Skip to main content
SpringerLink
Log in

Regularities in transient modes in the seismic process according to the laboratory and natural modeling

  • Published:
Izvestiya, Physics of the Solid Earth Aims and scope Submit manuscript

Abstract

Regularities in the excitation and relaxation of rock failure were revealed in a series of laboratory experiments. Similar regularities are found also in natural conditions. A physical idea and its mathematical description are suggested for explaining the obtained experimental data. The aim of the experiments was to understand the character of excitation of the failure, triggered by the external impact, and its relaxation after the cessation of the pressure, depending on the intensity of the acting stresses. Different rates of increase in the initiating strains result in different acoustic responses that reflect the development of failure. At the higher rates of deformation, the observed process was similar to the aftershock sequences, and at the lower, to the seismic swarms. The character and parameters of the acoustic response change with the increase in the acting strains. The patterns of the changes exhibit several regularities. In case of the swarm-like activity, the time of maximum activity (and, correspondingly, the beginning in its decay) increases with the increase in acting strains. In case of the aftershock-like activity, the level of applied strains determines the parameters of the Omori’s law. The delay in the power-law’s decrease in activity increases with the growth of the load (similar to the increasing time until the beginning of the decay in the swarm-like activity). Similar regularities are defined in natural conditions in the experiments on the rock’s failure induced by water infusion into a borehole (Soultz-sous-Forêts, France). A hypothesis of competitive excitation and relaxation is suggested for explaining the observed experimental data. Mathematical modeling has confirmed the validity of this hypothesis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Aki, “Probabilistic Synthesis of Precursory Phenomena in Earthquake Prediction,” Amer. Gephys. Union. An International Review, 556–574 (1981).

  2. P. Audigane, J.-J. Royer, and H. Kaieda, “Permeability Characterization of the Soultz and Ogachi Large-scale Reservoir Using Induced Microseismicity,” Geophysics 67, 2004–211 (2002).

    Article  Google Scholar 

  3. M. R. Ayling, P. G. Meredith, and S. Murrell, “Microcracking during Triaxial Deformation of Porous Rocks Monitored by Changes in Rock Physical Properties, I. Elastic-wave Propagation Measurements on Dry Rocks,” Tectonophysics 245, 205–221 (1994).

    Article  Google Scholar 

  4. P. Bak et al., “Unified Scaling Law for Earthquakes,” Phys. Rev. Lett. 88(17). DOI: 10.1103/Phys Rev-Lett.88.178501.

  5. P. Bird, “An Updated Digital Model of Plate Boundaries,” Geochemistry, Geophysics, Geosystems 4(2). 1027, DOI: 10.1029/23001 GC 000252.

  6. S. Bourouis and P. Bernard, “Evidence for Couplet Seismic and Aseismic Fault Slip during Water Injection in the Geothermal Site of Soultz (France), and Implication for Seismogenic Transients,” Geophys. I. Int. 169, 723–732 (2007).

    Article  Google Scholar 

  7. T. T. Cladouhos and R. Marrett, “Are Faults Grows and Linkage Models Consistent with Power-low Distributions of Fault Lengths?” J. Struct. Geol. 18, 281–293 (1996).

    Article  Google Scholar 

  8. F. H. Cornet, “Comment on “Large-scale in situ Permeability Tensor of Rocks from Induced Microseismicity,” by S. A. Shapiro, P. Augidane, J.-J. Royer,” Geophys. J. Int. 140, 465–469 (2000).

    Article  Google Scholar 

  9. F. H. Cornet et al., “Seismic and Aseismic Slips Induced by Large-scale Fluid Injections,” Pure Appl. Geophys. 10, 563–583 (1997).

    Article  Google Scholar 

  10. A. Corral, “Renormalization-group Transformations and Correlations of Seismicity” Phys. Rev. Lett. 95 (2005). DOI: 10.1103/PhysRevLett.95.028501.

  11. A. J. DiGiovanni, T. Fredrich, D. J. Holcomb, and W.A. Olsson, “Micromechanics of Compaction in an Analogue Reservoir Sandstone, in Proceedings of the North American Rock Mechanics Symposium, July 31, 2000, Ed. by J. Girard et al., (2000), pp. 1153–1158.

  12. Earthquakes: Radiated Energy and the Physics of Faulting, Ed. by R. Abercrombie et al. AGU Geophysical Monograph (2000).

  13. K. F. Evans et al., “Microseismicity and Permeability Enhancement of Hydrogeologic Structures during Massive Fluid Injections into Granite at 3 km Depth at the Soultz HDR Site, Geoph. J. Int. 160, 388–412 (2005a).

    Article  Google Scholar 

  14. K. F. Evans, “Permeability Creation and Damage due to Massive Fluid Injections into Granite at 3.5 km at Soultz: 1. Borehole Observation,” J. Geoph. Res. 110, B04203 (2005b). doi: 10.1029/2004JB003168.

    Article  Google Scholar 

  15. K. F. Evans, “Permeability Creation and Damage due to Massive Fluid Injections into Granite at 3.5 km at Soultz: 1. Critical Stress and Fracture Strength,” J. Geoph. Res. 110, B04203, (2005). doi: 10.1029/2004JB003168.

    Article  Google Scholar 

  16. J. Fortin, S. Stanchits, G. Dresen, and Y. Gue’guen, “Acoustic Emission and Velocities Associated with the Formation of Compaction Bands in Sandstone,” J. Geophys. Res. 111, B10203 (2006). doi: 10.1029/2005JB003854

    Article  Google Scholar 

  17. A. Gerard et al., “The Deep EGS (Enhanced Geothermal System) Project at Soultz-sous-Forêts (Alsace, France),” Geothermics 35, 473–483 (2006).

    Article  Google Scholar 

  18. G. S. Golitsyn, “Size distribution of the number of lithospheric plates, Physics of the Earth, No. 3, (2008).

  19. K. Goto and K. Otsuki, “Size and Spatial Distributions of Fault Populations: Empirically Synthesized Evolution Laws for the Fractal Geometries,” Geoph. Res. Lett. 31 (2004) L05601, doi: 10.1029/2003GL018868.

  20. S. S. Grigoryan, “On the mechanism of Earthquake Initiation and Meaning of Empirical Regularities in Seismology,” Dokl. Akad. Nauk SSSR 299(5), (1988).

  21. D. J. Hart and H. F. Wang, “Laboratory Measurements of a Complete Set of Poroelastic Moduli for Berea Sandstone and Indian Limestone,” J. Geoph. Res. 100, 17741–17751 (1995).

    Article  Google Scholar 

  22. D. P. Hill, “A Model for Earthquake Swarms,” J. Geoph. Res. 82, 1347–1352 (1977).

    Article  Google Scholar 

  23. T. Hirata, “Omori’s Power Law Aftershock Sequences of Microfracturing in Rock Fracture Experiment,” J. Geoph. Res. 92, 6215–6221 (1987).

    Article  Google Scholar 

  24. Li Hong, Li Shiyu, Xu Zhengyu, and Yin Xiangchu, “Experiment on Fracture Confining Pressure,” Acta Seismologica Sinica 5, 891–895 (1992).

    Article  Google Scholar 

  25. Li Hong, Yin Xiangchu, Li Shiyu, and Li Jihan, “The Experimental Research on b-vale of AE for the Rock Specimens with Pre-existing Crack or Notch under Uniaxial Compression,” Acta Seismologica Sinica 5, 867–875 (1992).

    Article  Google Scholar 

  26. H. Kawakata and M. Shimada, “Theoretical Approach to Dependence of Crack Growth Mechanism on Confining Pressure,” Earth Planets Space 52, 315–320 (2000).

    Google Scholar 

  27. G. King, “The Accommodation of Large Strain in the Upper Lithosphere of the Earth and Other Solids by Selfsimilar Fault System: The Geometrical Origin of b-value,” Pure Appl. Geophys. 121, 761–815 (1983).

    Article  Google Scholar 

  28. A. V. Kol’tsov et al., “The Study of Destruction Preparation and Development in Rock Samples by the Geophysical Methods,” Acta Geophysica Polonica 32, 238–298 (1984).

    Google Scholar 

  29. B. V. Kostrov and Sh. Das, Principles of Earthquake Source Mechanisms (Cambridge Univ. Press, Cambridge, 1988).

    Google Scholar 

  30. V. S. Kuksenko, “Model of Transition from Microto Macrofracturing in Solid Bodies,” in Reports on the 1st All-Union Seminar “Physics of Strength and Plasticity (Nauka, Leningrad, 1986. pp. 36–41 [in Russian].

    Google Scholar 

  31. A. V. Lavrov, V. L. Shkuratnik, and Yu. L. Filimonov, Acoustic-Emission Memory Effect in Rocks (MGU, Moscow, 2004) [in Russian].

    Google Scholar 

  32. X. Lei, O. Nishizawa, K. Kusunose, and T. Satoh, “Fractal Structure of the Hypocenter Distributions and Focal Mechanism Solutions of Acoustic Emission in Two Granites of Different Grain Sizes,” J. Phys. Earth 40, 617–634 (1992).

    Google Scholar 

  33. X. Lei, K. Kususnose, M. V. M. S. Rao, O. Nishizawa, and T. Stoh, “Quasi-static Fault Growth and Cracking in Homogenous Brittle Rock under Triaxial Compression Using Acoustic Emission Monitoring,” J. Geophys. Res. 105, 6127–6139 (2000).

    Article  Google Scholar 

  34. D. A. Lockner, “The Role of Acoustic Emission in the Study of Rock Fracture,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 883–399 (1993).

    Article  Google Scholar 

  35. D. A. Lockner and S. A. Stanchitts, “Undrained Poroelastic Response of Sandstones to Deviatoric Stress Change,” J. Geophys. Res 107(B12), (2002). 2553, doi: 10.1029/2001JB001460.

    Article  Google Scholar 

  36. D. A. Lockner, D. E. Moore, and Z. Reches, “Microcrack Interaction Leading to Shear Fracture,” in Proc. Thirty-third U.S. Symp. Rock. Mech. (1992), pp. 807–816.

  37. D. A. Lockner et al., “Quasi-static Fault Growth and Shear Fracture Energy in Granite,” Nature 50, 39–42 (1991).

    Article  Google Scholar 

  38. D. A. Lockner et al., “Observations of Quasistatic Fault Growth from Acoustic Emissions,” in Fault Mechanics and Transport Properties of Rocks, Ed. by B. Evans and T.-F. Wong (Academic Press, London, 1992), pp. 3–31.

    Chapter  Google Scholar 

  39. A. V. Lyusina and V. B. Smirnov, “Temporal Grouping of Aftershock Sequences (Exemplified by Koalinga and Idaho Earthquakes on May 2, 1983 and October 28, 1983, Respectively),” Physics of the Earth, No. 8, 9–14 (1993).

  40. I. G. Main, P. G. Meredith, and S. Jones, “A Reinterpretation of the Precursory Seismic b-value Anomaly from Fracture Mechanics,” Geophys. J. 96, 131–138 (1989).

    Article  Google Scholar 

  41. G. G. Malinetskii and A. B. Potapov, Actual Problems in Nonlinear Dynamics (URSS, Moscow, 2002) [in Russian].

    Google Scholar 

  42. A. I. Malyshev and I. N. Tikhonov, “Nonlinear regular features in the development of the seismic process in time,” Physics of the Earth, No. 6, 37-51 (2007).

  43. D. Marsan and C. J. Bean, “Seismicity Response to Stress Perturbations, Analised for a Worldwide Catalogue,” Geophys. J. Int. 154, 179–195 (2003).

    Article  Google Scholar 

  44. P. G. Meredith, I. G. Main, and C. Jones, “Temporal Variations in Seismicity during Quasi-static and Dynamic Rock Failure,” Tectonophysics 175, 249–268 (1990).

    Article  Google Scholar 

  45. V. I. Mjachkin, W. F. Brace, G. A. Sobolev, and J. H. Dietrich, “Two Models for Earthquake Precursors,” PAGEOPH 113(1/2), 169–181 (1975a).

    Article  Google Scholar 

  46. V. I. Mjachkin, B. V. Kostrov, G. A. Sobolev, and O.G. Shamina, “Basics of the Physics of the Source and Earthquake Precursors,” in Physics of the Earthquake Center (Nauka, Moscow, 1975b, pp. 6–29 [in Russian].

    Google Scholar 

  47. D. Moore and D. Lockner, “The Role of Microcracking in Shear-fracture Propagation in Granite,” J. Struct. Geol. 17, 95–114 (1995).

    Article  Google Scholar 

  48. C. Narteau, P. Shebalin, and M. Holschneider, “Temporal Limits of the Power Law Aftershock Decay Rate,” J. Geophys. Res. 107(B12) (2202). 2359, doi: 10.1029/2002JB001868.

  49. A. Nicol et al., “Fault Size Distributions — Are They Really Power Law?” J. Struct. Geol. 18, 191–197 (1996).

    Article  Google Scholar 

  50. NMSOP, IASPEI New Manual of Seismological Observatory Practice, Ed. by P. Borman (GeoForschungZentrum, 2002).

  51. M. S. Paterson and T. F. Wong, Experimental Rock Deformation — The Brittle Field (Springer, Berlin, 2005).

    Google Scholar 

  52. V. F. Pisarenko, On the Law of Earthquake Recurrence (Nauka, Moscow, 1975), pp. 6–29 [in Russian].

    Google Scholar 

  53. A. V. Ponomarev et al., “Physical Modeling of the Formation and Evolution of Seismically Active Fault Zones,” Tectonophysics 277, 57–81 (1997).

    Article  Google Scholar 

  54. A. V. Ponomarev et al., “Seismic Parameters and Geophysical Variations before Zhangbei Earthquake,” in 22th General Assembly of International Union of Geodesy and Geophysics, Abstracts (Birmingham, 1999).

  55. M. D. Read, M. R. Ayling, P. G. Mertedith, and S. Murrell, “Microcracking during Triaxial Deformation of Porous Rocks Monitored by Changes in Rock Physical Properties, II. Pore Volumometry and Acoustic Emission Measurements on Water-saturated Rocks,” Tectonophysics 245, 223–235 (1994).

    Article  Google Scholar 

  56. Z. Reches and D. Lockner, “Nucleation and Growth of Faults in Brittle Rocks,” J. Geophys. Res. 99, 18159–18173 (1994).

    Article  Google Scholar 

  57. V. R. Regel, A. I. Slutsker, and E. E. Tomashevskii, Kinetic Nature of Strength of Solid Bodies (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  58. G. Yu. Riznichenko, Mathematical Modeling in Biophysics and Ecology (IKI, Moscow, 2003) [in Russia].

    Google Scholar 

  59. Yu. M. Romanovskii, N. V. N. V. Stepanova, and D. S. Chernavskii, Mathematical Biophysics (1984) [in Russian].

  60. M. A. Sadovskii and V. F. Pisarenko, Seismic Process and the Block Medium (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  61. M. A. Sadovskii, L. G. Bolkhovitinov, and V. F. Pisarenko, Deformation of the Geophysical Medium and Seismic Process (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  62. A. A. Samarskii and A. P. Mikhailov, Mathematical Modeling. Ideas. Methods. Examples, (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  63. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press, Cambridge, 2002).

    Google Scholar 

  64. A. A. Semerchan et al., “The Study of Precursors of Large Specimen Mechanical Fracturing,” Dokl. Akad. Nauk SSSR 260, 616–619 (1981).

    Google Scholar 

  65. S. A. Shapiro, P. Audigane, J.-J. Royer, “Large-scale in Situ Permeability Tensor of Rocks from Induced Microseismicity,” Geoph. J. Int. 137, 207–213 (1999).

    Article  Google Scholar 

  66. S. A. Shapiro, P. Audigane, J.-J. Royer, “Reply to Comment by F.H. Cornet on ‘Large-scale in Situ Permeability Tensor of Rocks from Induced Microseismicity,” Geoph. J. Int. 140, 470–473 (2000).

    Article  Google Scholar 

  67. S. A. Shapiro, E. Huenges, and G. Born, “Estimating the Crust Permeability from Fluid-injection-induced Seismic Emission at the KTB Site,” Geoph. J. Int. 131, F15–F18 (1997).

    Article  Google Scholar 

  68. M. Shimada and A. Cho, “Two Types of Brittle Fracture of Silicate Rocks under Confining Pressure and Their Implication in the Earth’s Crust,” Tectonophysics 175, 221–235 (1990).

    Article  Google Scholar 

  69. V. B. Smirnov, “The Assessment of Representativeness of Data on Earth Catalogues,” Vulkalnol. Seismol., No. 4, 93–105 (1997a).

  70. V. B. Smirnov, “Spatial and Temporal Variations in Parameters of Seismic Self-similarity,” Vulkalnol. Seismol., No. 6, 31–41 (1997b).

  71. V. B. Smirnov, “Assessment of the Duration of the Earth’s Lithosphere Failure Cycle Based on Data from Earthquake Catalogues,” Physics of the Earth, No. 10, 13–32 (2003).

  72. V. B. Smirnov and V. D. Feofilaktov, “Fractal Properties of the Lithosphere Based on Code-waves of Local Earthquakes,” Vulkanol. Seismol., No. 4, 52–56 (2000a).

  73. V. B. Smirnov and V. D. Feofilaktov, “Fractal Properties of the Lithosphere Based on Code-waves of Local Earthquakes and Seismicity Structure in the Center of the Rachinskoe Earthquake,” Vulkanol. Seismol., No. 6, 44–48 (2000b).

  74. V. B. Smirnov and I. P. Gabsatarova, “Representativeness of the Earthquake Catalogue for the North Caucasus: Calculation Data and Statistical Estimates,” Vestnik OGGGGN RAN, No. 4, 83–95 (2000).

  75. V. B. Smirnov and A. V. Lyusina, “On Temporal Structure of Aftershock Sequences (Exemplified by the Alaska and Kamchatka Earthquakes),” Vulkanol. Seismol., No. 6, 45–54 (1990).

  76. V. B. Smirnov and A. V. Ponomarev, “Regularities in Relaxation of the Seismic Regime according to Natural and Laboratory Data,” Physics of the Earth, No. 10, 26–36 (2004).

  77. V. B. Smirnov, A. V. Ponomarev, and A. D. Zav’yalov, “Peculiarities in the Formation and Evolution of the Acoustic Regime Structure in Rock Samples, Dokl. Akad. Nauk 343, 818–823 (1995).

    Google Scholar 

  78. V. B. Smirnov, A. V. Ponomarev, and A. D. Zav’yalov, “The Structure of the Acoustic Regime in Rock Specimen and Seismic Process,” Physics of the Earth, No. 1, 38–58 (1995).

  79. Smith W.D. The b-value As an Earthquake Precursor, Nature 289(5794), 136–139 (1981).

    Article  Google Scholar 

  80. G. A. Sobolev, Basics of Earthquake Prediction (Nauka, Moscow, 1993) [in Russian].

    Google Scholar 

  81. G. A. Sobolev and A. V. Ponomarev, “Acoustic Emission and Preparation Stages of Failure in the Laboratory Experiment,” Vulkanol. Seismol., Nos. 4–5, 50–62 (1999).

  82. G. A. Sobolev and A. V. Kol’tsov, Large-scale Modeling of Earthquake Preparation and Precursors (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  83. G. A. Sobolev et al., “Precursors of the Failure in Water-containing Blocks of Rocks,” Jour. Earthq. Prediction Res., No.1, 63–91 (1996).

    Google Scholar 

  84. D. Sornette and V. Pisarenko, “Fractal Plate Tectonics,” Geoph. Res. Let. 30, No. 3, 1105 (2003), doi:10.1029 / 2002GL015043.

    Article  Google Scholar 

  85. Yu. M. Svirezhev, “Volterra and Recent Mathematical Biology,” in Afterword to the Book: “V. Volterra: Mathematical Theory of Struggle for Existence” (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  86. P. Tapponnier and W. F. Brace, “Development of Stress-induced Microcracks in Westerly Granite,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 13, 103–112 (1976).

    Article  Google Scholar 

  87. B. D. Thompson, R. P. Young R.P., and D. A. Lockner, “Fracture in Westerly Granite under AE Feedback and Constant Strain Rate Loading: Nucleation, Quasi-static Propagation, and the Transition to Unstable Fracture Propagation,” Pure Appl. Geophys. 163, 995–1019 (2006). doi 10.1007/s00024-006-0054-x.

    Article  Google Scholar 

  88. N. G. Tomilin, Hierarchic Properties of Acoustic Emission under Rock Destruction (FTI RAN, St. Petersburg, 1997) [in Russian].

    Google Scholar 

  89. D. Turcotte, Fractals and Chaos in Geology and Geophysics. Cambridge University Press, London, 1992).

    Google Scholar 

  90. M. Vogels, R. Zoeckler, D. M., Stasiw, and L.C., Cerny, “P. F. Verhulst’s “notice sur la loi que la populations suit dans son accroissement” from correspondence mathematique et physique. Ghent, vol. X, London, 1838,” J. Biol. Phys. 3(4), 183–192 (1975).

    Article  Google Scholar 

  91. J. Watterson, “Scaling Systematic of Fault Sizes on a Large-scale Range Fault Map,” J. Struct. Geol. 18, 199–214 (1996).

    Article  Google Scholar 

  92. Lei Xinglin, K. Kusunose, T. Satoh, and O. Nishizawa, “The Hierarchical Rupture Process of a Fault: An Experimental Study, “Physics of the Earth and Planetary Interiors 137, 213–228 (2003).

    Article  Google Scholar 

  93. T. Yanagidani et al., “Localization of Dilatancy in Ohshima Granite under Constant Uniaxial Stress, J. Geophys. Res. 90, 6840–6858 (1985).

    Article  Google Scholar 

  94. G. Yielding, T. Needham, and H. Jones, “Sampling of Faults Populations using Sub-subsurface Data: A Review,” J. Struct. Geol. 18, 135–146 (1996).

    Article  Google Scholar 

  95. H. Yukutake, “Fracture Nucleation Process in Intact Rocks,” Tectonophysics 211, 247–257 (1992).

    Article  Google Scholar 

  96. A. Zang, F. C. Wagner, S. Stanchits, C. Janssen, and G. Dresen, “Fracture Process Zone in Granite,” J. Geophys. Res., 105, 23651–23661 (2000).

    Article  Google Scholar 

  97. A. D. Zav’yalov, Intermediate-term Prediction of Earthquakes: Basics, Methods, Realization (Nauka, Moscow, 2006) [in Russian].

    Google Scholar 

  98. G. Zhang and Z. Fu, “Some features of Medium- and Short-term Anomalies before Great Earthquakes,” in Earthquakes Prediction. An International Review (Amer. Geophys. Union. M. Ewing Ser., 1981), vol. 4, pp. 497–509.

    Google Scholar 

  99. J. Zhang J., T.-F. Wong, T. Yanagidani, and D. Davis, “Pressure-induced Microcracking and Grain Crushing in Berea and Boise Sandstones: Acoustic Emission and Quantitative Microscopy Measurements,” Mechanics of Materials 9, 1–15 (1990).

    Article  Google Scholar 

  100. S. N. Zhurkov, “Kinetic Concept of Strength of Solid Bodies,” Vestn. Akad. Nauk SSSR, No. 3, 46–52 (1968).

  101. S. N. Zhurkov et al., “On Prediction of Rock Failure,” Izv.AN SSSR. Fizika Zemli, No. 6, 11–18 (1977).

  102. S. N. Zhurkov, V. S. Kuksenko, V. A. Petrov, et al., “Concentration Criterion of Volumetric Failure of Solid Bodies,” in Physical Processes in Earthquake Centers (Nauka, Moscow, 1980), pp. 78–86 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995, Russia

    V. B. Smirnov & A. V. Ponomarev

  2. Faculty of Physics, Moscow State University, Moscow, Russia

    V. B. Smirnov

  3. Institute de Physique du Globe de Paris, Paris, France

    P. Benard

  4. Borok Geophysical Observatory, Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Borok, Nekouz, Yaroslavl’ region, 152742, Russia

    A. V. Patonin

Authors
  1. V. B. Smirnov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Ponomarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Benard
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. V. Patonin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.B. Smirnov, A.V. Ponomarev, P. Benard, A.V. Patonin, 2010, published in Fizika Zemli, 2010, No. 2, pp. 17–49.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smirnov, V.B., Ponomarev, A.V., Benard, P. et al. Regularities in transient modes in the seismic process according to the laboratory and natural modeling. Izv., Phys. Solid Earth 46, 104–135 (2010). https://doi.org/10.1134/S1069351310020023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1069351310020023

Keywords

Search

Navigation