Skip to main content
Log in

Hydraulic fracturing assessment on seismic hazard by Tsallis statistics

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Nowadays, because of the intensive use of hydraulic fracturing (HF) in mining, the study of its impact on mining extraction becomes crucial. Here we use the Sotolongo-Costa–Posadas (SCP) model, which is based on Tsallis formalism, to assess the impact of HF on the microearthquakes’ magnitudes and interevent times in a Chilean underground mine. In this regard, we analyse the seismic hazard at regions with HF and HF-free, which is an important issue for workers’ safety and continuity of the mining operations. The results reveal that the HF diminishes the value of the q entropic index associated with the SCP model, which implies that the magnitude and the autocorrelation of the microearthquakes decrease.

Graphical Abstract

“Hydraulic fracturing assessment on seismic hazard by Tsallis statistics” Erick de la Barra, Pedro Vega-Jorquera, Sérgio Luiz E. F. da Silva and Héctor Torres.

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

Similar content being viewed by others

Data availability statement

The data is confidential but can be provided if it is requested.

References

  1. A. Catalan, G. Chitombo, I. Onedarre, Trans. Inst. Min. Metall. Sect. A: Min. Technol. 126(4), 209 (2017)

    Google Scholar 

  2. A. Catalan, G. Chitombo, I. Onedarre, Trans. Inst. Min. Metall. Sect. A: Min. Technol. 126(4), 221 (2017)

    Google Scholar 

  3. B. Gutenberg, C.F. Richter, Bull. Seismol. Soc. Am. 34, 185 (1944)

    Google Scholar 

  4. C.C.W.C. Chen, Y.F. Wang, Y.M.W. Chang, Y.H. Lee, Geophys. J. Int. 167, 1215 (2006)

    ADS  Google Scholar 

  5. A. De Santis, G. Cianchini, P. Favali, L. Beranzoli, E. Boschi, Bull. Seismol. Soc. Am. 101, 1386 (2011)

    Google Scholar 

  6. W.B. Banerdt, S.E. Smrekar, D. Banfield, D. Giardini, M. Golombek, C.L. Johnson, P. Lognonné, A. Spiga, T. Spohn, C. Perrin, S.C. Stähler, D. Antonangeli, S. Asmar, C. Beghein, N. Bowles, E. Bozdag, P. Chi, U. Christensen, J. Clinton, G.S. Collins, I. Daubar, V. Dehant, M. Drilleau, M. Fillingim, W. Folkner, R.F. Garcia, J. Garvin, J. Grant, M. Grott, J. Grygorczuk, T. Hudson, J.C.E. Irving, G. Kargl, T. Kawamura, S. Kedar, S. King, B. Knapmeyer-Endrun, M. Knapmeyer, M. Lemmon, R. Lorenz, J.N. Maki, L. Margerin, S.M. McLennan, C. Michaut, D. Mimoun, A. Mittelholz, A. Mocquet, P. Morgan, N.T. Mueller, N. Murdoch, S. Nagihara, C. Newman, F. Nimmo, M. Panning, W.T. Pike, A.-C. Plesa, S. Rodriguez, J.A. Rodriguez-Manfredi, C.T. Russell, N. Schmerr, M. Siegler, S. Stanley, E. Stutzmann, N. Teanby, J. Tromp, M. van Driel, N. Warner, R.M. Weber, Nat. Geosci. 13, 183–189 (2020)

    ADS  Google Scholar 

  7. D. Schorlemmer, S. Wiemer, M. Wyss, Nature 437, 539 (2005)

    ADS  Google Scholar 

  8. F. Yamashita, E. Fukuyama, S. Xu, S. Kawakata, Nat. Commun. 12, 4302 (2021)

    ADS  Google Scholar 

  9. J. Mori, R.E. Abercrombie, J. Geophys. Res. Solid Earth 102, 15081 (1997)

    Google Scholar 

  10. Z. Zhan, Earth Planet. Sci. Lett. 461, 1 (2017)

    ADS  Google Scholar 

  11. O. Sotolongo-Costa, A. Posadas, Phys. Rev. Lett. 92, 048501 (2004)

    ADS  Google Scholar 

  12. C. Tsallis, J. Stat. Phys. 52, 479 (1988)

    ADS  Google Scholar 

  13. H.J. Herrmann, G. Mantica, D. Bessis, Phys. Rev. Lett. 65, 3223–3226 (1990)

    ADS  MathSciNet  Google Scholar 

  14. R. Silva, G.S. França, C.S. Vilar, J.S. Alcaniz, Phys. Rev. E 73, 026102 (2006)

    ADS  Google Scholar 

  15. L. Telesca, Phys. A: Stat. Mech. Appl. 389, 1911 (2010)

    Google Scholar 

  16. L. Telesca, Entropy 13, 1267 (2011)

    ADS  Google Scholar 

  17. F. Vallianatos, G. Michas, G. Papadakis, A. Tzanis, Nat. Hazards Earth Syst. Sci. 1391, 177–185 (2013)

    ADS  Google Scholar 

  18. F. Vallianatos, G. Michas, Entropy 22, 1194 (2020)

    ADS  Google Scholar 

  19. F. Vallianatos, P. Sammonds, Tectonophysics 509, 50 (2011)

    ADS  Google Scholar 

  20. F. Vallianatos, EPL 102, 28006 (2013)

    ADS  Google Scholar 

  21. S.L.E.F. da Silva, G. Corso, Eur. Phys. J. B 94, 25 (2021)

    ADS  Google Scholar 

  22. F. Vallianatos, G. Michas, G. Papadakis, A description of seismicity based on non-extensive statistical physics: a review, in Earthquakes and Their Impact on Society, 1st edn., ed. by S. D’Amico (Springer Natural Hazards, Springer, Berlin, 2002)

    Google Scholar 

  23. V. Saltas, F. Vallianatos, D. Triantis, I. Stavrakas, Complexity in laboratory seismology: from electrical and acoustic emissions to fracture, in Complexity of seismic time series, Measurement and Application. ed. by T. Chelidze, L. Telesca, F. Vallianatos (Elsevier, 2018)

  24. V. Saltas, F. Vallianatos, D. Triantis, T. Koumoudeli, I. Stavrakas, Physica A 528, 15 (2019)

    Google Scholar 

  25. F. Vallianatos, P. Benson, P. Meredith, P. Sammonds, Eur. Phys. Lett. (EPL) 97, 58002 (2012)

    ADS  Google Scholar 

  26. F. Vallianatos, G. Chatzopoulos, Entropy 20(10), 754 (2018)

    ADS  Google Scholar 

  27. C.G. Antonopoulos, G. Michas, F. Vallianatos, T. Bountis, Phys. A: Stat. Mech. Appl. 409, 71 (2014)

    Google Scholar 

  28. A. Alonso-Ayuso, F. Carvallo, L.F. Escudero, M. Guignard, J. Pi, R. Puranmalka, A. Weintraub, Eur. J. Oper. Res. 233, 711 (2014)

    Google Scholar 

  29. A. Catalan, G. Dunstan, M. Morgan, S. Green, S. Jorquera, T. Thornhill, “Intensive” preconditioning methodology developed for the Cadia East panel cave project, NSW, Australia. In 6th International Conference and Exhibition on Mass Mining, MassMin. (10-14) (2012)

  30. O. Sotolongo-Costa, Acta Geophys. 60, 526 (2012)

    ADS  Google Scholar 

  31. S. Abe, Phys. Lett. A 275, 250–253 (2000)

    ADS  MathSciNet  Google Scholar 

  32. T. Lay, T.C. Wallace, Modern Global Seismology (Academic Press, New York, 1995)

    Google Scholar 

  33. L. Telesca, Bull. Seismol. Soc. Am. 102, 886 (2012)

    Google Scholar 

  34. S. Abe, N. Suzuki, Phys. A: Stat. Mech. Appl. 350, 588 (2005)

    Google Scholar 

  35. F. Vallianatos, P. Sammonds, Tectonophysics 590, 52 (2013)

    ADS  Google Scholar 

  36. J. Woessner, S. Wiemer, Bull. Seismol. Soc. Am. 95, 684 (2005)

    Google Scholar 

  37. Á. González, J. Seismol. 21, 435 (2017)

    ADS  Google Scholar 

  38. S.L.E.F. da Silva, Chaos Solitons Fractals 143, 110622 (2021)

    Google Scholar 

  39. S. Wiemer, M. Wyss, Bull. Seismol. Soc. Am. 90, 859 (2000)

    Google Scholar 

  40. H. Elmonser, K. Brahim and A. Fitouhi, J. Inequal. Special Functions. 3, 4, 50–58 (2012). ISSN: 2217-4303, URL: http://www.ilirias.com

  41. D.S. McAnally, J. Math. Phys. 36, 574 (1995). https://doi.org/10.1063/1.531323

    Article  ADS  MathSciNet  Google Scholar 

  42. A. Mathai, H.J. Haubold, Phys. A: Stat. Mech. Appl. 375, 110 (2007)

    Google Scholar 

  43. P. Vega-Jorquera, E. de la Barra, H. Torres, Y. Vásquez, Entropy 24, 695 (2022). https://doi.org/10.3390/e240506

    Article  ADS  Google Scholar 

  44. R.A. Estay, J.A. Vallejos, vol. 15 (Chile, 2017)

  45. J.B. Fletcher, L.R. Sykes, J. Geophys. Res. 82, 3767 (1977)

    ADS  Google Scholar 

  46. J.P. Vermylen, M.D. Zoback, Soc. Pet. Eng. (2011)

  47. S. Maxwell, C. Waltman, N.R. Warpinski, M. Mayerhofer, N. Boroumand, S.P.E. Reserv, Eval. Eng. 12, 48 (2009)

    Google Scholar 

  48. J.T. Rutledge, W.S. Phillips, M.J. Mayerhofer, Bull. Seismol. Soc. Am. 94, 1817 (2004)

    Google Scholar 

  49. X. Lei, G. Yu, S. Ma, X. Wen, Q. Wang, J. Geophys. Res. 113, B10310 (2008)

    ADS  Google Scholar 

  50. X. Lei, S. Ma, W. Chen, C. Pang, J. Zeng, B. Jiang, J. Geophys. Res. 118, 4296 (2013)

    ADS  Google Scholar 

  51. J. Ake, K. Mahrer, D. O’Connell, L. Block, Bull. Seismol. Soc. Am. 95, 664 (2005)

    Google Scholar 

  52. S.M. Mousavi, P.O. Ogwari, S.P. Horton, C.A. Langston, Phys. Earth Planet. 267, 53 (2017)

    ADS  Google Scholar 

  53. L. Telesca, T. E. Cherkaoui, M. Rouai, arXiv preprint arXiv:1103.1043, [physics.geo-ph] (2011)

  54. C.S. Vilar, G.S. França, R. Silva, J.S. Alcaniz, Phys. A: Stat. Mech. Appl. 377, 285 (2007)

    Google Scholar 

  55. L. Telesca, Tectonophysics 494(1–2), 155 (2010)

    ADS  Google Scholar 

  56. A. Tzanis, E. Tripoliti, arXiv:1901.09628, [physics.geo-ph] (2019)

  57. F. Vallianatos, G. Michas, G. Papadakis, P. Sammonds, Acta Geophys. 60, 758 (2012)

    ADS  Google Scholar 

  58. C.R. Shalizi, arXiv:math/0701854. https://doi.org/10.48550. (2007)

  59. F. Vallianatos, G. Papadakis, G. Michas, Proc. Math. Phys. Eng. Sci. 472, 20160497 (2016)

    Google Scholar 

  60. S. Rogers, D. Elmo, G. Webb, A. Catalan, Rock Mech. Rock Eng. 48, 633–649 (2015)

    ADS  Google Scholar 

Download references

Acknowledgements

Thanks to the Direction of Research of Development of the University of La Serena (DIDULS), and Project: PTE202138 of the Post-graduate program of the Department of Physics of the University of La Serena.

Author information

Authors and Affiliations

Authors

Contributions

All authors have contributed equally to the research work as well as all have approved the final manuscript.

Corresponding author

Correspondence to Pedro Vega-Jorquera.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de la Barra, E., Vega-Jorquera, P., da Silva, S.L.E.F. et al. Hydraulic fracturing assessment on seismic hazard by Tsallis statistics. Eur. Phys. J. B 95, 92 (2022). https://doi.org/10.1140/epjb/s10051-022-00361-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-022-00361-6

Navigation