Nonextensive models for earthquakes

Abstract

We have revisited the fragment-asperity interaction model recently introduced by Sotolongo-Costa and Posadas (Physical Review Letters 92, 048501, 2004) [1] by considering a different definition for mean values in the context of Tsallis nonextensive statistics and introducing a new scale between the earthquake energy and the size of fragment ǫ ∝ r 3 . The energy distribution function (EDF) deduced in our approach is considerably different from the one obtained in the above reference. We have also tested the viability of this new EDF with data from two different catalogs (in three different areas), namely, NEIC and Bulletin Seismic of the Revista Brasileira de Geofísica. Although both approaches provide very similar values for the nonextensive parameter q, other physical quantities, e.g., the energy density differs considerably, by several orders of magnitude.

Tsallis-Based Nonextensive Analysis of the Southern California Seismicity

“…Equation 14 is slightly different from that obtained by Silva et al [9], who used the relation m = log(İ)/3.…”

“…The use of the nonextensive Tsallis formalism [8] was, then, implied by the physical picture of such a model and a fragment size distribution was derived, which, combined with the roughness of the fault planes, leads to a mechanism of earthquake triggering. The Sotolongo-Costa and Posadas' model was revisited by Silva et al [9], who adopted a more realistic relationship between earthquake energy and fragment size, in full agreement with the standard theory of seismic moment scaling with rupture length [10]; as a consequence, a slightly different magnitude distribution was deduced, providing an excellent fit to seismicity generated in various seismic regions. This model was recently applied to regional seismicity, covering diverse geological faults, down to specific seismic zones [11][12][13][14].…”

“…The model, as developed by Silva et al [9], assumes that the eventual relative position of fragments filling the space between two irregular faults can hinder their relative motion. Stress increases until a displacement of one of the asperities, due to the displacement of the hindering fragment, or even its breakage in the point of contact with the fragment leads to a relative displacement of the fault planes of the order of the size ȡ of the hindering fragment, with the subsequent energy release İ [7].…”

Correlação De Longa-Duração E Analíse Bayesiana Da Evolução Temporal Dos Terremotos Ao Longo Da Falha De Samambaia, Nordeste Do Brasil

“…No contexto de sistemas com falha, como é o caso da Falha de Samambaia, isto representa um fenômeno com complexidade espaço-temporal, investigado através da deformação e ruptura repentina de algumas partes da crosta terrestre controlada pelo movimento convectivo no manto, isto é, a radiação de energia na forma de ondas sísmicas. Em particular, a Falha de Samambaia é, segundo Silva et al (2006), um exemplo característico de sistema complexo auto-organizado na natureza. Assim como inúmeros estudos a respeito dos sistemas complexos na natureza, a investigação sobre o comportamento dos terremotos passa pela questão da previsibilidade, ou seja, que parâmetros e variáveis extraídas dos dados sismológicos, ou outra espécie de registro, são indicadores que possam prever determinado evento?…”

Multidimensional earthquake frequency distributions consistent with Non-Extensive statistical physics: The interdependence of magnitude, interevent time and interevent distance in North California

“…The frequency-magnitude distribution has been approximated with a number of NSEP-compatible models (Sotolongo-Costa and Posadas, 2004;Silva et al, 2006;Telesca 2011Telesca , 2012. These all consider the interaction of two rough fault walls (asperities) and the fragments filling space between them, which is supposed to modulate earthquake triggering (the fragment-asperity model).…”