An Analytic Study of Frictional Effect on Slip Pulses of Earthquakes
Annals of Geophysics
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/Δ (u=the displacement and Δ=the characteristic distance) or linear, velocity-weakening
... W) friction: f=1-v/υ (v=the velocity and υ=the characteristic velocity). Let ω 0 and t r are, respectively, the predominant angular frequency of the system and the arrival time at a site and define γ=(1-1/Δ) 1/2 and σ=(1-1/4υ 2 ) 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 υ>>1; while the CS shows a cracklike rupture for VW friction when υ 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 ω 0 and γ 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 Δ>1.6 for SW friction and when υ>0.6 for VW friction. T p /T D decreases with increasing Δ. For the two types of friction, T o /T D decreases when v R and L increase. Jeen-Hwa WANG 2 FIGURE 1. An N-degree-of-freedom dynamical spring-slider system. FIGURE 10. The plots of T p /T p versus υ: (a) for v R T 0 =0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 km (from bottom to top) when L=80 km; and (b) for L=20, 40, 60, 80, 100, 120, 160, and 180 km (from top to bottom) when v R T 0 =2.0 km.