Abstract
A comparative study is performed on volcanic seismicities at Icelandic volcano, Eyjafjallajökull, and Mt. Etna in Sicily from the viewpoint of complex systems science, and the discovery of remarkable similarities between them is reported. In these seismicities as point processes, the jump probability distributions of earthquakes (i.e., distributions of the distance between the hypocenters of two successive events) are found to obey the exponential law, whereas the waiting-time distributions (i.e., distributions of inter-occurrence time of two successive events) follow the power law. A careful analysis is made about the finite size effects on the waiting-time distributions, and the previously reported results for Mt. Etna (Abe and Suzuki 2015) are reinterpreted accordingly. It is shown that the growth of the seismic region in time is subdiffusive at both volcanoes. The aging phenomenon is commonly observed in the “event-time-averaged” mean-squared displacements of the hypocenters. A comment is also made on (non-)Markovianity of the processes.
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26 April 2017
An erratum to this article has been published.
References
Abe S, Suzuki N (2003) Law for the distance between successive earthquakes. J Geophys Res 108(B2):2113. doi:10.1029/2002JB002220
Abe S, Suzuki N (2005) Scale-free statistics of time interval between successive earthquakes. Physica A 350(2–4):588–596. doi:10.1016/j.physa.2004.10.040
Abe S, Suzuki N (2009) Violation of the scaling relation and non-Markovian nature of earthquake aftershocks. Physica A 388(9):1917–1920. doi:10.1016/j.physa.2009.01.031
Abe S, Suzuki N (2012) Aftershocks in modern perspectives: complex earthquake network, aging, and non-Markovianity. Acta Geophys 60(3):547–561. doi:10.2478/s11600-012-0026-8
Abe S, Suzuki N (2015) Anomalous diffusion of volcanic earthquakes. EPL 110(5):59001. doi:10.1209/0295-5075/110/59001
Bardou F, Bouchaud JP, Aspect A, Cohen-Tannoudji C (2002) Lévy statistics and laser cooling: how rare events bring atoms to rest. Cambridge University Press, Cambridge
Barndorff-Nielsen OE, Benth FE, Jensen JL (2000) Markov jump processes with a singularity. Adv Appl Probab 32(3):779–799. doi:10.1017/S0001867800010259
Boon JP, Lutsko JF (2017) Temporal diffusion: from microscopic dynamics to generalised Fokker–Planck and fractional equations. J Stat Phys 166(6):1441–1454. doi:10.1007/s10955-017-1716-z
Bouchaud JP, Georges A (1990) Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys Rep 195(4–5):127–293. doi:10.1016/0370-1573(90)90099-N
Hill DP, Pollitz F, Newhall C (2002) Earthquake–volcano interactions. Phys Today 55(11):41–47. doi:10.1063/1.1535006
Metzler R, Jeon JH, Cherstvy AG, Barkai E (2014) Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys Chem Chem Phys 16(44):24128–24164. doi:10.1039/c4cp03465a
Omori F (1894) On the after-shocks of earthquakes. J Coll Sci Imp Univ Tokyo 7(2):111–200
Roman DC, Cashman KV (2006) The origin of volcano-tectonic earthquake swarms. Geology 34(6):457–460. doi:10.1130/G22269.1
Schulz JHP, Barkai E, Metzler R (2014) Aging renewal theory and application to random walks. Phys Rev X 4(1):011028. doi:10.1103/PhysRevX.4.011028
Shlesinger MF, Zaslavsky GM, Frisch U (eds) (1995) Lévy flights and related topics in physics. Springer, Heidelberg
Tejedor V, Bénichou O, Voituriez R, Jungmann R, Simmel F, Selhuber-Unkel C, Oddershede LB, Metzler R (2010) Quantitative analysis of single particle trajectories: mean maximal excursion method. Biophys J 98(7):1364–1372. doi:10.1016/j.bpj.2009.12.4282
Tsuji D, Katsuragi H (2015) Temporal analysis of acoustic emission from a plunged granular bed. Phys Rev E 92(4):042201. doi:10.1103/PhysRevE.92.042201
Turcotte DL (1997) Fractals and chaos in geology and geophysics, 2nd edn. Cambridge University, Cambridge
Utsu T (1961) A statistical study on the occurrence of aftershocks. Geophys Mag 30(4):521–605
Zobin VM (2012) Introduction to volcanic seismology, 2nd edn. Elsevier, London
Acknowledgements
The works of SA and NS have been supported in part by the Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science under the contracts (No. 26400391 and No. 16K05484). SA has also been supported in part by the High-End Foreign Expert Program of China and by the Program of Competitive Growth of Kazan Federal University by the Ministry of Education and Science of the Russian Federation.
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The original version of this article was revised: modifications have been made to the Figure 1. Full information regarding corrections made can be found in the erratum for this article.
An erratum to this article is available at https://doi.org/10.1007/s11600-017-0042-9.
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Abe, S., Suzuki, N. Subdiffusion of volcanic earthquakes. Acta Geophys. 65, 481–489 (2017). https://doi.org/10.1007/s11600-017-0029-6
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DOI: https://doi.org/10.1007/s11600-017-0029-6