Two Memorable Dates in Seismology: Conclusion and References

Table of Links

Abstract and Introduction

Omori (1894)

Hirano (1924)

Discussion

Conclusion and References

Conclusion

So, at the end of the century before last in Japan, the birth of modern seismology occurred due to the fact that at this time and in this place the urgent need of society, state support and human genius miraculously united. We recalled the background and briefly told the story of the discovery of the first law of earthquake physics.

At the beginning of the last century, Hirano drew attention to the fact that the Omori formula does not always satisfactorily describe the flow of aftershocks, and proposed his own version of the law of evolution. Several decades later, Utsu carried out a series of studies using Hirano's formula to process and analyze observations.

The results obtained by Utsu aroused keen interest, were continued, and generated an extensive literature. A thorough study of research carried out using the Utsu method led us to the idea of constructing a phenomenological theory of aftershocks, starting from the simplest differential evolution equation with quadratic nonlinearity.

Within the framework of the phenomenological approach to the physics of aftershocks, it was possible to obtain a number of previously unknown results. In conclusion, we list some of them again:

1. It has been established that Omori’s law is true, but only for a limited period of time after the main shock,

   
   

2. The phenomenon of bifurcation at the end of the epoch of harmonic evolution of the source was discovered,

   
   

3. The Hirano-Utsu formula has been analyzed and shown that it can be used as a fitting formula, but does not have the status of a geophysical law,

   
   

4. The cumulative effect of round-the-world seismic echo was predicted and discovered,

   
   

5. Modulation of global seismicity by spheroidal oscillations of the Earth was discovered,

   
   

6. The phenomenon of aftershock migration was discovered, and an interpretation of migration was proposed within the framework of the Kolmogorov-Petrovsky-Piskunov theory of nonlinear diffusion waves.

   
   

The work was carried out according to the plan of state assignments of Schmidt Institute of Physics of the Earth, Russian Academy of Sciences.

References

1. Hirano R. Investigation of aftershocks of the great Kanto earthquake at Kumagaya // Kishoshushi. Ser. 2. 1924. V. 2. P. 77–83

   
   

2. Omori F. On the aftershocks of earthquake // J. Coll. Sci. Imp. Univ. Tokyo. 1894. V. 7. P. 111–200.

   
   

3. Guglielmi A.V., Zavyalov, A.D., Zotov, O., Klain B.I. Theory of aftershocks of a strong earthquake // Phys. Usp. 2024 (presenfed).

   
   

4. Guglielmi A.V. Foreshocks and aftershocks of strong earthquakes in the light of catastrophe theory // Physics – Uspekhi. 2015. V. 58 (4). P. 384–397.

   
   

5. Guglielmi A.V. Interpretation of the Omori Law // arXiv:1604.07017. // Izv. Phys. Solid Earth. 2016. V. 52. P. 785–786.

   
   

6. Zavyalov, A., Zotov, O., Guglielmi, A., Klain, B. On the Omori Law in the physics of earthquakes // Appl. Sci. 2022, vol. 12, issue 19, 9965. https://doi.org/10.3390/app12199965

   
   

7. Guglielmi A.V. Omori's law: a note on the history of geophysics // Phys. Usp. 2017. V. P. 319–324. DOI: 10.3367/UFNe.2017.01.038039.

   
   

8. Guglielmi A.V., Zavyalov A.D., Zotov O.D. A project for an Atlas of aftershocks following large earthquakes // J. Volcanology and Seismology. 2019. V. 13. No. 6. P. 415–419. DOI: 10.1134/S0742046319060034.

   
   

9. Guglielmi A., Zotov O. Bifurcation of the earthquake source at the end of the Omori epoch // arXiv:2303.02582 [physics.geo-ph]. 2023.

   
   

10. Guglielmi, A.V.; Zotov, O.D. Impact of the Earth’s oscillations on the earthquakes // arXiv:1207.0365. Submitted on 2 Jul 2012. // On the near-hourly hidden periodicity of earthquakes // Izv. Phys. Solid Earth. 2013. V. 49. No. 1. P. 1–8. DOI: 10.1134/S1069351313010047

    
    

11. Zotov, O.D.; Zavyalov, A.D.; Guglielmi, A.V.; Lavrov, I.P. On the possible effect of round-the-world surface seismic waves in the dynamics of repeated shocks after strong earthquakes // Izv. Phys. Solid Earth. 2018. V. 54. No. 1. P. 178–191. DOI: 10.1134/S1069351318010159

    
    

12. Guglielmi, A.V.; Zotov, O.D.; Zavyalov, A.D. The aftershock dynamics of the Sumatra– Andaman earthquake // Izv. Phys. Solid Earth. 2014. V. 5. No. 1. P. 64–72. DOI: 10.1134/S1069351313060037

    
    

13. Zotov O.D.; Guglielmi A.V. Mirror triad of tectonic earthquakes // arXiv:2109.05015 [physics.geo-ph]. 2021.

    
    

14. Zotov O.D, Zavyalov A.D., Klain B.I. On the spatial-temporal structure of aftershock sequences // In: Yanovskaya T. et al. (eds). Problems of Geocosmos–2018, Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. 2020. P. 199. DOI: 10.1007/978-3-030-21788-4_16

    
    

15. Davison Ch. The founders of seismology // Cambridge: University Press. 1930.

    
    

16. Zavyalov A.D., Zotov O.D. A New way to determine the characteristic size of the source zone // Journal of Volcanology and Seismology, Springer Verlag (Germany), 2021 V.15, № 1. P. 19–25. DOI:10.1134/S0742046321010139

    
    

17. Guglielmi A., Zotov O.D. Dependence of the source deactivation factor on the earthquake magnitude // arXiv:2108.02438 [physics.geo-ph]. 2021.

    
    

18. Guglielmi A., Zotov O. Bifurcation of the earthquake source at the end of the Omori epoch // arXiv:2303.02582 [physics.geo-ph]. 2023.

    
    

19. Jeffreys H. Aftershocks and periodicity in earthquakes // Gerlands Beitr. Geophys. 1938. V. 56. P. 111–139.

    
    

20. 
    

    20. Utsu T. A statistical study on the occurrence of aftershocks // Geophys. Mag. 1961. V. 30. P. 521–605.

    
    

21. Utsu T. On the Nature of Three Alaskan Aftershock Sequences of 1957 and 1958 // Bull. Seismol. Soc. Am. 1962. V. 52. P. 279–297.

    
    

22. Utsu T., Ogata Y., Matsu’ura R.S. The centenary of the Omori formula for a decay law of aftershock activity // J. Phys. Earth. 1995. V. 43. № 1. P. 1–33.

    
    

23. Guglielmi A.V., Klain B.I. The Phenomenology of Aftershocks // arXiv:2009.10999 [physics.geo-ph]. 2020.

    
    

24. Faraoni V. Lagrangian formulation of Omori’s law and analogy with the cosmic Big Rip // Eur. Phys. J. C. 2020. V. 80. P. 445.

    
    

25. Zavyalov A.D., Guglielmi A.V., Zotov O.D. Three problems in aftershock physics // J. Volcanology and Seismology. 2020. V. 14. No. 5. P. 341–352.

    
    

26. Kolmogorov A.N., Petrovsky I.G., Piskunov N.S. A study of the diffusion equatio related to increase of material, and its application to a biological problem // Bull. MGU, Ser. A. Matematika i Mekhanika. 1937. V. 1(6). P. 1‒26.