Earthquakes induced by the seismic faulting are the most dangerous and unpredictable natural hazards known to man. A typical case was the 1999 Chi-Chi earthquake (Mw 7.7), induced by faulting along the Chelungpu fault resulting in many casualties and enormous damage to property in Taiwan. The earthquake caused a total surface rupture of about 80 - 90 km along the Chelungpu fault and large vertical offsets reaching as high as 8 - 9 m (Chen et al. 2001). The rupture behavior of this earthquake was well recorded by the Taiwan Strong Motion Network (~600 stations) and GPS (130 stations). Using the strong motion and teleseismic data, and GPS displacement, several groups of researchers have produced models of spatial distribution of slip and slip velocity for the earthquake (Johnson et al. 2001; Pathier et al. 2003; Yu et al. 2003). Common results of these studies show that slip occurred over an area of about 80 by 40 km with the hypocenter in the southern region and rupture propagation mainly to the north. Inverted slip distribution have correlated very well with the geological observations. Such studies show that most of the co-seismic slip is at a depth of less than 10 km (Ma et al. 1999; Kao and Chen 2000). A large slip of up to 12 m was found at the northern end of the fault near the surface (Ma et al. 2003). In the northern region of the fault where displacements are very large, the level of ground acceleration and associated building damage is relatively low. Estimates of the slip velocity show that faulting occurred very rapidly (1 - 3 m sec-1) but slip was smooth producing low levels of high-frequency radiation (Wang 2006a, b). In contrast, the southern portion of the fault had much smaller displacements, but the level of accelerations was higher (Wang 2006a, b). One explanation for such very large slips was that a lubrication mechanism may have occurred during the earthquake to reducing dynamic frictional resistance (Ma et al. 2003).