## 4 Results and Discussion  
### F-K Analysis of the Microtremor Array Data  
We first divided the observed vertical-component recordings into multiple time segments by overlapping one-half of each window length. The window length was 20.48 s for S-array recordings and 40.96 s for L-array recordings. We inspected the data quality of recordings and eliminated certain segments contaminated by human activity and instrument noise. Subsequently, we calculated the phase velocities of the Rayleigh wave by using the FK method based on the MLM [21].  
Figure 5 depicts the _f_-_k_ spectra from the MLM using the microtremor data observed at site DTE. We calculated the _f_-_k_ spectra at 51 \(\times\) 51 grid points at each frequency. This figure displays the _f_-_k_ spectra at 3.42 Hz (the left panel) and 0.39 Hz (the right panel) from the recordings generated by the S and L arrays, respectively. The propagation direction (\(\theta\)) was measured clockwise from north in degrees. For the two frequencies, the propagation directions were approximately 239\({}^{\circ}\) and 17\({}^{\circ}\), respectively. The phase velocity (V) in km/s  
Figure 4: S-wave velocity structures (adopted from [PERSON] and [PERSON] [11]) estimated using the differential inversion technique at sites DAK (thin black line) and TCD (thick black line) compared with those from the TCDP velocity logs (red line) and the depth function (blue line; [PERSON] et al. [24]).  
can be estimated from the maximum peak in the _f_-_k_ spectrum. Since we identified the maximum peaks within the wavenumber windows that we set beforehand, the minimum phase velocities were limited, whereas the maximum phase velocities were not.  
Figure 6 illustrates the estimated phase velocities at site DTE. The symbols represent the observed results from the different size arrays and K values. The observed phase velocities were selected by following the sequence of the L (0.29 Hz \(\leq\)\(f\)\(\leq\) 1.56 Hz) and S arrays (1.66 Hz \(\leq\)\(f\)\(\leq\) 4.0 Hz) from low to high frequencies. The results of the L-array measurements were stable at lower frequencies, whereas those of the S-array measurements were stable at higher frequencies.  
Figure 7 depicts the dispersion curves of phase velocities obtained from recordings observed at all 53 sites. The estimated phase velocities varied between sites. Similar dispersion curves were categorized in the same group according to their amplitude and shape, yielding four groups. The Group 1 sites (14 sites) had the highest phase velocities, whereas those of Group 4 (9 sites) had the lowest phase velocities. The phase velocities of Groups 2 (14 sites) and 3 (16 sites) were between those of Groups 1 and 4. The sites illustrated in Figure 2 are color-coded with triangles according to this classification scheme. The sites of Group 4 (green triangles) appear on the Western Coastal Plain, whereas the sites of Group 3 (pink triangles) are distributed along the Changhua Fault and the southern Taichung Basin (i.e., old Taichung City). The sites of Group 2 (blue triangles) are on the Tatushan Anticline and the area north of it (which contain lateritic terrace deposits and terrace deposits). The sites of Group 1 (brown triangles) are on the northern Taichung Basin and near to or along the Chelungpu Fault (the eastern side). Furthermore, at most sites of Groups 2 and 3, the observed phase velocities were almost flat and were approximately 800-1300 m/s at frequencies between 0.6 and 2 Hz.  
Figure 5: The _f_–_k_ power spectra generated using the MLM method at the frequencies of 3.42 and 0.39 Hz produced from the data of the S and L arrays at site DTE.  
Figure 6: Average and average \(\pm\) 1 standard deviation of the phase velocities obtain from the recordings at site DTE. Symbols represent the results from the arrays of different sizes and K values. The black line is the final dispersion curve used in the study.  
Figure 7: Phase velocities obtained from recordings observed at all 53 arrays. The estimated phase velocities vary between sites.