We have taken advantage of the great collection of ground-motion acceleration records from the Central Weather Bureau of Taiwan to derive new attenuation relations corresponding to different geological settings: the shallow crustal earthquakes in the active tectonic region and the subduction zone. The new equations use a shape of magnitude dependence modulated by depth effect. For shallow crustal earthquakes, the focal depth also plays an adjusting factor for the geometrical spreading. A two-step stratified regression is used to decouple the evaluations of the distance dependence of data from that of magnitude and focal depth. The resultant attenuation relations are as follows.

Using the data from shallow crustal earthquakes, we obtained:  
\[\begin{array}{l}\mathrm{ln}{\ }A=2.8096+0.8993\mathbf{M}-0.4381{\ }\mathrm{ln}{\ }D_{\mathrm{p}}-(1.0954-0.0079D_{\mathrm{p}}){\ }\mathrm{ln}{\ }D_{\mathrm{e}},\\{\sigma}=0.60.\end{array}\]
Using the data from the subducting-plate earthquakes, we obtained:  
\[\mathrm{ln}{\ }A=4.7141+0.8468\mathbf{M}-0.1745{\ }\mathrm{ln}{\ }D_{\mathrm{p}}-1.2972{\ }\mathrm{ln}{\ }D_{\mathrm{h}},{\sigma}=0.56,\]

where A is the ground-motion acceleration in gal (cm/sec2), De and Dh are the epicentral and the hypocentral distances (km), respectively, Dp is the focal depth (km), M is the moment magnitude, and σ the standard deviation.

Several comparisons between our resulting attenuation relations and the others are presented in this study. Compared with other empirical attenuation models of Taiwan, our results show a better fit for the Chi-Chi earthquake. These new attenuation laws predict a stronger ground motion in the far distance for the shallow crustal earthquakes as compared with previous studies. Our results also show lower ground motions than the other countries for subduction zone events. The residual ground-motion maps show a high consistency with the local geology of Taiwan.

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