Nonextensive Gutenberg–Richter law and the connection between earthquakes and marsquakes

Abstract

The physical analysis of earthquakes is essential for the exploration of the interior structure of a region. Nowadays, the statistics of earthquakes’ occurrence are dominated by the Gutenberg–Richter (GR) law. Here, we report evidence of the similarity between earthquakes and marsquakes by using the generalized GR law in the context of Tsallis nonextensive statistical mechanics. We analyze the Martian quakes that were recorded by the InSight’s seismometer in the Elysium Planitia region, Mars, from January 2019 to December 2019, which corresponds to the first year of geophysical observations by Nasa’s InSight mission. The results show evidence for the similarity between the triggering mechanism of earthquakes and marsquakes. They also reveal the fractal nature of the Martian geological faults.

Graphic Abstract

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data supporting the results of this study are freely available as indicated in the manuscript.]

References

  1. 1.

    W.B. Banerdt, S.E. Smrekar, D. Banfield, D. Giardini, M. Golombek, C.L. Johnson, P. Lognonn, A. Spiga, T. Spohn, C. Perrin, S.C. Sthler, 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. Weber, M. Wieczorek, Nat. Geosci. 13, 183 (2020)

    ADS  Google Scholar 

  2. 2.

    D. Giardini, P. Lognonn, W.B. Banerdt, W.T. Pike, U. Christensen, S. Ceylan, J.F. Clinton, M. van Driel, S.C. Sthler, M. Bse, R.F. Garcia, A. Khan, M. Panning, C. Perrin, D. Banfield, E. Beucler, C. Charalambous, F. Euchner, A. Horleston, A. Jacob, T. Kawamura, S. Kedar, G. Mainsant, J.-R. Scholz, S.E. Smrekar, S. Spiga, C. Agard, D. Antonangeli, S. Barkaoui, E. Barrett, P. Combes, V. Conejero, I. Daubar, M. Drilleau, C. Ferrier, T. Gabsi, T. Gudkova, K. Hurst, F. Karakostas, S. King, M. Knapmeyer, B. Knapmeyer-Endrun, R. Llorca-Cejudo, A. Lucas, L. Luno, L. Margerin, J.B. McClean, D. Mimoun, N. Murdoch, F. Nimmo, M. Nonon, C. Pardo, A. Rivoldini, J.A.R. Manfredi, H. Samuel, M. Schimmel, A.E. Stott, E. Stutzmann, N. Teanby, T. Warren, R.C. Weber, M. Wieczorek, C. Yana, Nat. Geosci. 13, 205 (2020)

    ADS  Google Scholar 

  3. 3.

    M. Golombek, R. Phillips, Chapter 5, Mars tectonics, in Planetary Tectonics, 1st edn., ed. by T. Watters, R. Schultz (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  4. 4.

    A. Yin, Lithosphere 4, 286 (2012)

    ADS  Google Scholar 

  5. 5.

    P. Talwani, Intraplate Earthquakes, 1st edn. (Cambridge University Press, Cambridge, 2014)

    Google Scholar 

  6. 6.

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

    ADS  Google Scholar 

  7. 7.

    C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World, 1st edn. (Springer Science Business Media, Berlin, 2009)

    Google Scholar 

  8. 8.

    R. Burridge, L. Knopoff, Bull. Seismol. Soc. Am. 57, 341 (1967)

    Google Scholar 

  9. 9.

    Z. Olami, H.J.S. Feder, K. Christensen, Phys. Rev. Lett. 68, 1244 (1992)

    ADS  Google Scholar 

  10. 10.

    V. De Rubeis, R. Hallgass, V. Loreto, G. Paladin, L. Pietronero, P. Tosi, Phys. Rev. Lett. 76, 2599 (1996)

    ADS  Google Scholar 

  11. 11.

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

    ADS  Google Scholar 

  12. 12.

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

    Google Scholar 

  13. 13.

    B. Gutenberg, C.F. Richter, Seismicity of the Earth and Associated Phenomena, 1st edn. (Princeton University Press, Princeton, 1944b)

    Google Scholar 

  14. 14.

    K. Aki, Bull. Earthq. Eng. 43, 237 (1965)

    Google Scholar 

  15. 15.

    T. Hirata, J. Geophys. Res. 96, 07507 (1989)

    ADS  Google Scholar 

  16. 16.

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

    Google Scholar 

  17. 17.

    V.G. Kossobokov, V.I. Keilis-Borok, B. Cheng, Phys. Rev. E 61, 3529 (2000)

    ADS  Google Scholar 

  18. 18.

    D. Sornette, A. Helmstetter, Phys. Rev. Lett. 89, 158501 (2002)

    ADS  Google Scholar 

  19. 19.

    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 

  20. 20.

    F. Vallianatos, G. Michas, G. Papadakis, Chapter 2, Nonextensive statistical seismology: an overview, in Complexity of Seismic Time Series, edited by T. Chelidze, F. Vallianatos, L. Telesca (Elsevier, Amsterdam, Netherlands 2018)

  21. 21.

    V. Saltas, F. Vallianatos, D. Triantis, I. Stavrakas, Chapter 8, Complexity in laboratory seismology: from electrical and acoustic emissions to fracture, in Complexity of Seismic Time Series, edited by T. Chelidze, F. Vallianatos, L. Telesca (Elsevier, Amsterdam, Netherlands, 2018)

  22. 22.

    L. Telesca, Phys. A 389, 1911 (2010)

    Google Scholar 

  23. 23.

    L. Telesca, Entropy 13, 1267 (2011)

    ADS  Google Scholar 

  24. 24.

    F. Vallianatos, G. Michas, G. Papadakis, A. Tzanis, Nat. Hazards Earth Syst. Sci. 13, 177 (2013)

    ADS  Google Scholar 

  25. 25.

    C. Papadimitriou, M. Kalimeri, K. Eftaxias, Phys. Rev. E 77, 036101 (2008)

    ADS  Google Scholar 

  26. 26.

    G. Papadakis, F. Vallianatos, P. Sammonds, Pure Appl. Geophys. 172, 1923 (2015)

    ADS  Google Scholar 

  27. 27.

    C. Tsallis, http://tsallis.cat.cbpf.br/TEMUCO.pdf. Accessed 25 Sep 2020

  28. 28.

    M. Bertero, M. Piana, Inverse Problems in Biomedical Imaging: Modeling and Methods of Solution, 1st edn. (Springer-Verlag Italia, Milano, 2006)

    Google Scholar 

  29. 29.

    S.L.E.F. da Silva, C.A.N. da Costa, P.T.C. Carvalho, J.M. de Arajo, L.S. Lucena, G. Corso, Phys. A 548, 124473 (2020)

    MathSciNet  Google Scholar 

  30. 30.

    M. Prato, L. Zanni, J. Phys. Conf. Ser. 135, 012085 (2008)

    Google Scholar 

  31. 31.

    F. Vallianatos, G. Papadakis, G. Michas, Proc. R. Soc. A 472, 0497 (2016)

    Google Scholar 

  32. 32.

    I.P. de Lima, S.L.E.F. da Silva, G. Corso, J.M. de Arajo, Entropy 22, 464 (2020)

    ADS  Google Scholar 

  33. 33.

    E.T. Jaynes, Phys. Rev. 106, 620 (1957)

    ADS  MathSciNet  Google Scholar 

  34. 34.

    E.T. Jaynes, Phys. Rev. 108, 171 (1957)

    ADS  MathSciNet  Google Scholar 

  35. 35.

    A. Sumiyoshi, G.B. Bagci, Phys. Rev. E 71, 016139 (2005)

    Google Scholar 

  36. 36.

    C. Beck, F. Schlogl, Thermodynamics of Chaotic Systems: An Introduction, 1st edn. (Cambridge University Press, Cambridge, 1993)

    Google Scholar 

  37. 37.

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

    ADS  MathSciNet  Google Scholar 

  38. 38.

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

    ADS  Google Scholar 

  39. 39.

    C. Beck, Phys. A 342, 139 (2004)

    Google Scholar 

  40. 40.

    A.H. Darooneh, G. Naeimi, A. Mehri, P. Sadeghi, Entropy 12, 2497 (2010)

    ADS  MathSciNet  Google Scholar 

  41. 41.

    C.S. Vilar, G.S. Frana, R. Silva, J.S. Alcaniz, Phys. A 377, 285 (2007)

    Google Scholar 

  42. 42.

    S.M. Valverde-Esparza, A. Ramrez-Rojas, E.L. Flores-Mrquez, L. Telesca, Acta Geophys. 60, 833 (2012)

    ADS  Google Scholar 

  43. 43.

    L. Telesca, T.-E. Cherkaoui, M. Rouai, J. Nonlinear Sci. 14, 287 (2012)

    Google Scholar 

  44. 44.

    S.L.E.F. da Silva, J. Juli, F.H.R. Bezerra, Bull. Seismol. Soc. Am. 107, 1495 (2017)

    Google Scholar 

  45. 45.

    Mars Seismic Catalogue, InSight Mission, http://www.insight.ethz.ch/seismicity/catalog/v2 (2020). Accessed 15 July 2020

  46. 46.

    K. Pearson, O.M.F.E. Henrici, Philos. Trans. R. Soc. Lond. A 187, 253 (1896)

    ADS  Google Scholar 

  47. 47.

    T.M. Scherrer, G.S. Frana, R. Silva, D.B. Freitas, C.S. Vilar, Braz. J. Geophys. 36, 559 (2018)

    Google Scholar 

  48. 48.

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

    ADS  Google Scholar 

  49. 49.

    F. Vallianatos, EPL 102, 28006 (2013)

    ADS  Google Scholar 

  50. 50.

    F. Vallianatos, E. Kokinou, P. Sammonds, Acta Geophys. 59, 770 (2011)

    ADS  Google Scholar 

  51. 51.

    G. Michas, F. Vallianatos, P. Sammonds, Earth Planet. Sci. Lett. 431, 150 (2015)

    ADS  Google Scholar 

  52. 52.

    L.C. Malacarne, R.S. Mendes, E.K. Lenzi, Phys. Rev. E 65, 017106 (2001)

    ADS  Google Scholar 

  53. 53.

    J.C. Carvalho, J.D. do Nascimento, R. Silva, J.R. de Medeiros, Astrophys. J. Lett. 696, L48 (2009)

  54. 54.

    F. Vallianatos, P. Sammonds, Phys. A 389, 4989 (2010)

    Google Scholar 

  55. 55.

    Y. Liu, S.Q. Liu, K. Xu, Phys. Plasmas 19, 073702 (2012)

    ADS  Google Scholar 

  56. 56.

    F. Vallianatos, P. Benson, P. Meredith, P. Sammonds, EPL 97, 58002 (2012)

    ADS  Google Scholar 

  57. 57.

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

    ADS  Google Scholar 

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Acknowledgements

G.C. thanks Brazilian National Council for Scientific and Technological Development (CNPq, Portuguese: Conselho Nacional de Desenvolvimento Cientfico e Tecnolgico) for his productivity fellowship (Grant no. 304421/2015-4).

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All authors developed the clarification of the method used in this article and wrote the manuscript. SLEFDS did all analytically calculations, including formula derivation, and created all figures under the supervision of GC, which checked the results and revised the paper.

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Correspondence to Sérgio Luiz E. F. da Silva.

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da Silva, S.L.E.F., Corso, G. Nonextensive Gutenberg–Richter law and the connection between earthquakes and marsquakes. Eur. Phys. J. B 94, 25 (2021). https://doi.org/10.1140/epjb/s10051-020-00015-5

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