By using the maximum entropy principle with Tsallis entropy and under the assumption that the gouge plays an active role in the triggering of earthquakes, we obtain a functional dependence for energy distribution function for earthquakes which fits very well with observations in the region of small energies. This distribution function is related to the size distribution function of fragments in the gouge.
Mediante el principio de máxima entropía con la entropía de Tsallis, y asignando un papel activo al gouge en la generación de terremotos, se obtiene una dependencia funcional que describe la distribución de terremotos por energía que exhibe muy buena correspondencia con las observaciones en la región de bajas energías. Esta distribución está relacionada con la distribución de fragmentos existente entre las placas tectónicas.
The Gutenberg-Richter law (1) has motivated a mass of research. This is due to the importance of the knowledge of the energy distribution of earthquakes and its physical and practical implications. Some famous models like those of Burridge- Knopoff (2) and Olami-Feder-Christiansen (3) have focused in the mechanical phenomenology of earthquakes through simples images which capture essentials of the nature and genesis of a seism: the relative displacement of tectonics plates or the relative movement of the hanging wall and footwall in a fault and also, the existence of a threshold for a catastrophic release of energy in the system.
The irregular geometry of then profiles of the tectonic plates was highlighted in (4) using a geometric viewpoint to deduce the power law dependence of earthquake energy distribution with good results. The importance of a geometric viewpoint for this phenomenon has been also highlighted in (5), where an idealized representation of the fragmented core of a fault (gouge) was presented.
Today it is widely accepted that most earthquakes are originated by relative motion of fault planes, whereas the images to model this energy release are diverse. The standard earthquake picture usually assigns the cause of an earthquake to some kind of rupture or some stick-slip mechanism in which the friction properties of the fault play the determinant role. A review of these viewpoints and some generated paradoxes can be found in (6). Though the gouge has been recognized as an important factor in the dynamics of the earth's crust, we think that its role is more active in small faults and we intend to corroborate this viewpoint in this paper.
In (5) the gouge was idealized to be medium formed by circular disk-shaped pieces filling the space between two planes acting like bearings. Here, we present a more realistic approximation, considering that the surfaces of the tectonic plates are irregular and the space between them contains fragments of very diverse shape.
We will present the geometric image of what we will call a "gouge earthquake" and we will justify the attempt in next sections to find the size distribution function of the fragments. Finally, we will compare our theoretical results with the earthquakes registered in the South of the Iberian...