Thermal Energy Production and Temperature Distribution in Seismic Faults Based on the Nonlinear Dynamics of a One-Body Spring-Slider

Abstract

This study focuses on thermal energy production by frictional forces between the walls of a seismic fault, and equally analyzes the temperature distribution. Consequently, we consider a one-dimensional spring-slider model of earthquake fault in the presence of nonlinear elasticity and viscosity. Based on the method of multiple scales, we determine the analytical solutions of the resultant equation of motion. It is shown that the viscosity and cubic nonlinear parameters strongly modifies the time evolution of the block displacement. The amplitude of block displacement decreases with increasing viscosity, and increases as the cubic nonlinear parameter is gradually stepped up. Results of numerical simulations based on the Gaussian quadrature method reveals that the thermal energy increases abruptly after a certain amount of time when the frictional forces is stronger than viscous effect; otherwise, the thermal energy regularly increases until it reaches an asymptotic value. In both cases, the amplitude of the thermal energy decreases with increasing viscosity and cubic nonlinear parameter. The system generally displays a regular temperature change during a long time interval, followed by abrupt temperature increase. However in the regime of very strong viscosity of the medium, the temperature increases, attains a maximum value before decreasing and thenmigrates toward a stationary state. The calculated thermal energy can be validated by direct measurement via geophysical resistivity method.

Keywords: Earthquake dynamics, Thermal energy, Viscosity, Cubic nonlinear parameter, Temperature distribution.