## 4 Recommendation on Improving the Efficiency of Intensity Measures
### EDP-IM Relationship
#### 4.2.2 Magnitude and Epicentral Distance  
To further discuss the sufficiency of the selected IMs, we examine the dependence of correlations with event magnitude and epicentral distance, considering three different magnitude bins: \(5.0\leq M_{w}\leq 6.0\) (I), \(6.0<M_{w}\leq\)7.0 (II) and \(7.0<M_{w}\leq 8.0\) (III). We compute correlations between ISD and IMs using a moving window approach for each magnitude bin. From all 2D-RC frames, we select three frames with fundamental periods to represent a short (\(T_{f}\) = 0.35 s), intermediate (\(T_{f}\) = 0.82 s) and a long period (\(T_{f}\) = 1.21 s) structure (frames #3, #9, and #14 of Table 1) (henceforth denoted as SP, IP, and LP structures). The distance-dependent correlations of peak, spectral, and energy measures for the different magnitude classes are summarized in Figures 7-9.  
Figure 7: Distance-dependent correlations of peak measures (_PGA_, _PGV_, _PGD_) for different magnitude bins (\(M_{w}\) 5–6, \(M_{w}\) 6–7 and \(M_{w}\) 7–8) (panels **a–i**). Rows correspond to variations in correlations of _PGA_, _PGV_ and _PGD_ for three different types of structures—short period, intermediate period and long period (SP, IP and LP). Correlations of _PGA_ and _PGV_ are almost invariant for SP and IP/LP structures, respectively (panels **a,e,f**). For IP/LP structures, correlations of _PGV_ increase with distance for magnitude bins \(M_{w}\) 6–7 and \(M_{w}\) 7–8. _PGD_ shows significant distance and magnitude dependence for all types of structures.  
From the ten IMs, we find that correlations of \(PGA\) and \(ASI\) are invariant with magnitude and distance for SP structures (Figures 7a and 8a). For IP and LP structures, correlations of \(PGA\) and \(ASI\) decrease for magnitude bin \(M_{\rm w}\) 6-7 in the distance range of 40-70 km. Similar findings appear for energy measures (\(A_{RMS}\), \(I_{A}\) and \(CAV\)). This may be a consequence of several seismological effects such as directivity effects and/or site effects. Correlations with peak measures are strongest for small magnitude events and then decrease with magnitude, especially in the case of \(PGV\) and \(PGD\). The dependence on event magnitude is not significant for \(Sa(T)\) at different distance bins (Figure 8). Among all energy measures, \(A_{RMS}\) and \(I_{A}\) show the lowest correlation with respect to magnitude and distance (Figure 9).  
For the epicentral distance range 30-80 km, distance-dependent correlations are larger for small magnitude events, while correlations with IMs are similar across all magnitude classes beyond 80 km. This behavior of the IMs is expected, because the building response is non-linear close to the source and tends to a more elastic at larger distances from the source. Figure 10 shows the logarithmic ratio of observed response (EDP) and elastic limit for SP, IP and LP structures for different magnitude classes. The elastic limit is taken as the total elastic drift ratio and is computed from pushover analysis. As distance increases, the response becomes linear (ordinate less than zero). Since at far distances, the response is linear for most of the records, the correlations are similar for all magnitude classes. For intermediate distances, the response is significantly linear only for magnitude bin I (\(5<M_{w}<6\)), with stronger higher correlation than the other two classes.  
Figure 8: Distance-dependent correlations of spectral measures (\(ASI\), \(VSI\), \(Sa(T)\)) for different magnitude classes (\(M_{w}\) 5–6, \(M_{w}\) 6–7 and \(M_{w}\) 7–8) (**a–l**). Rows correspond to variations in correlations of \(ASI\), \(VSI\) and \(Sa(T)\) for three different types of structures (SP, IP, LP). Correlations of \(ASI\) (**a–c**) and \(VSI\) (**d–f**) are almost invariant for SP and IP/LP structures, respectively, and do not show any noticeable magnitude dependence. Correlations of \(Sa(T)\) vary less for SP structures than IP or LP.  
Let us now analyze the relationship between IM and EDP based on another seismological parameter, the site class.