## 4 Discussion
### Effects of Height Ratio, Mass Ratio, and Inertial Interaction  
Several previous researches have reported an increment in structure response because of the appearance of a neighboring structure which is taller and more massive or has a lower fixed-base frequency [16; 17; 18; 30; 31; 32]. However, in the present study, the influence of fixed-base frequency on SSSI phenomena could be neglected because a reduction in response of S1 structure was observed when located near S2 or S3 building, although S2 building had a lower fixed-base frequency, while S3 structure had a higher fixed-base frequency compared to S1 structure (Table 1). Furthermore, an increment in S2 structure response was obtained when higher fixed-base frequency S1 structure was placed nearby regardless of the distance between two structures, type, or level of input motions. Figure 10 illustrates the relationship between height ratio (\(\chi\)) and \(\Delta\)PSD at low and high input intensities of two input motions. The results of [PERSON] et al. [32] were also included for comparison indicating a similar observation: There was a decrease in response of higher structure (where \(\chi\) was smaller than unity) and an increase in lower structure regardless of types or levels of input excitation. Transferred seismic vibration of higher structure might have increased the response of a shorter structure during an earthquake excitation and vice versa [30]. Moreover, maximum and minimum values of \(\Delta\)PSD were found at height ratio of 0.88, and 1.14, respectively. Less significant change in \(\Delta\)PSD was observed at lower height ratio (i.e., \(\chi\) = 0.31) or at greater height ratio (i.e., \(\chi\) = 3.16), with \"S\" shaped trend of relationship between height ratio and \(\Delta\)PSD similar to results of [PERSON] et al. [32]. An approximate unity of height ratio could be considered as a threshold value to separate, whether SSSI effect increased or reduced structure motion during an excitation based on experimental results of this study. However, the increment and the decrement in estimated \(\Delta\)PSD in this study were excessive compared to previous research, especially at L_Input excitation, as shown in Figure 10a,b. Estimated \(\Delta\)PSD values were around 80% and minus 30% at \(\chi\) = 1.14, and \(\chi\) = 0.88, respectively. These values are much higher, and lower than those suggested by [PERSON] et al. [32], respectively. Note that in their study, mass ratio between structures was approximately unity, and the maximum acceleration level of input motions was around 0.1 g, which was approximately the same as the L_Input excitation used in the present study. Therefore, such over-estimation of SSSI effects could be attributed to significant difference in mass between structures. Figure 11 shows the relation of \(\Delta\)PSD and mass ratio (\(\mathrm{b}\)) with the same input motions (i.e., artificial and Hachinohe earthquakes) and input intensities (i.e., L_Input and H_Input) used in Figure 10 for comparison. A reduction in total power spectral density of more massive structure and an increment in that of the lighter structure in SSSI phenomena were observed, consistent with previous studies [17; 30]. Trends influenced by the mass ratio on the variation of \(\Delta\)PSD are similar to those of the height ratio shown in Figure 10, indicating that height and mass ratio had the same effect of on \(\Delta\)PSD. In addition, a higher and more massive structure exhibited higher inertial interaction in SSFI as indicated by Max.RRS\({}_{\mathrm{II}}\) value (solid circle points) in Figure 5. Therefore, relative Max.RRS\({}_{\mathrm{II}}\) values between structures, which implicitly contain both mass and height ratios could be a key factor in controlling SSSI phenomena.