Abstract
Laboratory experiments on studying the aftershock regime are carried out on sandstone specimens at different levels of axial loading and uniform compression and at constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control, which ensures the regular generation of aftershock sequences. The experiments are conducted on intact specimens and on those with preliminarily formed shear macrofractures simulating natural faults. The multichannel recording of the signals of acoustic emission (AE) during the experiments allowed locating the AE sources. Several types of the dependence of the parameters of relaxation of the acoustic activity—parameters p and c of the modified Omori law and the Gutenberg–Richter b-value—on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of a fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses; parameter c—the time delay before the onset of relaxation—decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged with the growth of axial stresses, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the relaxation of the aftershock activity is determined by the kinetics of a fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by the exponential dependences of parameter c on stresses and the effective strength of the medium which are revealed in the experiments. Under this hypothesis, based on Zhurkov’s formula for the durability of materials, it is possible to unify the dependences of parameter c on the Coulomb stresses at different effective strength values. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, thus indicating how far the stress state of the medium is from critically corresponding to the ultimate strength.
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REFERENCES
Bohnenstiehl, D.R., Tolstoy, M., Dziak, R.P., Fox, C.G., and Smith, D.K., Aftershock sequences in the mid-ocean ridge environment: an analysis using hydroacoustic data, Tectonophysics, 2002, vol. 354, pp. 49–70.
Creamer, F.H. and Kissslinger, C., The relationship between temperature and the decay parameter for aftershock sequences near Japan, EOS Trans. Am. Geophys. Union, 1993, vol. 74, F417.
Davidsen, J., Gu, C., and Baiesi, M., Generalized Omori-Utsu law for aftershock sequences in southern California. Geophys. J. Int., 2015, vol. 201, no. 2, pp. 965–978.
Earthquakes: Radiated Energy and the Physics of Faulting, Abercombie, R., McGarr, Art., Di Toro, G., and Kanamori, H., Eds., AGU Geophysical monograph 170, Washington: AGU, 2000.
Enescu, B., Mori, J., and Miyazawa, M., Quantifying early aftershock activity of the 2004 mid-Niigata Prefecture earthquake (Mw 6.6), J. Geophys. Res., 2007, vol. 112, B04310. doi https://doi.org/10.1029/2006JB004629
Goebel, T.H.W., Becker, T.W., Schorlemmer, D., Stanchits, S., Sammis, C., Rybacki, E., and Dresen, G., Identifying fault heterogeneity through mapping spatial anomalies in acoustic emission statistics, J. Geophys. Res., 2012, vol. 117. B03310. doi https://doi.org/10.1029/2011JB008763
Gupta, H.K., A review of recent studies of triggered earthquakes by artificial water reservoirs with special emphasis on earthquakes in Koyna, India, Earth Sci. Rev., 2002, vol. 58, pp. 279–310.
Hatano, T., Narteau, C., and Shebalin, P., Common dependence on stress for the statistics of granular avalanches and earthquakes, Sci. Rep., 2015, no. 5, p. 12280.
Helmstetter, A. and Shaw, B.E., Relation between stress heterogeneity and aftershock rate in the rate-and-state model, J. Geophys. Res. Solid Earth, 2006, vol. 111, no. B7.
Hirata, T., Omori’s power law aftershock sequences of microfracturing in rock fracture experiment, J. Geophys. Res., 1987, vol. 92, pp. 6215–6221.
Holschneider, M., Narteau, C., Shebalin, P., Peng, Z., and Schorlemmer, D., Bayesian analysis of the modified Omori law, J. Geophys. Res., 2012, vol. 117, B06317. doi https://doi.org/10.1029/2011JB009054
Jaeger, J.C., Cook, N.G.W., and Zimmerman, R., Fundamentals of Rock Mechanics, Malden: Wiley-Blackwell, 2007.
Kagan, Y.Y., Short-term properties of earthquake catalogs and models of earthquake source, Bull. Seismol. Soc. Am, 2004, vol. 94, no. 4, pp. 1207–1228.
Kagan, Y.Y. and Houston, H., Relation between mainshock rupture process and Omori’s law for aftershock moment release rate, Geophys J. Int, 2005, vol. 163, no. 3, pp. 1039–1048.
Kanamori, H., Earthquake Seismology, Treatise on geophysics, vol. 4, San Diego: Elsevier, 2015.
King, G.C.P., Fault interaction, earthquake stress changes, and the evolution of seismicity, in Earthquake Seismology, vol. 4 of Treatise on Geophysics, Kanamori, H., Ed., 4th ed., Oxford: Elsevier, 2009, pp. 225–257.
Kisslinger, C. and Jones, L.M., Properties of aftershock sequences in southern California, J. Geophys. Res., 1991, vol. 96, no. 11, pp. 947–958.
Lei, X. and Ma, Sh., Laboratory acoustic emission study for earthquake generation process, Earthquake Sci., 2014, vol. 27, no. 6, pp. 627–646. doi https://doi.org/10.1007/s11589-014-0103-y
Lei, X., Masuda, K., Nishizawa, O., Jouniaux, L., Liu, L., Ma, W., and Satoh, T., Detailed analysis of acoustic emission activity during catastrophic fracture of faults in rock, J. Struct. Geol, 2004, vol. 26, pp. 247–258.
Leonard, M. and Kennett, B.L.N., Multi-component autoregressive techniques for the analysis of seismograms, Phys. Earth Planet. Inter., 1999, vol. 113, nos. 1–4, pp. 247–263.
Lippiello, E., Giacco, F., Marzocchi, W., Godano, C., and de Arcangelis, L., Mechanical origin of aftershocks, Sci. Rep., 2015, vol. 5, p. 15560. doi https://doi.org/10.1038/srep15560
Lockner, D.A., The role of acoustic emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci. Geomech. Abstr, 1993, vol. 30, pp. 883–899.
Lockner, D.A. and Byerlee, J.D., Acoustic emission and fault formation in rocks, Proc. 1st Conf. on Acoustic Emission in Microseismic Activity in Geological Structures and Materials, Hardy, H.R. and Leighton, F.W., Eds., Clausthal-Zellerfeld: Trans Tech Publications, 1977, pp. 99–107.
Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A., and Sidorin, A., Quasi-static fault growth and shear fracture, Nature, 1991, vol. 350, no. 6313, pp. 39–42.
Lockner, D.A., et al., Observations of quasistatic fault growth from acoustic emissions, in Fault Mechanics and Transport Properties of Rocks, Evans, B. and Wong, T.-F., Eds., London: Academic, 1992, pp. 3–31.
Lolli, B. and Gasperini, P., Aftershocks hazard in Italy. Part I: estimation of time-magnitude distribution model parameters and computation of probabilities of occurrence, J. Seismol, 2003, vol. 7, no. 2, pp. 235–257.
Mekkawi, M., Grasso, J.-R., and Schnegg, P.A., A long-lasting relaxation of seismicity at Aswan reservoir, Egypt, 1982–2001, Bull. Seismol. Soc. Am., 2004, vol. 94, pp. 479–492.
Mogi, K., Study of elastic shocks caused by the fracture of heterogeneous materials and its relation to earthquake phenomena, Bull Earthquake Res. Inst., 1962, vol. 40, pp. 125–173.
Nanjo, K., Enescu, B., Shcherbakov, R., Turcotte, D., Iwata, T., and Ogata, Y., Decay of aftershock activity for Japanese earthquakes, J. Geophys. Res. Solid Earth, 2007, vol. 112, no. B8.
Narteau, C., Shebalin, P., and Holschneider, M., Temporal limits of the power law aftershock decay rate, J. Geophys. Res., 2002, vol. 107, p. B2359. doi https://doi.org/10.1029/2002JB001868
Narteau, C., Shebalin, P., and Holschneider, M., Loading rates in Valifornia inferred from aftershocks, Nonlinear Processes Geophys., 2008, vol. 15, pp. 245–263.
Narteau, C., Byrdina, S., Shebalin, P., and Schorlemmer, D., Common dependence on stress for the two fundamental laws of statistical seismology, Nature, 2009, vol. 462, no. 3, pp. 642–646. doi https://doi.org/10.1038/nature08553
Nelder, J. and Mead, R., A simplex method for function minimization, Comput. J, 1965, vol. 7, pp. 308–312.
Nur, A. and Booker, J.R., Aftershocks caused by pore fluid flow?, Science, 1972, vol. 175, pp. 885–888.
Ojala, I.O., Main, I.G., and Ngwenya, B.T., Strain rate and temperature dependence of Omori law scaling constants of ae data: implications for earthquake foreshock-aftershock sequences, Geophys. Rev. Lett., 2004, vol. 31, L24617. doi https://doi.org/10.1029/2004GL020781
Ommi, S., Zafarani, H., and Smirnov, V.B., Bayesian estimation of the modified Omori law parameters for the Iranian Plateau, J. Seismol., 2016, vol. 20, pp. 953–970. doi https://doi.org/10.1007/s10950-016-9574-8
Ouillon, G. and Sornette, D., Magnitude-dependent Omori law: theory and empirical study, J. Geophys. Res., Solid Earth, 2005, vol. 110, nol .B4.
Page, R., Aftershocks and microaftershocks of the Great Alaska Earthquake of 1964, Bull. Seismol. Soc. Am., 1968, vol. 58, no. 3, pp. 1131–1168.
Paterson, M.S. and Wong, T.F., Experimental Rock Deformation—The Brittle Field, Berlin: Springer, 2005.
Peng, Z., Vidale, J.E., and Houston, H., Anomalous early aftershock decay rate of the 2004 Mw 6.0 Parkfield, California, earthquake, Geophys. Rev. Lett., 2006, vol. 33, L17307. doi https://doi.org/10.1029/2006GL026744
Peng, Z., Vidale, J.E., Ishii, M., and Helmstetter, A., Seismicity rate immediately before and after mainshock rupture from highfrequency waveforms in Japan, J. Geophys. Res., 2007, vol. 112, B03306. doi https://doi.org/10.1029/2006JB004386
Pickering, G., Bull, J.M., and Sanderson, D.J., Sampling power-low distribution, Tectonophysics, 1995, vol. 248, pp. 1–20.
Rabinowitz, N. and Steinberg, D.M., Aftershock decay of three recent strong earthquakes in the Levant, Bull. Seismol. Soc. Am., 1998, vol. 88, pp. 1580–1587.
Regel’, V.R., Slutsker, A.I., and Tomashevskii, E.E., Kineticheskaya priroda prochnosti tverdykh tel (Kinetic Nature of the Strength of Solids), Moscow: Nauka, 1974.
Rodkin, M.V. and Tikhonov, I.N., The typical seismic behavior in the vicinity of a large earthquake, Phys. Chem. Earth, 2016. doi https://doi.org/10.1016/j.pce.2016.04.001
Rudajev, V., Vilhelm, J., and Lokajicek, T., Laboratory studies of acoustic emission prior to uniaxial compressive rock failure, Int. J. Rock Mech. Mining Sci, 2000, vol. 37, pp. 699–704.
Scholz, C., Experimental study of the fracturing process in brittle rock, J. Geophys. Res., 1968a, vol. 73, pp. 1447–1454.
Scholz, C., Microfractures, aftershocks, and seismicity, Bull Seismol. Soc. Am., 1968b, vol. 58, no. 3, pp. 1117–1130.
Schubnel, A., Thompson, B.D., Fortin, J., Gueguen, Y., and Young, R.P., Fluid-induced rupture experiment on Fontainebleau sandstone: premonitory activity, rupture propagation, and aftershocks, Geophys. Rev. Lett., 2007, vol. 34, L19307. doi https://doi.org/10.1029/2007GL031076
Shcherbakov, R., Turcotte, D.L., and Rundle, J.E., A generalized Omori’s law for earthquake aftershock decay, Geophys. Rev. Lett., 2004, vol. 31, L11613. doi https://doi.org/10.1029/2004GL019808
Shebalin, P. and Narteau, C., Depth dependent stress revealed by aftershocks, Nat. Commun., 2017, no. 8, p. 1317. doi https://doi.org/10.1038/s41467-017-01446-y
Shebalin, P., Narteau, C., and Holschneider, M., From alarm-based to rate-based earthquake forecast models, Bull. Seimol. Soc. Am., 2012, vol. 102, no. 1, pp. 64–72.
Smirnov, V.B., Earthquake catalogs: evaluation of data completeness, Volcanol. Seismol., 1998, vol. 19, pp. 497–510.
Smirnov, V.B., Prognostic anomalies of seismic regime. I. Technique for preparation of original data, Geofiz. Issled., 2009, vol. 10, no. 2, pp. 7–22.
Smirnov, V.B. and Gabsatarova, I.P., Completeness of the North Caucasian earthquake catalog: calculation data and statistical estimates, Vestn. OGGGGN RAN, 2000, vol. 14, no. 4, pp. 35–41.
Smirnov, V.B. and Ponomarev, A.V., Seismic regime relaxation properties from in situ and laboratory data, Izv., Phys. Solid Earth, 2004, no. 10, pp. 807–816.
Smirnov, V.B. and Zavyalov, A.D., Seismic response to electromagnetic sounding of the Earth’s lithosphere, Izv., Phys. Solid Earth, 2012, vol. 48, nos. 7–8, pp. 615–639.
Smirnov, V.B., Ponomarev, A.V., and Sergeeva, S.M., On the similarity and feedback in experiments on rock fracture, Izv., Phys. Solid Earth, 2001, no. 1, pp. 82–89.
Smirnov, V.B., Ponomarev, A.V., Benard, P., and Patonin, A.V., Regularities in transient modes in the seismic process according to the laboratory and natural modeling, Izv., Phys. Solid Earth, 2010, vol. 46, no. 2, pp. 104–135.
Smirnov, V.B., Ponomarev, A.V., Kartseva, T.I., Mikhailov, V.O., Chadha, R.K., and Aidarov, F., Dynamics of induced seismicity during the filling of the Nurek reservoir, Izv., Phys. Solid Earth, 2018, vol. 54, no. 4. doi https://doi.org/10.1134/S1069351318040110
Sobolev, G.A. and Ponomarev, A.V., Fizika zemletryasenii i predvestniki (Physics of the Earthquakes and the Precursors), Moscow: Nauka, 2003.
Stanchits, S., Vinciguerra, S., and Dresen, G., Ultrasonic velocities, acoustic emission characteristics and crack damage of basalt and granite, Pure Appl. Geophys, 2006, vol. 163, nos. 5–6, pp. 975–994. doi https://doi.org/10.1007/s00024-006-0059-5
Stanchits, S., Fortin, J., Gueguen, Y., and Dresen, G., Initiation and propagation of compaction bands in dry and wet Bentheim sandstone, Pure Appl. Geophys., 2009, vol. 166, pp. 843–868. doi https://doi.org/10.1007/s00024-009-0478-1
Thompson, B.D., Young, R.P., and Lockner, D.A., Premonitory acoustic emissions and stick-slip in natural and smooth-faulted westerly granite, J. Geophys. Res., 2009, vol. 114, B02205. doi https://doi.org/10.1029/2008JB005753
Utsu, T., Ogata, Y., and Matsu’ura, R.S., The centenary of the Omori formula for a decay law of aftershock activity, J. Phys. Earth, 1995, vol. 43, pp. 1–33.
Vilhelm, J., Rudajev, V., Ponomarev, A.V., Smirnov, V.B., and Lokajicek, T., Statistical study of acoustic emissions generated during the controlled deformation of migmatite specimens, Int. J. Rock Mech. Mining Sci., 2017, vol. 100, pp. 83–89. doi https://doi.org/10.1016/j.ijrmms.2017.10.011
Vinogradov, S.D., On the distribution of the number of pulses by energy at rock fracture, Izv. Akad. Nauk SSSR, Ser. Geofiz., 1959, no. 12, pp. 1850–1852.
Wiemer, S. and Katsumata, K., Spatial variability of seismicity parameters in aftershock zones, J. Geophys. Res. Solid Earth, 1999, vol. 104, no. B6, pp. 13135–13151.
Wim Dubelaar, C. and Nijland, T.G., The Bentheim sandstone: geology, petrophysics, varieties and its use as dimension stone, in Engineering Geology For Society And Territory, vol. 8, Lollino, G., Eds., Cham: Springer, 2015, vol. 8, pp. 557–563. doi https://doi.org/10.1007/978-3-319-09408-3_100
Zang, A., Wagner, F.C., and Dresen, G., Acoustic emission, microstructure, and damage model of dry and wet sandstone stressed to failure, J. Geophys. Res., 1996, vol. 101, no. 8, pp. 17507–17521.
Zhurkov, S.N., Kinetic concept of the strength of solids, Int. J. Fract. Mech., 1965, vol. 1, pp. 311–323.
Zhurkov, S.N., Kinetic concept of the strength of solids, Vestn. Akad. Nauk SSSR, 1968, no. 3, pp. 46–52.
ACKNOWLEDGMENTS
The work was partially supported under the joint Russian–Indian project of the Russian Science Foundation and DST India: project no. 16-47-02003 of the Russian Science Foundation and project INT/RUS/ RSF/P-13 of the Department of Science and Technology of the Government of India in the part concerning the analysis of the data of the experiments and the interpretation of the obtained results.
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Smirnov, V.B., Ponomarev, A.V., Stanchits, S.A. et al. Laboratory Modeling of Aftershock Sequences: Stress Dependences of the Omori and Gutenberg–Richter Parameters. Izv., Phys. Solid Earth 55, 124–137 (2019). https://doi.org/10.1134/S1069351319010105
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DOI: https://doi.org/10.1134/S1069351319010105