The Chi-Chi 1999 earthquake: Correlation between the spatio-temporal distribution of aftershocks and viscoelastic stress changes

The Chi-Chi 1999 (M_L = 7.3) earthquake generated a large number of aftershocks in the vicinity of the rupture plane. The spatial-temporal distribution of these aftershocks was recorded with high precision and thus provided a unique possibility to study whether the correlation between aftershocks and stress changes are primary due to coseismically induced stress changes (static), or whether stress relaxation processes (viscoelastic) in the lower crust contribute significantly to this correlation. From our analysis of a 3D finite element model simulating the viscoelastic stress changes due to the coseismic displacement and tectonic loading we found that the aftershocks are highly correlated with the stress variations (static and viscoelastic) caused by the main shock. Although we found that the correlation between seismicity rate changes and viscoelastic stress fluctuation is slightly better than that of the static stress changes, these differences can only be identified well in the lower crust. As a result, it is reasonable to conclude that static stress changes are the key mechanism for triggering early and shallow aftershocks in the upper crust. It is reasonable to infer that the viscoelastic relaxation in the lower crust does affect the occurrence of early aftershocks in the deep crust, but it does not significantly affect the shallow aftershocks. However, the stress changes induced from the lower crust gradually transfer to the upper crust and may influence the occurrence of aftershocks after a longer time period (>four Maxwell times).     

Study of nonlinear behaviors of geological materials

Two polynomial constitutive equations of nonlinear stress–strain relationship were used to construct two nonlinear 1-D wave equations with external pressure (source term) applied. Nonlinear model 1 was a concave downward curve, and nonlinear model 2 was a concave upward curve. The time-dependent stress and strain of a 300-m length were calculated. The computation for nonlinear model 1 terminated at time t?=?5.0 s. The evaluated stress versus position at different times was mainly at position x?=?0 m. The stress versus position had a concave point at position x?=?0.3 m. Between x?=?0 m and x?=?0.3 m, the graph of stress versus position showed a small convex upward curve. Moreover, at the two sides of x?=?0.3 m, the strain position had distinctively different slopes. The distinctive difference in the slope of strain at position x?=?0.3 m can therefore be used to estimate the rupture position of a rock. The terminal evaluation time for nonlinear model 2 was at t?=?1.55 s. The stress versus position and the strain versus position to time change were within the 0–3 m interval from the pressure end. Time increase produced the phenomenon of stress and strain solitons. These stress and strain solitons moved forward and increased in peak value with time. During the compression process, the stress and strain soliton resulted in instability which rendered the rock situation more easily broken. The position of the rock rupture might have occurred away from the pressure side.