Open dissipative seismic systems and ensembles of strong earthquakes: Energy balance and entropy funnels

Abstract

A concept of seismic system (SS), which is responsible for the preparation of an ensemble of strong earthquakes, is considered as an open dissipative system exchanging energy and entropy with the environment. Open dissipative SS allow one to describe the equilibrium and non-equilibrium states of SS, and the lithosphere evolution under different plate tectonic settings on the basis of seismostatistics. Several new seismic parameters ('seismic temperature', 'seismic time', dissipation function, efficiency, inelastic energy, dynamical probability) are defined and proposed for better understanding and describing the dynamical processes. The Sakhalin SS is considered to illustrate the behaviour of proposed parameters. By analogy to Liouville's equation in thermodynamics, it is shown that there is no criterion of instability in the domain where the Gutenberg-Richter law is true. In the proposed approach, the instability origination and the formation of seismogenic structures in the lithosphere are based on the energy versus information entropy power law; the existence of 'time arrow' also proceeds from such a dependence. Application of energy and trajectory diagrams enables to describe the preparation of strong earthquakes within an ensemble in terms of slow and fast timescales. These diagrams help perform the spatiotemporal-energy monitoring of the instability origination in the lithosphere. It is shown that the information entropy parameter can serve as a measure of the unknown external energy flow into the system (this energy is supplied for the elastic radiation energy in the earthquake sources and for inelastic processes in the system volume). The property of the ensemble of strong earthquakes is periodically to restore the SS equilibrium state that enables to describe the SS energy balance. The results offer possibilities to estimate the fraction of inelastic energy released by the SS medium during the preparation and occurrence of seismic catastrophes. The construction of phase diagrams and 'entropy funnels' in the virtual space (with time, energy and entropy coordinates) can provide new opportunities for the visualization of undetectable processes leading to disastrous earthquakes.