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.

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