κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes

Sérgio Luiz E.F. da Silva

Chaos, Solitons & Fractals, 2021, vol. 143, issue C

Abstract: The earthquakes statistical analysis are essential for understanding the seismic activity of a region and consequently, in seismic hazard studies. Nowadays, the statistics that describe the relationship between the earthquake magnitude and the total number of quakes in a given region has been dominated by the Gutenberg–Richter (GR) power-law. However, the GR law is only valid from a threshold magnitude (local scale invariance). To mitigate this limitation, we introduce in this work a statistical mechanics approach to appropriately describe the earthquakes in a wide range of magnitudes. In this way, we formulate a generalisation of the GR law based on a κ-probability function, which is a distribution linked to Kaniadakis statistics (or κ-statistics). We have tested the viability of our proposal using real data sets recorded in 6 different regions of the Earth by considering more than 150,000 earthquakes. The results show that the κ-generalised GR law describes appropriately enough the energy distribution in an ample range of magnitudes, especially for low magnitude earthquakes where the standard GR law fails. Besides, the entropic index of the Kaniadakis entropy is a universal parameter with a value close to 1. Furthermore, the results reveal the fractal nature of the fragments filling the space between tectonic plates. They also show the self-similarity of earthquakes regardless of their magnitude.

Keywords: Self-similarity; Kaniadakis statistics; Earthquakes; Fractal distribution; Scale invariance (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077920310134
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310134

DOI: 10.1016/j.chaos.2020.110622

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().