Estimation of shallow S-wave velocity structure in the Puli basin, Taiwan, using array measurements of microtremors
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2012
Received: 30 May 2011
Accepted: 20 December 2011
Published: 28 June 2012
The September 21, 1999, Chi-Chi earthquake induced strong shaking, resulting in severe damage in the Puli area. According to Huang and Tarng (2005), the collapse of many structures during the earthquake was very closely related to site effects. Shallow shear-wave velocities are widely used for earthquake ground-motion site characterization. Thus, we investigate S-wave velocity structures for the Puli area by performing microtremor array measurements at 16 sites. Dispersion curves at these sites are calculated using the F-K method (Capon, 1969) for the vertical component; S-wave velocity structures for the Puli area are then estimated by surface wave inversion (Herrmann, 1991). If the S-wave velocity of the bedrock is assumed to be 2000 m/s, the depths of the Quaternary sediments in the Puli area are between 300 m (FAL, PIP) and 870 m (DAH). Moreover, there are 3∼6 distinct interfaces in the shallow velocity structure (0∼1000 m). The depth of the bedrock gradually increases from the edge (SIN, PIP) to the center (PUL, DAH) of the basin and the thickest Quaternary sediments appear near Heng-Chih-Cheng (DAH).
The S-wave velocity is a very important factor in theoretical simulations and ground motion predictions. It is now largely obtained using well-logging which is a time-consuming and costly method. Compared to the direct borehole method, non-intrusive surface methods (e.g. conventional exploration methods and microtremor array measurements) are considerably less expensive for obtaining shallow velocity structures. A number of studies have inverted surface-wave phase velocities, obtained from microtremor recordings, to derive near-surface material properties (Horike, 1985; Matsushima and Okada, 1990; Satoh et al., 2001a, b). However, methods reliant on microtremor data to assess site effects are still the subject of debate amongst many geophysics research groups. A research project (Site EffectS assessment using AMbient Excitations (SESAME), 2001–2004) was financed by the European Community to assess site effects using microtremor-based techniques for seismic risk mitigation, especially in urban areas. One of its main functions was to clarify the composition and characteristics of microtremor behavior, and to investigate the analytical capacities of different microtremor-based techniques for obtaining a quantitative description of site features, by analyzing and comparing observational data with simulations. Kind et al. (2005) applied the high-resolution beamforming method to derive phase velocities from ambient vibrations. Tests with synthetic ambient vibrations confirm the capability of the method to extract the correct phase velocities of the excited Rayleigh mode. The inverted S-wave velocity structure corresponds well to data from an S-wave reflection survey and the geological information for two measurement sites. Di Giulio et al. (2006) deployed five small-aperture array measurements of microtremors to study wave-field properties and shallow velocity structures in the Colfiorito plain, Italy. They pointed out that the vertical and horizontal components of the microtremor signals were dominated by Rayleigh waves and Love waves (Arai and Tokimatsu, 2000), respectively. The inverted shear-wave velocity profiles are consistent with a priori information for four different sites that can be approximated by a simplistic 1D model. Maresca et al. (2006) analyzed the ambient noise recorded in the Colfiorito Basin, Italy, using H/ V spectral ratios and array techniques. They correlated the frequency variation with the structure of the basin, investigated the directional properties of the noise wave field and recognized the possible influence of the basin structure on the propagation of seismic waves. Huang and Wu (2006) performed microtremor array measurements for a total of 28 arrays at seven sites to estimate the S-wave velocity structures in Chia-Yi City. According to the f -k analysis, at frequencies lower than about 1 Hz, the generation of microtremors may be attributed to the ocean waves of the Taiwan Strait. Based on the inverted results, the alluvial layer of the city is about 1000∼ 1200 m thick if the S-wave velocity of the bedrock is assumed to be 1,500 m/s. The depth of the alluvium gradually increases from the east to the west and from the north to the south.
The Chi-Chi earthquake (ML 7.3) occurred on September 21, 1999, in the Nantou prefecture of central Taiwan. The mainshock and subsequent aftershocks destroyed over 8,500 buildings and seriously damaged another 6,200. Damage was heaviest in the central Taiwan counties (Taichung, Nantou, and Yunlin). In the central mountain city of Puli, large ground shaking caused devastating effects in the center of the town, with many buildings either being seriously damaged or totally collapsed. In order to investigate the site characterization of the Puli area, Huang and Tarng (2005) carried out dense microtremor measurements at 87 sites inside the basin. They concluded that the building damage during the Chi-Chi earthquake was very closely related to site effects in Puli.
Owing to a lack of drilling and geophysical data, many ambiguities still exist about the underground structure. In this study, therefore, we conduct microtremor array measurements at 16 sites to explore shallow S-wave velocity structures and the depths of bedrock in the Puli basin.
2. Sites and Data
The basic geophysical aspects for understanding seismic response in the Puli basin are its bedrock geometry and P-wave and S-wave velocity distribution. Wang et al. (2003) studied the shallow velocity structures of the northern part of the Puli basin using the shallow seismic reflection method. Their results showed that the largest depth of the bedrock is about 500 m, and the shape of bedrock in the Puli basin is roughly symmetrically concave. In order to explain the forms of the Tertiary basement and the Quaternary formations of the basin, Huang (2008) used a high-resolution shallow seismic reflection method in combination with the results of Wang et al. (2003). After careful combination of both sets of results, Huang (2008) proposed the following conclusions: (1) the deepest part of the basement of the Puli basin does not exceed 600 m, and the western portion is deeper. The top 100 m of basin sediment is dominantly gravel and the deeper part, sand and mud. (2) P-wave velocity of the Quarternary sediments in the basin is 2200 m/s, and S-wave velocity is 950 m/s. On the other hand, P-wave velocity of the basement rock is 4300 m/s and S-wave velocity, 2000 m/s. (3) The basement rock belongs to the pre-Tertiary Paileng formation. (4) Sediment layers within the basin are not flat, and have apparent dipping angles. (5) No apparent faults have been discovered in the basin. (6) Down warping may have been the dominant formation mechanism during the basin’s early history; however, in its later stages, formation has been controlled by river erosion.
Array locations, sizes, maximum and minimum separations between instruments for 16 sites.
Min. separation (m)
Max. separation (m)
Array measurements of microtremors were performed using seven sets of portable instruments. Each set of instruments includes a tri-axial servo velocity sensor (VSE-315D), an amplifier, and a 24-bit analog-to-digital recorder (SAMTAC-801B). This velocity sensor has a flat amplitude response from 0.1 to 70 Hz. The accuracy of the internal clock is within 1 ppm and is corrected by the Global Positioning System (GPS) before each measurement. The timing accuracy from GPS correction is within 1 ms. The positions of the sensors are determined using Trimble’s GPS Pathfinder System receivers, that provide real-time submeter accuracy. At each observation point, microtremor data was continuously recorded for about 68 minutes during the day time at a sampling frequency of 200 Hz.
3. Methods of Analysis
3.1 F-K spectral analysis method
3.2 Inversion of the velocity structure
To solve model parameters (Δβ i ) of Eq. (3), we employ a surface-wave inversion program based on damped least-squares and developed by Herrmann (1991). Moreover, the program used here is based on the assumption that the fundamental mode of the Rayleigh wave is dominant. Smoothing constraints, the difference between adjacent model parameters as an approximation of a derivative to control solution roughness, were also used (e.g., Menke, 1984). In this study, an initial layered model at each site is first constructed with assigned values of thickness, S-wave velocities, and Poisson’s ratio for each layer. We take a half-space structure with an S-wave velocity, which is the maximum phase velocity divided by 0.92 at the lowest frequency used, as the S-wave velocity in the initial model. Also, the total layer number and the thickness of each layer are designed to be 80 and 30 m. If we are using a maximum frequency of 8 Hz, and assuming a phase velocity of 700 m/s, the minimum expected wavelength is about 90 m. Accordingly, by rule-of-thumb calculation, the highest resolution of thickness can be estimated as being about one-third of the observed minimum wavelength. Therefore, we expect to resolve a 30-m-thick layer. A damping value of 1.0 is adopted to stabilize the inversion. The inversion process will be terminated when the difference in S-wave velocity for each layer between the adjacent inversions is less than 0.001 km/s. Although the inversion of phase velocity is non-unique, we carefully inspect the rationality of the inverted S-wave velocity and any misfit between observed and theoretical phase velocities for each inversion. Hence, a reasonable velocity model can be obtained. The above inversion process is the differential inversion technique (Herrmann, 1991).
In the study, the total layer number is designed to be 80 for the differential inversion. Because the layer number is too great, the inverted structure is not suitable to enable ground motion simulation in the future. Therefore, in addition, we use a stochastic inversion technique. First, based on the differential inverted result, we regroup the layered structure. On the basis of the gradient changes in the differential inverted results, we are able to determine the boundaries between the layers. The inverted structure with 80 layers is simplified to be a structure with fewer layers. Secondly, we choose the simplified structure as the initial model and then invert the structure using the stochastic inversion technique. During the stochastic inversion process, the parameters (e.g. velocity and thickness) between layers are independent. Besides, the damping value and the termination condition of the program used are the same with the differential inversion technique.
4. Results and Discussions
4.1 F-K analysis of microtremor array data
4.2 Inversion of the S-wave velocity structures
Inverted S-wave velocity structures at the 16 sites of the Puli basin.
449.1 (30) 573.7 (30)
610.6 (30) 671 (60)
622.6 (30) 876.7 (30)
630.8 (30) 858.7 (60)
642.6 (30) 761.6 (30)
617.3 (30) 800.5 (30) 896.6 (120)
921 (60) 1123.8 (90)
964.2 (120) 1239.5 (150)
905.3 (30) 1220.2 (180)
1560 (90) 1669.1 (660)
1414.9 (240) 1677.6 (180)
1428.9 (60) 1662.9 (480)
1523.1 (90) 1785 (90)
2028.9 (120) 2237.9 (120)
1848.8 (120) 2137.6 (120)
1893.9 (120) 2241.9 (120)
2387.9 (210) 2657.7 (840)
2336.9 (120) 2531.4 (1710) 2627.8
2335 (450) 2690.3 (600)
2381.5 (1080) 2543.6 (270)
2303.3 (120) 2509.5 (150) 2637 (210)
2754.4 (300) 2926.5
2732.3 (600) 2979.3
2815 (360) 2975.5
3161.1 (270) 3330
3220.1 (1500) 3563.9
3144.8 (750) 3243.2
3160.4 (1530) 3568.2
3073.4 (210) 3248.2
3016.6 (390) 3123.8
3336.8 (450) 3451.9
4.3 Comparison of the S-wave velocity structures
In the Puli basin, the depths of the bedrocks are about 300∼870 m by the microtremor array measurements (Fig. 14(a)) while these are about 300∼600 m by Huang (2008) (Fig. 14(b)). The depth of the bedrock is deeper in the central part (e.g. PUL, DAH) of the basin while it is relatively shallower at the edges (e.g. SIN, PIP). The depth of the bedrock gradually increases from the edge to the center of the basin and the deepest area is near Heng-Chih-Cheng (DAH). Moreover, some sites (SIG and CUF) with deeper bedrocks are found in the northern and eastern parts using the microtremor array measurements (Fig. 14(a)). We deploy three sites (CUH, NAK and PUL) at the downtown area while the explosion experiment is not easy to survey (Huang, 2008; Fig. 14(b)). According to the inverted results, we can get the detailed S-wave velocity structures in the study. However, the explosion experiments can clearly describe the stratum and attitude of stratum (e.g. Fig. 13(b)). Overall, the results from microtremor array measurements and from Huang (2008), regarding the bedrock depths, present similar patterns though there are some differences in detail. The possible reasons causing the discrepancies between these results are due to the differences of the measured sites, the measurement methods and the techniques of data processing used.
The aim of this study was to estimate the S-wave velocity structure of the Puli basin using microtremor array measurements. The measurements were carried out with 64 different size arrays whose radii range from 50 to 400 m at 16 sites. Based on the results of the propagation direction estimated from the f -k spectra, we find that the microtremor wavefield at the higher frequencies is dominated by anthropogenic sources in the Puli basin. At frequencies lower than about 0.66 Hz, the propagation directions concentrate in the northwest and west quadrants, coinciding with the direction of the Taiwan Strait coast line.
We can, however, estimate the phase velocity from the frequency and the wavenumber of the maximum peak in the f -k spectrum. The estimated phase velocities at the 16 sites vary from site to site. The derived dispersion curves indicate that sites AIL, DAH and YUY have higher phase velocities while frequencies are greater than 3 Hz, however, at frequencies between 1.0 and 2.7 Hz, the phase velocities become flat at 1.3–1.5 km/s. The results from the stochastic inversion technique (Herrmann, 1991) show that the thicknesses of the Quaternary sediments are between 300 m and 870 m in the Puli basin, if the S-wave velocity of the bedrock is assumed to be 2000 m/s. Also, the shallow velocity structure (0∼ 1000 m) can be roughly divided into 3–6 layers.
To validate the S-wave velocity structures obtained from the microtremor array measurements, theoretical H/ V ratios based on the velocity model were compared with the H/ V ratios of microtremor data at three sites. The results show good agreement at the predominant frequencies; however, both the peak and trough amplitudes between the simulated results and observational results do not match well. We also compare our results with those from seismic exploration calculations conducted by other researchers and find the patterns are similar overall although there are some discrepancies in the detail. Both patterns indicate the depth of the bedrock gradually increasing from the basin’s edge to its center.
The authors would like to express their gratitude to Drs. R. D. Hwang and W. G. Huang for providing the programs and for their stimulating discussions. The authors appreciate the efforts of the Engineering Seismology Laboratory of NCCU, which provided microtremor measurements in the field. They also wish to thank Drs. E. D. Pezzo and H. Kawase for their valuable comments and suggestions to improve this paper. The National Science Council, Taiwan has supported this research (NSC 97-2745-M-194-002).
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