthquake Dynamics Driven by a Viscous Fluid,” Phys. Rev. A 46 (8), 4689–4692 (1992).
A. Nur and J. R. Booker, “Aftershocks Caused by Pore Fluid Flow,” Science 175, 885 (1972).
Y. Ogata, “Estimation of the Parameters in the Modified Omori Formula for Aftershock Frequencies by the Maximum Likelihood Procedure,” J. Phys. Earth 31, 115–124 (1983).
F. Omori, “Investigation of Aftershocks,” Rep. Earthq. Inv. Comm. 2, 103–139 (1894).
R. Page, “Aftershocks and Microaftershocks of the Great Alaska Earthquake of 1964,” Bull. Seismol. Soc. Am. 58 (3), 1131–1168 (1968).
A. G. Prozorov and S. A. Iskenderov, “Intensity Decay of Aftershock Flows of the Strongest Earthquakes in the Kyrgyz Region,” Izv. Akad. Nauk Kirg. SSR, Ser. Fiz.-Mat. Mat Nauk, No. 2, 71–77 (1987).
L. L. Romashkova and V. G. Kosobokov, “Dynamics of Seismic Activity before and after the Strongest Earthquakes of the World, 1985–2000,” in Computational Seismology (Moscow, 2001), No. 32, 162–189.
C. H. Scholz, “The Mechanism of Creep in Brittle Rock,” J. Geophys. Res. 73, 3295–3302 (1968a).
C. H. Scholz, “Microfractures, Aftershocks, and Seismicity,” Bull. Seismol. Soc. Am. 58, 1117–1130 (1968b).
C. H. Scholz, “The Frequency-Magnitude Relation of Microfracturing in Rock and Its Relation to Earthquakes,” Bull. Seismol. Soc. Am. 58, 399–415 (1968c).
C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press, New York, 1990a).
C. H. Scholz, “Earthquakes as Chaos,” Nature 348, 197–198 (1990b).
C. H. Scholz, “Earthquakes and Faulting: Self-Organized Critical Phenomena with a Characteristic Dimension,” in Spontaneous Formation of Space-Time Structures and Criticality, Ed. by T. Riste and D. Sherrington (Kluwer, Dordrecht, 1991), pp. 41–56.
M. G. Serebrennikov and A. A. Pervozvanskii, Identification of Hidden Periodicities (Nauka, Moscow, 1965) [in Russian].
B. E. Shaw, “Generalized Omori Law for Aftershocks and Foreshocks from a Simple Dynamics,” Geophys. Res. Lett. 20 (10), 907–910 (1993).
R. Shcherbakov, D. L. Turcotte, and J. B. Rundle, “A Generalized Omori’s Law for Earthquake Aftershock Decay,” Geophys. Res. Lett. 31 (2004).
V. N. Shebalin, “Aftershocks as Indicators of the Stress State in a Fault System,” Dokl. Akad. Nauk 398 (2), 249–254 (2004).
R. F. Smalley, D. L. Turcotte, and S. A. Solla, “A Renormalization Group Approach to the Stick-Slip Behavior of Faults,” J. Geophys. Res. 90, 1894–1900 (1985).
R. F. Smalley et al., “A Fractal Approach to the Clustering of Earthquakes: Applications to the Seismicity of the New Hebrides,” Bull. Seismol. Soc. Am. 77 (4), 1368–1381 (1987).
V. B. Smirnov and A. V. Ponomarev, “Seismic Regime Relaxation Properties from in Situ and Laboratory Data,” Fiz. Zemli, No. 10, 26-36 (2004) [Izvestiya, Phys. Solid Earth 40, 807–816 (2004)].
G. A. Sobolev and Yu. S. Tyupkin, “Analysis of Energy Release Process during Main Rupture Formation in Laboratory Studies and before Strong Earthquakes,” Fiz. Zemli, No. 2, 44–55 (2000) [Izvestiya, Phys. Solid Earth 36, 138–149 (2000)].
D. Sornette and C. G. Sammis, “Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications for Earthquakes Predictions,” J. Phys. Inst. France 5, 607–619 (1995).
D. L. Turcotte, “Fractals and Fragmentation,” J. Geophys. Res. 91, 1921–1926 (1986).
D. L. Turcotte, “Fractals in Geology and Geophysics,” Pure Appl. Geophys. 131 (1/2), 171–196 (1989a).
D. L. Turcotte, “A Fractal Approach to Probabilistic Seismic Hazard Assessment,” J. South Am. Earth Sci. 167, 171–177 (1989b).
D. L. Turcotte, “Earthquake Prediction,” Ann. Rev. Earth Planet. Sci. 19, 263–281 (1991).
D. L. Turcotte, “Crustal Deformation and Fractals, a Review,” in Fractals and Dynamic Systems in Geoscience, Ed. by J. H. Kruhl (1994), pp. 7–23.
D. L. Turcotte, R. F. Smalley, and S. A. Solla, “Collapse of Loaded Fractal Trees,” Nature 313, 671–672 (1985).
Yu. S. Tyupkin, “Kinetics of Aftershock Sequence,” Dokl. Akad. Nauk 373 (5), 684–687 (2000).
T. Utsu, “A Statistical Study of the Occurrence of Aftershocks,” Geophys. Mag. 30, 521–605 (1961).
T. Utsu, “On the Nature of Three Alaskan Aftershock Sequences of 1957 and 1958,” Bull. Seismol. Soc. Am. 52, 279–297 (1962).
T. Utsu, “Aftershocks and Earthquake Statistics (1). Some Parameters Which Characterize an Aftershock Sequence and Their Interaction,” J. Fac. Sci., Hokkaido Univ., Ser. VII (Geophysics) 3 (3), 129–195 (1969).
T. Utsu, “Aftershocks and Earthquake Statistics (2). Future Investigation of Aftershocks and Other Earthquake Sequences Based on a New Classification of Earthquake Sequences,” J. Fac. Sci., Hokkaido Univ., Ser. VII (Geophysics) 3 (4), 197–266 (1970).
T. Utsu, “Statistical Features of Seismicity,” in International Handbook of Earthquake and Engineering Seismology, Ed. by W. H. Lee et al. (Academic, 2002), pp. 719–732.
T. Utsu, Y. Ogata, and R. Matsu’ura, “The Centenary of the Omori Formula for a Decay Law of Aftershock Activity,” J. Phys. Earth 43, 1–33 (1995).
T. Utsu and Y. Ogata, “Statistical Analysis of Seismicity,” in Algorithms for Earthquake Statistics and Prediction (IASPEI Software Library 6), Ed. by J. H. Healy, V. I. Keilis-Borok, and W. H. K. Lee (Seismol. Soc. Am., El Cerrito, 1997).
T. Yamashita and L. Knopoff, “Models of Aftershock Occurrence,” Geophys. J. R. Astron. Soc. 91, 13–26 (1987).
S. L. Yunga, Study of Seismotectonic Deformations: Methods and Results (Nauka, Moscow, 1990) [in Russian].