## 4 Results and Discussion
### Inversion of the S-Wave Velocity Structure  
On the basis of the results of the dispersion curves (Figure 7), we calculated S-wave velocity structures by using [PERSON]'s inversion technique [22]. Figure 8 depicts the estimated S-wave velocity structures (-230-2350 m/s) at depths of 0-2500 m at site DTE. The inverted S-wave velocity gradually increased with depth. Figure 9 depicts the observed (open circles) and calculated (red lines) phase velocities for the initial (red dashed lines) and inverted (red solid line) S-wave velocity structures at site DTE. The theoretical phase velocities (red solid line) from the inverted results (Figure 8) closely resemble the observed phase velocities (open circles). Figure 8: The S-wave velocity structures estimated using the surface-wave inversion technique ([PERSON] [22]) at site DTE. Figure 9: Observed (open circles) and theoretical (red line) phase velocities for the inverted S-wave velocity structures at site DTE. The phase velocities for the initial and inverted S-wave velocity structures are shown in red dashed lines and red solid lines, respectively. Figure 10 displays the one-dimensional (1D) S-wave velocity structures at depths of 0-2000 m estimated using the surface-wave (differential) inversion technique at all 53 sites. These structures were divided into four groups following the classification scheme in Figure 7. At most sites of Groups 2 and 3, the shallow S-wave structures have a convex shape at depths of 0-500 m. This means that they have a high-velocity zone at shallow depths. This result is consistent with the phenomenon that the observed phase velocities were almost flat in frequencies between 0.6 and 2 Hz. Moreover, if we assume the S-wave velocity of the Tertiary basement to be 1500 m/s, the Quaternary alluvial thickness overlying the bedrock is between 270 m (i.e., SGJ) and 1550 m (i.e., WNE) in the Taichung area. Among these sites, site FNJ (near the Chelungpu Fault) has the highest S-wave velocities and thinnest alluvium, whereas the lowest S-wave velocities and thickest alluvium occur at site WNE (on the Western Coastal Plain). Figure 10: S-wave velocity structures estimated using the surface-wave inversion technique (Herrmann [22]) at all 53 sites. To elucidate the variation of the shallow S-wave velocities in the Taichung area, we include contour maps of the S-wave velocities at depths of 50-1800 m in Figure 11, based on the results of Figure 10. The contour maps indicate the presence of lateral heterogeneity and that velocities change with depth. The results are as follows:  
1. [label=(0)]
2. Depths of 50-300 m: The highest velocities appear at the central part (YMI), whereas the lowest velocities appear at the western part (WNE). The area with the highest S-wave velocities gradually shifts from the central part (YMI) to the northeastern part (SGJ) as depth increases. 3. Depths of 300-600 m: The area with the highest S-wave velocities gradually shifts from the central part (SGJ) to the eastern part (FNJ), which is near the Chelungpu Fault, as depth increases. The lower velocities still appear at the western part (WNE). 4. Depths of 600-1200 m: The highest velocities appear at the eastern part (FNJ, FCE), whereas the lower velocities appear at the western (WNE) and southwestern (HCJ) parts. 5. Depths of 1200-1800 m: The highest velocities remain at the eastern part (FNJ, FCE). The second highest velocity zone appears at the area near sites SHI and ZHM. Similarly, the western part (WNE, HCJ) still exhibits the lowest velocities. Overall, the S-wave velocities gradually decrease from the east to the west as depths increase between 0 and 1800 m.  
To clarify depth variations at the same velocity, a depth-contour map (upper panel) and 3D depth structure (lower panel) at a velocity of 1000 m/s were drawn (Figure 12). The depths are between 50 m (e.g., YMI, at the central part) and 850 m (e.g., WNE, at the western part). The shallowest depths appear at the central and eastern parts, whereas the deepest depths appear at the western part.