Statistical physics approach to earthquake occurrence and forecasting

There is striking evidence that the dynamics of the Earth crust is controlled by a wide variety of mutually dependent mechanisms acting at different spatial and temporal scales. The interplay of these mechanisms produces instabilities in the stress field, leading to abrupt energy releases, i.e., earthquakes. As a consequence, the evolution towards instability before a single event is very difficult to monitor. On the other hand, collective behavior in stress transfer and relaxation within the Earth crust leads to emergent properties described by stable phenomenological laws for a population of many earthquakes in size, time and space domains. This observation has stimulated a statistical mechanics approach to earthquake occurrence, applying ideas and methods as scaling laws, universality, fractal dimension, renormalization group, to characterize the physics of earthquakes. In this review we first present a description of the phenomenological laws of earthquake occurrence which represent the frame of reference for a variety of statistical mechanical models, ranging from the spring-block to more complex fault models. Next, we discuss the problem of seismic forecasting in the general framework of stochastic processes, where seismic occurrence can be described as a branching process implementing space–time-energy correlations between earthquakes. In this context we show how correlations originate from dynamical scaling relations between time and energy, able to account for universality and provide a unifying description for the phenomenological power laws. Then we discuss how branching models can be implemented to forecast the temporal evolution of the earthquake occurrence probability and allow to discriminate among different physical mechanisms responsible for earthquake triggering. In particular, the forecasting problem will be presented in a rigorous mathematical framework, discussing the relevance of the processes acting at different temporal scales for different levels of prediction. In this review we also briefly discuss how the statistical mechanics approach can be applied to non-tectonic earthquakes and to other natural stochastic processes, such as volcanic eruptions and solar flares.