Nonlinear Processes in Geophysics
www.nonlin-processes-geophys.net
1023-5809
1607-7946
15
1
2008
10.5194/npg-15-209-2008
http://www.nonlin-processes-geophys.net/15/209/2008/
http://www.nonlin-processes-geophys.net/15/209/2008/npg-15-209-2008.html
http://www.nonlin-processes-geophys.net/15/209/2008/npg-15-209-2008.pdf
209
220
2008-02-27
Transformation of frequency-magnitude relation prior to large events in the model of block structure dynamics
A. Soloviev
soloviev@mitp.ru
International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Russia
ESP, The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
The <i>b</i>-value change in the frequency-magnitude (FM)
distribution for a synthetic earthquake catalogue obtained by means of the
model of block structure dynamics has been studied. The catalogue is divided
into time periods preceding strong earthquakes and time periods that do not
precede strong earthquakes. The separate analysis of these periods shows
that the <i>b</i>-value is smaller before strong earthquakes. The similar phenomenon
has been found also for the observed seismicity of the Southern California.
The model of block structure dynamics represents a seismic region as a
system of perfectly rigid blocks divided by infinitely thin plane faults.
The blocks interact between themselves and with the underlying medium. The
system of blocks moves as a consequence of prescribed motion of the boundary
blocks and of the underlying medium. As the blocks are perfectly rigid, all
deformation takes place in the fault zones and at the block base in contact
with the underlying medium. Relative block displacements take place along
the fault zones. Block motion is defined so that the system is in a
quasistatic equilibrium state. The interaction of blocks along the fault
zones is viscous-elastic ("normal state") while the ratio of the stress to
the pressure remains below a certain strength level. When the critical level
is exceeded in some part of a fault zone, a stress-drop ("failure") occurs
(in accordance with the dry friction model), possibly causing failure in
other parts of the fault zones. These failures produce earthquakes.
Immediately after the earthquake and for some time after, the affected parts
of the fault zones are in a state of creep. This state differs from the
normal state because of a faster growth of inelastic displacements, lasting
until the stress falls below some other level. This numerical simulation
gives rise a synthetic earthquake catalogue.
Aki, K.: Maximum likelihood estimate of b in formula log N=a–b M and its confidence limits, Bull. Earthquake Res. Inst. Univ. Tokyo, 43, 237–239, 1965.
Allègre, C. J., Le Mou\"el, J.-L., and Provost, A.: Scaling rules in rock fracture and possible implications for earthquake prediction, Nature, 297, 47–49, 1982.
Allègre, C. J., Le Mou\"el, J.-L., Chau, H. D., and Narteau, C.: Scaling organization of fracture tectonics (SOFT) and earthquake mechanism, Phys. Earth Planet. Inter., 92, 215–233, 1995.
Amelung, F. and King, G.: Earthquake scaling laws for creeping and noncreeping faults, Geophys. Res. Lett., 24, 507–510, 1997.
Amitrano, D.: Brittle-ductile transition and associated seismicity: Experimental and numerical studies and relationship with the $b$ value, J. Geophys. Res., 108, 2044, doi:10.1029/2001JB000680, 2003.
Bak, P. and Tang, C.: Earthquakes as a self-organized critical phenomenon, Geophys. Res. Lett., 94, 15 635–15 637, 1989.
Barenblatt, G. I, Keilis-Borok, V. I, and Monin, A. S.: Filtration model of earthquake sequence, Transactions (Doklady) Acad. Sci. SSSR, 269, 831–834, 1983.
Ben-Zion, Y. and Rice, J. R.: Earthquake failure sequence along a cellurar fault zone in a three-dimensional elastic solid containing asperity and nonasperity regions, J. Geophys. Res., 98, 14 109–14 131, 1993.
Ben-Zion, Y. and Lyakhovsky, V.: Analysis of aftershocks in a lithospheric model with seismogenic zone governed by damage rheology, Geophys. J. Int., 165, 197–210, 2006.
Blanter, E. M., Shnirman, M. G., and Le Mou\"el, J.-L.: Hierarchical model of seismicity: Scaling and predictability, Phys. Earth Planet. Inter., 103, 135–150, 1998.
Burridge, R. and Knopoff, L.: Model and theoretical seismicity, Bull. Seismol. Soc. Am., 57, 341–360, 1967.
Burroughs, S. M. and Tebbens, S. F.: The upper-truncated power law applied to earthquake cumulative frequency-magnitude distributions: evidence for a time-independent scaling parameter, Bull. Seismol. Soc. Am., 92, 2983–2993, 2002.
Christensen, K. and Olami, Z.: Variation of the Gutenberg-Richter $b$ values and nontrivial temporal correlations in a spring-block model for earthquakes, J. Geophys. Res., 97, 8729–8735, 1992.
Dieterich, J. H.: Time-dependent friction as a possible mechanism for aftershocks, J. Geophys. Res., 77, 3771–3781, 1972.
Dieterich, J. H.: A constitutive law for earthquake production and its application to earthquake clustering, J. Geophys. Res., 99, 2601–2618, 1994.
Eneva, M. and Ben-Zion, Y.: Techniques and parameters to analyze seismicity patterns associated with large earthquakes, J. Geophys. Res., 102, 17 785–17 795, 1997.
Fitzenz, D. D. and Miller, S. A.: A forward model for earthquake generation on interacting faults including tectonics, fluids, and stress transfer, J. Geophys. Res., 106, 26 689–26 706, 2001.
Gabrielov, A. M. and Keilis-Borok, V. I.: Patterns of stress corrosion: Geometry of the principal stresses, Pure Appl. Geophys., 121, 477–494, 1983.
Gabrielov, A. M., Levshina, T. A., and Rotwain, I. M.: Block model of earthquake sequence, Phys. Earth and Planet. Inter., 61, 18–28, 1990.
Gabrielov, A. M., Keilis-Borok, V.I., Zaliapin, I. V., and Newman, W. I.: Critical transitions in colliding cascades, Phys. Rev. E, 62, 237–249, 2000.
Gutenberg, R. and Richter, C. F.: Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 34, 185–188, 1944.
Ishimoto, M. and Iida, K.: Observations on earthquakes registered with the microseismograph constructed recently, Bull. Earthquake Res. Inst. Univ. Tokyo, 17, 443–478, 1939.
Ismail-Zadeh A., Le Mou\"el, J.-L., Soloviev, A., Tapponnier, P., and Vorovieva, I.: Numerical modeling of crustal block-and-fault dynamics, earthquakes and slip rates in the Tibet-Himalayan region, EPSL, 258, 465–485, 2007.
Ito, K. and Matsuzaki, M.: Earthquakes as self-organized critical phenomena, J. Geophys. Res., 95, 6853–6860, 1990.
Hainzl, S., Zöller, G., and Kurths, J.: Similar power laws for fore- and aftershock sequences in a spring-block model for earthquakes, J. Geophys. Res., 104, 7243–7253, 1999.
Henderson, J., Main, I., Meredith, P., and Sammonds, P.: The evolution of seismicity at Parkfield: observation, experiment and a fracture-mechanical interpretation, J. Struct. Geol., 14, 905–913, 1992.
Henderson, J., Main, I. G., Pearce, R. G., and Takeya, M.: Seismicity in north-eastern Brazil: fractal clustering and the evolution of the $b$ value, Geophys. J. Int., 116, 217–226, 1994.
Keilis-Borok, V. I. and Kossobokov, V. G.: Premonitory activation of earthquake flow: algorithm M8, Phys. Earth Planet. Inter., 61, 73–83, 1990.
Keilis-Borok, V. I., Rotwain, I. M., and Soloviev, A. A.: Numerical modeling of block structure dynamics: dependence of a synthetic earthquake flow on the structure separateness and boundary movements, J. Seismol., 1, 151–160, 1997.
Main, I. G., Meredith, P. G., and Jones, C.: A reinterpretation of the precursory seismic $b$-value anomaly from fracture mechanics, Geophys. J. Int., 96, 131–138, 1989.
Main, I. G., Meredith, P. G., and Sammonds, P. R.: Temporal variations in seismic event rate and $b$-values from stress corrosion constitutive laws, Tectonophysics, 211, 233–246, 1992.
Molchan, G. M. and Podgaetskaya, V. M.: Parameters of the global seismicity, I, in: Computational and Statistical Methods of Seismic Data Interpretation, edited by: Keilis-Borok, V. I., 44–66, Nauka, Moscow, 1973.
Narkunskaya, G. S. and Shnirman, M. G.: On an algorithm of earthquake prediction, in: Computational Seismology and Geodynamics, Vol. 1, edited by: Chowdhury, D. K., 20–24, AGU, Washington, D.C., 1994.
Nur, A. and Booker, J. R.: Aftershocks caused by pore fluid flow?, Science, 175, 885–887, 1972.
Ogata, Y., and Katsura, K.: Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophys. J. Int., 113, 727–738, 1993.
Olami, Z., Feder, H. J. S., and Christensen, K.: Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Lett., 68, 1244–1247, 1992.
Robinson, R. and Benites, R.: Synthetic seismicity models for the Wellington region, New Zeland: Implications for temporal distribution of large events, J. Geophys. Res., 101, 27 833–27 844, 1996.
Robinson, R. and Benites, R.: Upgrading a synthetic seismicity model for more realistic fault ruptures, Geophys. Res. Lett., 28, 1843–1846, 2001.
Rotwain, I., Keilis-Borok, V., and Botvina, L.: Premonitory transformation of steel fracturing and seismicity, Phys. Earth Planet. Inter., 101, 61–71, 1997.
SCEDC: web site http://www.data.scec.org/about/data_avail.html.
Smith, W. D.: Evidence for precursory changes in the frequency-magnitude $b$-value, Geophys. J. Int., 86, 815–838, 1986.
Soloviev, A. and Ismail-Zadeh, A.: Models of dynamics of block-and-fault systems, in: Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, edited by: Keilis-Borok, V. I. and Soloviev, A. A., 71–139, Springer-Verlag, Berlin-Heidelberg, 2003.
Utsu, T. and Seki, A.: A relation between the area of aftershock region and the energy of main shock, J. Seism. Soc. Japan, 7, 233–240, 1954.
Ward, S. N.: An application of synthetic seismicity in earthquake statistics: The Middle America Trench, J. Geophys. Res., 97, 6675–6682, 1992.
Ward, S. N.: San Francisco Bay Area earthquake simulation: A step toward a standard physical earthquake model, Bull. Seismol. Soc. Am., 90, 370–386, 2000.
Wiemer, S. and Wyss, M.: Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times?, J. Geophys. Res., 102, 15 115–15 128, 1997.
Wyss, M., Schorlemmer, D., and Wiemer, S.: Mapping asperities by minima of local recurrence time: San Jacinto-Elsinore fault zones, J. Geophys. Res., 105, 7829–7844, 2000.
Wyss, M. and Wiemer, S.: Change in the probability for earthquakes in Southern California due to the Landers magnitude 7.3 earthquake, Science, 290, 1334–1338, 2000.
Zaliapin, I., Keilis-Borok, V., and Ghil, M.: A Boolean delay model of colliding cascades. II: Prediction of critical transitions, J. Stat. Phys., 111, 839–861, 2003.
Zhou, S., Johnston, S., Robinson, R., and Vere-Jones, D.: Tests of the precursory accelerating moment release model using a synthetic seismicity model for Wellington, New Zealand, J. Geophys. Res., 111, B05308, doi:10.1029/2005JB003720, 2006.
Zöller, G., Hainzl, S., Holschneider, M., and Ben-Zion, Y.: Aftershocks resulting from creeping sections in a heterogeneous fault, Geophys. Res. Lett., 32, L03308, doi:10.1029/2004GL021871, 2005.
Zöller, G., Hainzl, S., Ben-Zion, Y., and Holschneider, M.: Earthquake activity related to seismic cycles in a model for a heterogeneous strike-slip fault, Tectonophysics, 423, 137–145, 2006.