An Analytic Study of Frictional Effect on Slip Pulses of Earthquakes

Abstract

Seismological observations show the existence of slip pulses with T_R/T_D<0.3, where T_R and T_D are, respectively, the rise time at a site on a fault and the duration time of ruptures over the fault. An analytical study of generation of a slip pulse is made based on the continuous form of 1-D spring-slider model, with uniform fault strengths, in the presence of linear, slip-weakening (SW) friction: f=1-u/D (u=the displacement and D=the characteristic distance) or linear, velocity-weakening (VW) friction: f=1-v/u (v=the velocity and u=the characteristic velocity). Let w_o and t_r are, respectively, the predominant angular frequency of the system and the arrival time at a site and define g=(1-1/D)^1/2 and s=(1-1/4u²)^1/2. There are complementary solution (CS), and particular solution (PS) of the equation of motion. The CS shows a slip pulse under some ranges of model parameters for SW friction and for VW friction when u>>1; while the CS shows a crack-like rupture for VW friction when u is not too large. For SW friction, T_R and T_R/T_D decrease when the slip pulse propagates in advance along the fault and when w_o and g increase. T_R and T_R/T_D also depend on v_R (rupture velocity) and increasing L (fault length). For the PS, T_p/T_D is a good indication to show the existence of pulse-like oscillations at a site, because T_p (the predominant period of oscillations at a site) is slightly longer than T_R. Results show the existence of a pulse-like oscillation at a site for the two types of friction. A pulse-like oscillation is generated when D>1.6 for SW friction and when u>0.6 for VW friction. T_p/T_D decreases with increasing D. For the two types of friction, T_o/T_D decreases when v_R and L increase.