The parameter study in the hypocentre space allows us to extract the PGVs of all 24 sim- ulations containing the dominant features of the two previously shown examples (e.g., basin wide shaking, fault-distance dependent ground motion, and ground motion elevation by the slip asperity). The variations of the hypocentre-dependent ground motions can be expressed by relating the variance and the maximum of the PGV to the mean PGV at each point of the surface grid. Two ratios are calculated and shown to characterize the variations: RSD – the one of the standard deviation relative to the mean value, and Rmax – the one between the maximum value and the mean value. The results are illustrated for all the three components in Fig. 6.6. The maximum value will provide the ground motion range excited by this set of hypothetic M7 earthquakes (different in hypocentre location). The ratios,RSD andRmax, are used to show the possible range of the variation.
In the region B, the maximum velocity of thex-component (Fig. 6.6top left) is compatible to that of they-component (Fig. 6.6middle left) and almost three times larger than that of
6.6 Inter-event Variations of Ground Motion 51
Figure 6.6: Statistics of the PGV distributions due to varying hypocentres. Left. Maximum value. Middle. The ratio between the standard deviation (SD) and the mean value (in percent). Right. The ratio between the maximum value and the mean value. From top to bottom are x-, y- and z-components, respectively. The dashed black rectangle indicates the fault trace. Thin curved white lines are contours of the depth of the shear wave velocity isosurface at 2.0 km/s. Regions A, B and C and stations D, E and F are picked up for more detailed discussion.
the vertical component (Fig. 6.6 bottom left). For the fault perpendicular component, the largest velocity happens right on the fault projection (Fig. 6.6middle left), while that is not the case for the other two components (Fig. 6.6top and bottom left). The largest velocity of thex-component is not right on but very close to the fault projection (Fig. 6.6top left). While the vertical component velocity has the largest value at the station E which is located at the basin edge and a certain distance from the fault projection (Fig. 6.6bottom left). Inside the basin, all three components of velocities are elevated (Fig. 6.6 left) and the x-component is the most obviously one when we focus on the small basin marked as region A.
The spatial distribution of the ratio,RSD, is also shown. The distribution of this variable shows where large variation will be introduced into the ground motions when the hypocentre location is varied. The results are shown in the middle column of Fig. 6.6. For thex-component (fault parallel component), in the region C where the basin depth changes dramatically, the largest RSD (around 70% ) is found (Fig. 6.6 top middle). The RSD in the region C is also larger than the left parts of the study area. This distribution is not observed for the other two components. For the other two components, RSD is large in the regions off the two tips of the fault trace, or at stations which are located at the position with angles to the fault trace smaller than 45◦. Right on the fault projection, the RSD of the fault perpendicular component (y-component) is around 50% and larger than that of the other two components. For thex-and z-components, whereas, smallerRSD is observed right on the fault projection, when compared to the neighboring regions. In the small basin (region A), there is always large RSD observed when compared to the neighboring area, which distinctly indicates that the medium will also amplify the variations.
The spatial distributions of the ratio Rmax (between the maximum value and the mean value) are shown in the right column of Fig. 6.6for all three components. For thex-component, the distribution of this ratio is quite similar to that of the ratio RSD (between the standard deviation and the mean value). Both the largest Rmax and the largest RSD happen at the same location, namely in the region C. The largestRmax for thex-,y-andz-components over the entire study area are around 3.3, 2.5 and 2.5, respectively, while the smallest ratios are 2.2, 1.3 and 2.1. Rmax of the vertical component is distributed inside a much narrower band than the other two components. The expansion in terms of RSD is almost equal between different velocity components. The slight difference is the different structure amplification effect on the y-component (at station D) and the z-component (at station F). For the y-component, the largest Rmax over the entire study area is located at station D at the basin edge. Since station F is right above the middle of the fault projection where the directivity effect is small, focusing on the Rmax at this station for thez-component, we conclude that the structure has bigger contribution to the variation of this ratio than the ratio RSD.
Observing the different distributions of the variations (RSD and Rmax) or the maximum value between different components, we would like to conclude that the directivity will domi- nate more obviously the fault perpendicular component than the other two components. This conclusion explains, also, why large variations are observed right on the fault trace for the
y-component, but not for the other two components.
The modulus of the two horizontal velocity components is used in the process of seis- mic hazard assessment. The resulting distribution for that component is shown in Fig. 6.7 which illustrates where large variations of ground motions are expected when we change the hypocentre location. These variations (ratio between the standard deviation and the mean value) are distributed symmetrically around the fault edges with some amplification from the basin edges particularly on the south east fault trace end (inside region A). Large variation
6.7 Comparison with the Empirical Results 53