A model of energy transport on networks for earthquakes and aftershocks

We propose a model of energy transport in which discrete energy quanta move on complex networks to investigate the dynamics of earthquakes and their aftershocks. In the model, we closely follow the observed dynamics of earthquakes, and thus incorporate energy dissipation after each earthquake and stress readjustments in our model. We introduce an intuitively simple definition of the magnitude of an earthquake as the deviation of the number of quanta from its mean in units of the standard deviation. The model generates time series of earthquakes and aftershocks naturally arising from internal fluctuations. The generated time series are in excellent agreement with the three fundamental empirical laws of seismology: the Omori-Utsu law, the Gutenberg–Richter law and the Bath’s law. We validate our model using data from real earthquakes.