A 1D Spring-Slider Model with a Simple Poly-Linear Failure Law Produces Rich Variations in Slip Behavior

ABSTRACT The failure law prescribed along the fault surface and the elastic stiffness of the surrounding medium play important roles in determining the characteristics of earthquakes. Here we use a 1D spring-slider model that includes inertia, along with a simple poly-linear failure law composed of multiple linear segments to provide insight into earthquake initiation and growth. The poly-linear failure law, which parameterizes shear resistance as a function of slip, allows analytical solutions describing the system for each failure law segment. Analytical solutions facilitate investigation of the effects of the slopes of the different failure law segments in relation to the slope of the elastic loading curve determined by the spring stiffness. Depending on the relation between the slope of the failure law segment and the elastic loading slope, there are three stability regimes in the system: harmonic oscillations, exponential growth, and cubic growth. By combining the different solution regimes within one earthquake cycle, we observe a wide range of behaviors of this simple system: interseismic oscillatory creep, precursory signals before the main event, a shorter or a much longer acceleration phase before the onset of instability, and varying durations of the preseismic and coseismic phases. These results provide a potential explanation for some seismic observations, including increased levels of “seismic noise” prior to an earthquake, precursory events, tremor and low-frequency earthquakes.