The supplemental figures exhibit some important results and discussions related to the manuscript. The electronic supplement includes six topics which are stated as follows.
The higher modes of Rayleigh waves are neglected during the inversion analysis because the fundamental mode is dominant in the study. They are discussed and verified as the followings:
(a) The use of any prior geological/geophysical knowledge about the soil structure may help to verify which mode is dominant. Unfortunately, we lack of reliable and detailed velocity structure from the ground surface to the bedrock in the Chiayi area.
(b) Figure S1 shows the observed and calculated phase velocities (including fundamental, first higher and second higher modes of Rayleigh waves) for the inverted S-wave velocity structures at site WET. The observed phase velocities increase at frequencies higher than 4.199 Hz. This phenomenon has been observed in short-period microtremors in previous studies and has been interpreted as resulting from contamination by the first and/or second higher mode of Rayleigh waves (e.g., Tokimatsu and Miyadera, 1992; Ohori et al., 2002; Satoh et al., 2004). Therefore, we estimate S-wave velocity structure using the data at frequencies between 0.195 and 4.199 Hz by fitting the observed data. Moreover, based on this inversion velocity model, we calculate the phase velocities of the fundamental, first higher and second higher modes of Rayleigh waves. From the figure, the fundamental mode is effectively dominant although the phase velocities of the first higher mode are close to those of the fundamental mode and the observed data at frequencies between 0.4 and 0.5 Hz.
(c) According to Horike’s study (1985, p.84-85), there are two prominent peaks in the f-k spectra at frequencies between 2.48 Hz and 2.98 Hz at site S2 near Kyoto, which suggests that microtremors at these frequencies consist of two different modes of Rayleigh waves. The peak farther to the origin corresponds to the fundamental-mode Rayleigh waves and the nearer one to the higher modes. However, the second peak within the f-k spectra (Figures S2 and S3) is not obvious in our study. It indicates that only a predominant mode of Rayleigh wave exists.
(d) Moreover, in a complex layered site, such as the layers with lower S-wave velocities embedded into the layers with higher S-wave velocities (Stokoe et al., 1994), higher modes can play a significant role and hide the fundamental mode within certain frequency bands. In the Chiayi area, the results of the geoelectric methods (Tong, 1999; Pi, 2000; You, 2003) indicate that the layer with low resistivity exists at shallow depth, and the electrical resistivity increases with depths. It implies that the low-velocity layer does not exist beneath this area and the higher modes are not expected to be excited in this relatively simple layered structure.
According to the above discussions, we think that the fundamental mode Rayleigh wave is effectively dominant in the Chiayi area.
Figure S1. Observed and calculated phase velocities for the inverted S-wave velocity structures at WET site. For observed phase velocities average one standard deviation are shown by vertical bars. The phase velocities for the first and second higher modes of Rayleigh waves are shown in red line and blue line, respectively.
Figure S2. Examples of the f-k spectrum at four different frequencies: 0.59, 1.17, 2.34, and 3.42 Hz are calculated from microtremors records observed of one time segment observed by X, L, M, and S arrays, respectively, at site WET.
Figure S3. Examples of the f-k spectrum at eight different frequencies (3.32~4.0 Hz) are calculated from microtremors records observed of one time segment observed by S arrays at site WET.
According to the menu of “surface wave inversion program” (Herrmann, 1991), there are two options including considering and not considering the standard error of observation while solving the least square problem during the inversion process.
We do not add uncertainties of phase velocities within the inversion analysis in the study. Here we choose WET site as an example to explain the difference of the inversion result between adding and not adding the uncertainties during the inversion process. Figure S4 shows the comparisons of (a) dispersion curves and (b) inverted velocity models between adding and not adding standard deviation during the inversion process. At WET site, the inverted Vs velocities from adding standard deviation are lower than those from not adding standard deviation at depths larger than 800 m. Moreover, at the frequencies lower than 0.5 Hz, the inverted models by not adding standard deviations match better with the observed phase velocities while compared with the inversion results by adding standard deviation.
Figure S4. Comparisons of (a) dispersion curves and (b) inverted velocity models between adding and not adding standard deviation during the inversion process.
First, we choose the velocity model from Hwang et al. (2003) as an initial model (red dashed line in Fig. S5(a)) and then invert the Vs structure (red line in Fig. S5(b)). Figure S5 shows comparisons of (a) dispersion curves and (b) final Vs velocity models between this study and another inversion result whose initial model is based on the result of Hwang et al. (2003). Basically, their patterns are similar.
Secondly, we choose a revised velocity model of Chung and Yeh (1997) as an initial model (red dashed line in Fig. S6(a)) and then invert the velocity structure (red line in Fig. S6(b)). Figure S6 shows comparisons of (a) dispersion curves and (b) final Vs velocity models between this study and another inversion result whose initial model is based on a revised velocity model of Chung and Yeh (1997). Although their dispersion curves are similar, the final velocity models are different at depths larger than 160 m. These two inversion results represent the best solutions for their initial models but some limitations still exist.
Figure S5. (a) Observed and calculated phase velocities for the initial and inverted S-wave velocity structures at WET site. (b) Comparison of the velocity structures between this study (black line) and another inversion analysis (red line) whose initial model is based on the result of Hwang et al. (2003).
Figure S6. (a) Observed and calculated phase velocities for the initial and inverted S-wave velocity structures at WET site. (b) Comparison of the velocity structures between this study (black line) and another inversion analysis (red line) whose initial model is based on a revised velocity model of Chung and Yeh (1997).
In order to clarify the resolution of the S-wave velocity models, we calculate the resolving kernel/sensitivity kernel at different depths/periods at five sites (Figures S7 and S8). According to the results, the resolution of depths is about 1500 m.
Figure S7. Estimated S-wave velocity structures (left panel) and their normalized resolving kernels (right panel) at different depths (indicated by the number [given in meters] on the top of each plot) at five sites.
Figure S8. Normalized sensitivity kernels at different periods (indicated by the number [given in sec] on the top of each plot) are estimated from the inverted S-wave velocity structures (left panels in Fig. S7) at five sites.
Because the layer number is too much; the estimated velocity structure using the differential inversion technique is not suitable to do ground motion simulation in the future. On the basis of the gradient changes in the differential inverted results, we are able to determine the boundaries between the layers. Therefore, the inverted velocity structure with 80 layers is simplified to be a structure with fewer layers. We choose this simplified velocity structure as an initial model and then invert the structure using the stochastic inversion technique. The parameters (e.g. velocity and thickness) between layers are independent during the stochastic inversion process. Besides, the damping value and the termination condition of program used are same with the differential inversion technique. Figure S9 shows the estimated S-wave velocity structures at all 46 sites.
Figure S9. Estimated S-wave velocity structures by stochastic inversion (Herrmann, 1991) at all 46 sites.
Figures S10 and S11 show comparisons between the Vs contour map from microtremor array measurements and the electrical resistivity distribution from geoelectric method (Tong, 1999) at depths of 40 m and 250 m in the Chiayi area. Basically, the S-wave velocity increases from west to east while the electrical resistivity also increases from west to east. Their patterns are very similar.
Figure S10. Comparison between the Vs contour map (the left panel) from microtremor array measurements and the electrical resistivity distribution (blue rectangular region at the right panel) from geoelectric method (Tong, 1999) at a depth of 40 m in the Chiayi area.
Figure S11. Comparison between the Vs contour map (the left panel) from microtremor array measurements and the electrical resistivity distribution (blue rectangular region at the right panel) from geoelectric method (Tong, 1999) at a depth of 250 m in the Chiayi area.
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