This variation includes a minimum near the fault, increasing up to about 140% of the target Dc value at a distance 2-3 km from the fault. Moreover, contrary to the results by Fukuyama and Mikumo, we observe a strong distance-dependence of the Dc estimates perpendicular to the fault. As a consequence, the method by Fukuyama and Mikumo over-estimates Dc when applied to strong motion data recorded on the earth's surface.
The particle motion recorded by surface instruments is amplified roughly by a factor of two due to the presence of the free surface. Our results show that both the free surface and the stopping phases strongly affect Dc estimates. We assume a vertical strike-slip fault governed by both linear and non-linear slip-weakening friction laws. We use spontaneous rupture propagation simulated by a recently developed and highly accurate approach, namely the staggered-grid split-node (SGSN) method in a fourth-order staggered- grid finite difference method (Dalguer and Day, JGR, 2007). Here, we re-examine the methodology proposed by Fukuyama and Mikumo by means of a more realistic approach.
The study by Fukuyama and Mikumo was based on simple two-dimensional Green's functions in a homogeneous full space for an anti-plane kinematic crack, and suffers from three fundamental omissions: 1) the free surface and heterogeneous structure, 2) the finiteness of the rupture surface and 3) the dynamic rupture complexity of real 3D earthquakes. They concluded that such method allows reliable Dc' estimates with negligible dependence on the perpendicular distance from the fault, and used it to obtain Dc' estimates for the 2000 M6.6 Tottori (0.3 m) and the 2002 M7.9 Denali (2.5 m) earthquakes. The factor of two arises from an equal amount of opposite displacement on either side of the fault. Fukuyama and Mikumo (GRL, 2007) proposed to extend this method beyond the fault plane, by estimating Dc as twice the rake-parallel particle displacement at the time of the peak particle velocity. (BSSA, 2003) proposed a method to estimate Dc on the fault plane as the slip at the time of the peak sliprate function (Dc'). However, such estimates are complicated because of both the limited band-width of the observed seismograms used to image the rupture process and the rapid decay of high frequencies with distance from the fault. Several studies have attempted to estimate Dc indirectly from kinematical analysis of fault ruptures (e.g., Ide and Takeo, JGR, 1997). Obtaining reliable estimates of the frictional behaviour on earthquake faults is a fundamental task, particularly the breakdown slip Dc, which has an important role on rupture propagation through the earthquake energy budget.
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