Skip to main content
Log in

Induced Seismicity Modeling Based on Two-Parameter Rate-and-State Law

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

Abstract—Numerical modeling of induced seismicity resulting from fluid injection into the subsurface is considered. One of important factors determining the slip dynamics of a tectonic fault during fluid injection loading is the form of the law of friction acting on the fault sides. The numerical analysis in the context of a slider model compared to the results of laboratory experiments has shown that a two-parameter rate-and-state friction law describes the widest spectrum of the observed sliding modes. A double porosity model and a slider model for fracture are used to simulate the induced seismicity in ​​the region of Basel, Switzerland, caused by geothermal stimulation. A physically complete model of embedded fractures which allows for calculating fluid flow in a rock with fractures or faults taking into account changes in the hydraulic properties of the latter is presented. Fault deformation process is described based on the displacement discontinuity method. Based on the model, the results of the field experiment on water injection into a fault in the southern France are analyzed. The development of fault slips is studied as a function of a number of parameters characterizing a fault, filtration properties of a rock, and injection pattern. The conditions for the emergence of seismic slip in the context of the proposed model are established.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.
Fig. 19.

Similar content being viewed by others

REFERENCES

  1. Adushkin, V.V. and Turuntaev, S.B., Tekhnogennaya seismichnost’ – indutsirovannaya i triggernaya (Manmade Seismicity: Induced and Triggered), Moscow: IDG RAN, 2015.

  2. Baisch, S., Voros, R., Rothert, E., Stang, H., Jung, R., and Schellschmidt, R., A numerical model for fluid injection induced seismicity at Soultz-sousForets, Int. J. Rock Mech. Min. Sci., 2010, vol. 47, no. 3, pp. 405–413.

    Article  Google Scholar 

  3. Bommer, J.J., Oates, S., Cepeda, J.M., Lindholm, C., Bird, J.F., Torres, R., Marroquín, G., and Rivas, J., Control of hazard due to seismicity induced by a hot fractured rock geothermal project, Eng. Geol., 2006, vol. 83, no. 4, pp. 287–306.

    Article  Google Scholar 

  4. Budkov, A.M. and Kocharyan, G.G., Experimental study of different modes of block sliding along interface. Part 3. Numerical modeling, Phys. Mesomech., 2017, vol. 20, no. 2, pp. 203–208. https://doi.org/10.1134/S1029959917020102

    Article  Google Scholar 

  5. Budkov, A.M., Kocharyan, G.G., Novikov, V.A., and Krasheninnikov, A.V., Modification of the empirical rate-and-state friction law for modeling slow slip events, in Sb. nauchn. tr. IDG RAN: Dinamicheskie protsessy v geosferakh, vyp. 7 (Collect. Pap. IDG RAS: Dynamic Processes in Geospheres, vol. 7), Moscow: GEOS, 2015, pp. 22–30.

  6. Cappa, F., Guglielmi, Y., Nussbaum, C., and Birkholzer, J., On the relationship between fault permeability increases, induced stress perturbation, and the growth of aseismic slip during fluid injection, Geophys. Res. Lett., 2018, vol. 45, no. 11, pp. 11–20.

    Article  Google Scholar 

  7. Carpenter, B.M., Scuderi, M.M., Collettini, C., and Marone, C., Frictional heterogeneities on carbonate-bearing normal faults: Insights from the Monte Maggio Fault, Italy, J. Geophys. Res.: Solid Earth, 2014, vol. 119, no. 12, pp. 9062–9076.

    Article  Google Scholar 

  8. Carpenter, B.M., Saffer, D.M., and Marone, C., Frictional properties of the active San Andreas Fault at SAFOD: Implications for fault strength and slip behavior, J. Geophys. Res.: Solid Earth, 2015, vol. 120, no. 7, pp. 5273–5289.

    Article  Google Scholar 

  9. Diechmann, N., Kraft, T., and Evans, K.F., Identification of faults activated during the stimulation of the Basel geothermal project from cluster analysis and focal mechanics of the larger magnitude events, Geothermics, 2014, vol. 52, pp. 84–97. https://doi.org/10.1016/j.geothermics.2014.04.001

    Article  Google Scholar 

  10. Dieterich, J.H., Modeling of rock friction: 1. Experimental results and constitutive, J. Geophys. Res., 1979, vol. 84, no. B5, pp. 2161–2168.

    Article  Google Scholar 

  11. Dinske, C., Interpretation of fluid induced seismicity and hydrocarbon of Basel and Cotton Valley, Dissertation zur Erlangung des akademischen Grades Doktor der Naturwissenschaften, Berlin: Freien Universität Berlin, 2011. https://doi.org/10.17169/refubium-15993

  12. Ellsworth, W., Llenos, A., McGarr, A., Michael, A., Rubinstein, J., Mueller, C., Petersen, M., and Calais, E., Increasing seismicity in the U.S. midcontinent: Implications for earthquake hazard, Leading Edge, 2015, vol. 34, no. 6, pp. 618–626. https://doi.org/10.1190/tle34060618.1

    Article  Google Scholar 

  13. Ellsworth, W.L., Giardini, D., Townend, J., Ge, S., and Shimamoto, T., Triggering of the Pohang, Korea, earthquake (M w 5.5) by enhanced geothermal system stimulation, Seismol. Res. Lett., 2019, vol. 90, no. 5, pp. 1844–1858. https://doi.org/10.1785/0220190102

    Article  Google Scholar 

  14. Erickson, B., Birnir, B., and Lavallée, D., A model for aperiodicity in earthquakes, Nonlin. Processes Geophys., 2008, vol. 15, pp. 1–12. https://doi.org/10.5194/npg-15-1-2008

    Article  Google Scholar 

  15. Gischig, V.S. and Wiemer, S., A stochastic model for induced seismicity based on non-linear pressure diffusion and irreversible permeability enhancement, Geophys. J. Int., 2013, vol. 194, no. 2, pp. 1229–1249.

    Article  Google Scholar 

  16. Gu, J.-C., Rice, J.R., Ruina, A.L., and Tse, S.T., Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction, J. Mech. Phys. Solids, 1984, vol. 32, no. 3, pp. 167–196.

    Article  Google Scholar 

  17. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 1st ed., New York: Springer-Verlag, 1983.

    Book  Google Scholar 

  18. Guglielmi, Y., Cappa, F., Avouac, J.-P., Henry, P., and Elsworth, D., Seismicity triggered by fluid injections induced aseismic slip, Science, 2015, vol. 348, no. 6240, pp. 1224–1226.

    Article  Google Scholar 

  19. Häring, M.O., Schanz, U., and Ladner, F., and Dyer, B.C., Characterisation of the Basel 1 enhanced geothermal system, Geothermics, 2008, vol. 37, no. 5, pp. 469–495.

    Article  Google Scholar 

  20. Hobbs, B.E., Chaotic behaviour of frictional shear instabilities, Proc. 2nd Int. Symp. on Rockbursts and Seismicity in Mine, Minneapolis, 1988, Mineapolis: University of Minnesota, 1990, pp. 87–91.

  21. Kanamori, H., The energy release in great earthquakes, J. Geophys. Res., 1977, vol. 82, no. 20, pp. 2981–2987. https://doi.org/10.1029/JB082i020p02981

    Article  Google Scholar 

  22. Kato, N., Repeating slip events at a circular asperity: numerical simulation with a rate-and-state-dependent friction law, Bull. Earthquake Res. Inst., Univ. Tokyo, 2003, vol. 78, pp. 151–166.

    Google Scholar 

  23. Kato, N., Interaction of slip on asperities: Numerical simulation of seismic cycles on a two-dimensional planar fault with nonuniform frictional property, J. Geophys. Res., 2004, vol. 109, Paper ID B12306. https://doi.org/10.1029/2004JB003001

  24. Kato, N. and Tullis, T.E., A composite rate- and state-dependent law for rock friction, Geophys. Res. Lett., 2001, vol. 28, no. 6, pp. 1103–1106.

    Article  Google Scholar 

  25. Kocharyan G.G., Kishkina S.B., Novikov V.A., and Ostapchuk A.A., Slow slip events: parameters, conditions of occurrence, and future research prospects, Geodinam. Tektonofiz., 2014a, vol. 5, no. 4, pp. 863–891.

    Article  Google Scholar 

  26. Kocharyan, G.G., Markov, V.K., Ostapchuk, A.A., and Pavlov, D.V., Mesomechanics of shear resistance along a filled crack, Phys. Mesomech., 2014b, vol. 17, no. 2, pp. 123–133, https://doi.org/10.1134/S1029959914020040

    Article  Google Scholar 

  27. Lie, K.-A., An Introduction to Reservoir Simulation Using MATLAB: User Guide for the Matlab Reservoir Simulation Toolbox (MRST), SINTED ICT, Cambridge: Cambridge Univ. Press, 2016.

  28. Marone, C. and Saffer, D.M., The mechanics of frictional healing and slip instability during the seismic cycle, in Treatise on Geophysics, 2nd ed., vol. 4, Oxford: Elsevier, 2015, pp. 111–138.

    Google Scholar 

  29. McClure, M.W., Modeling and characterization of hydraulic stimulation and induced seismicity in geothermal and shale gas reservoirs, Ph. D. Dissertation, Stanford: Stanford University, 2012.

  30. McGarr, A., Simpson, D., and Seeber, L., Case histories of induced and triggered seismicity, in International Handbook of Earthquake and Engineering Seismology, Lee, W.H.K. and Kanamori, H., Eds., Amsterdam: Academic Press, 2002, vol. 81A, pp. 647–660.

  31. Noda, H., Dunham, E., and Rice, J.R., Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels, J. Geophys. Res., 2009, vol. 114, no. B7, Paper ID B07302. https://doi.org/10.1029/2008JB006143

  32. Norbeck, J.H. and Horne, R.N., Evidence for a transient hydromechanical and frictional faulting response during the 2011 M w 5.6 Prague, Oklahoma earthquake sequence, J. Geophys. Res.: Solid Earth, 2016, vol. 121, pp. 8688–8705. https://doi.org/10.1002/2016JB013148

    Article  Google Scholar 

  33. Norbeck, J. and Horne, R., Maximum magnitude of injection-induced earthquakes: A criterion to assess the influence of pressure migration along faults, Tectonophysics, 2018, vol. 733, pp. 108–118. https://doi.org/10.1016/j.tecto.2018.01.028

    Article  Google Scholar 

  34. Okazaki, K. and Katayama, I., Slow stick slip of antigorite serpentinite under hydrothermal conditions as a possible mechanism for slow earthquakes, Geophys. Res. Lett., 2015, vol. 42, no. 4, pp. 1099–1104.

    Article  Google Scholar 

  35. Press, W.H., Teukolsky, S.A., Vatterling, W.T., and Flannery, B.P., Numerical Recipes: The Art of Scientific Computing, 3rd ed., Cambridge: Cambridge Univ. Press, 2007.

    Google Scholar 

  36. Rice, J.R., Spatio-temporal complexity of slip on a fault, J. Geophys. Res., 1993, vol. 98, no. B6, pp. 9885–9907.

    Article  Google Scholar 

  37. Riga, V.Yu., Turuntayev, S.B., and Ostapchuk, A.A., Numerical rate-and-state modeling of seismogenic slips in interblock sliding experiments, in Sb. nauchn. tr. IDG RAN: Dinamicheskie protsessy v geosferakh, vyp. 10 (Collect. Pap. IDG RAS: Dynamic Processes in Geospheres, vol. 10), Moscow: GEOS, 2018, pp. 99–109.

  38. Ruina, A., Slip instability and state variable friction laws, J. Geophys. Res., 1983, vol. 88, no. B12, pp. 10359–10370. https://doi.org/10.1029/JB088iB12p10359

    Article  Google Scholar 

  39. Segall, P., Earthquake and Volcano Deformation, Princeton: Princeton Univ. Press, 2010.

    Book  Google Scholar 

  40. Seismological Grand Challenges in Understanding Earth’s Dynamic Systems, Lay, T., Ed., Report to the National Science Foundation–IRIS Consortium, 2009.

  41. Shou, K.J. and Crouch, S.L., A higher order displacement discontinuity method for analysis of crack problems, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 1995, vol. 32, no. 1, pp. 49–55.

    Article  Google Scholar 

  42. Witherspoon, P.A., Wang, J.S.Y., Iwai, K., and Gale, J.E., Validity of cubic law for fluid flow in a deformable rock fracture, Water Resour. Res., 1980, vol. 16, pp. 1016–1024.

    Article  Google Scholar 

Download references

Funding

The study was carried out in partial fulfillment of the state contract with the Ministry of Science and Higher Education of the Russian Federation (project АААА-А17-117112350011-7).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to V. Yu. Riga or S. B. Turuntaev.

Additional information

Translated by M. Nazarenko

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Riga, V.Y., Turuntaev, S.B. Induced Seismicity Modeling Based on Two-Parameter Rate-and-State Law. Izv., Phys. Solid Earth 57, 627–643 (2021). https://doi.org/10.1134/S1069351321050153

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1069351321050153

Keywords:

Navigation