ALBERT

Description: I compare two one-state-variable, rate-dependent, and state-dependent friction laws, that is, the slip law and slowness law, through the analyses of stability conditions based on a dynamic one-degree-of-freedom spring-slider model, subjected to such two kinds of friction. Results show that at low velocities, the stability criteria for the two laws are equal and similar to the steady-state criteria deduced by Ruina (1983). On the other hand, at higher velocities, the stability criterion for the slip law depends not only on the parameters of the friction law, but also on the sliding velocity and state variable of the system, whereas the stability criterion for the slowness law is the same as that at low velocities.

Description: The frequency-dependent site amplifications at 87 free-field strong- motion station sites in central Taiwan are evaluated from the velocity and density structures constructed from borehole data measured at shallow depths and the velocity models inferred from earthquake data at great depths. Results based on the quarter- wavelength approximation method proposed by Boore and Joyner (1997) show that the site amplifications increase with frequency and are larger in the Western Plain with thick Holocene alluvium than in the Western Foothill with Pleistocene and Miocene formations. Considering wave attenuation, site amplification first increases and then decreases with increasing frequency. The turning frequency, f (sub t) , associated with the maximum amplification varies site by site.

Description: Friction is commonly considered an important factor in controlling earthquake rupture. In this work, it is assumed that viscosity is also a significant factor. A strike-slip-type, two-body spring-slider model in the presence of both friction and viscosity is applied to approximate the rupture processes of an earthquake along the fault-striking direction. Results show that in addition to friction, viscosity is also an important factor in controlling rupture. The M (sub s) 7.6 Chi-Chi earthquake which struck central Taiwan on 20 September 1999, ruptured a 100-km-long east-dipping transpressive fault (the Chelungpu fault). Measured and inferred results show that there are differences in physical properties between the northern and southern segments of the fault. Simulation results from a two-body model can explain the differences in displacement, velocity, acceleration, and predominant period between the two fault segments.

Description: The radiation efficiency, eta (sub R) , is an important parameter showing the source property. It is strongly affected by the variation in shear stress with slip. Thermal pressurization is considered to be a significant mechanism in controlling such a variation, thus influencing eta (sub R) . In this study, the formula of eta (sub R) as a function of slip, delta , on the basis of two end-member models of thermal pressurization, that is, the adiabatic-undrained-deformation (AUD) model and slip-on-a-plane (SOP) model proposed by Rice (2006), is derived. The controlling parameters of the AUD and SOP models are, respectively, delta (sub c) and L (super *) , which are dependent on thermal, mechanical, and hydraulic parameters of fault rocks. Modeled results suggest that thermal pressurization controls the variation in shear stress with slip and thus influences the radiation efficiency. Results show that eta (sub R) increases with delta . The increasing rate of eta (sub R) with delta is high at small delta and low at large delta . This indicates that eta (sub R) varies very much with delta for small earthquakes and only slightly depends on delta for large events. For the two end-member models, eta (sub R) increases with decreasing delta (sub c) (or L (super *) ). When delta (sub c) =L (super *) , epsilon (sub R) is higher for the AUD model than for the SOP model. The thermal pressurization model is also applied to investigate the shear stress-slip function in a 5X5 km square covering a drilled site on the fault plane of the 1999 Chi-Chi, Taiwan, earthquake inferred from seismograms. Results show that the AOD model is more appropriate to describe the inferred shear stress-slip function than the SOP model, and the proposed model is a modified one from the AUD model by including a small amount of loss of frictional heat from the slip zone during faulting.

Description: Some intrinsic properties of the two-dimensional (2D) dynamical spring-slider model, subjected to linear slip- or velocity-weakening friction with a uniform, isotropic distribution of static friction strengths at all sliders and loaded by an external constant driving force are studied. First, the continuum model of the spring-slider model is constructed. A comparison between the continuum model, without the driving force and friction, and a 2D wave equation indicates that some of the model parameters are a function of elastic properties of fault-zone materials. The occurrence of P and S waves must be included in the model. Second, the velocities of waves propagating in the model are investigated for three cases: case 1 includes the external force but excludes friction; case 2 includes the external force and slip-weakening friction; and case 3 includes the external force and velocity-weakening friction. Analytical results show that there are two types of waves for the first two cases: P-type waves for case 1 and S-type waves for case 2. The velocity is higher for the former than the latter. The velocities for the two types of waves are increased when the external force is added. Slip-weakening friction results in a decrease in the velocities of the two types of waves. For case 3, there are three types of waves. Velocity-weakening friction makes the velocities of the first type of wave higher than the P-type wave velocity, while it makes the velocity of the second type of wave higher or lower than the S-type wave velocity, depending on the degree of weakening. The velocity of the third type of wave is lower than the P-type wave velocity and higher than the S-type wave velocity.