Dynamics of the nonlinear viscoelastic slider-block model

Abstract:

The full understanding and modeling of earthquake physics remains a challenging task. Presently, there are several approaches to model the earthquake dynamics. They include the full elasto-dynamic simulation of rupture propagation and initiation. The stochastic approach employs the forward and inverse analysis of various point process models. Another approach assumes that the fault can be modeled by an array of blocks which interact with the loading plate and between each other. These approaches were successful in reproducing some aspects of observed seismicity.

In this work, we analyze the slider-block model where we introduce a nonlinear visco-elastic interaction between blocks and the tectonic loading plate, which mimics the rheology of the fault system. This approach preserves the full inertial effects in the system that are generally neglected in cellular automaton version of this model.

The slider-block model consists of N elements which are governed by non-linear differential equations. The fault zone is modelled by an array of N interacting elements, driven by tectonic loading force. The frictional force is also applied between the elements and the substrate. Earthquakes in this system are realized as slipping events with different sizes. The model is characterized by a set of tuning parameters with clear physical significance: the elasticity, the viscosity, the shear rate exponent which controls the nonlinearity. The properties of the model, including the motion pattern, the interevent time statistics, the frequency-size distributions are examined. By tuning the parameter sets, one can easily explore the phase space of the model, and determine the factors that control various aspects of the system behaviour, providing more insight into real earthquakes.