Limitations of Rayleigh Dispersion Curve Obtained from Simulated Ambient Vibrations

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1 Limitations of Rayleigh Dispersion Curve Obtained from Simulated Ambient Vibrations KEN TOKESHI and CARLOS CUADRA Department of Architecture and Environment Systems Akita Prefectural University 84-4 Ebinokuchi, Aza-Tsuchiya, Yuri-Honjo, Akita JAPAN Abstract: - The possible limitations and/or potentials of Rayleigh-wave dispersion curve obtained from simulated ambient vibrations at a fictitious TEST site are discussed. The ground model of this fictitious site is a horizontally layered half-space. Simulated ambient vibrations were calculated for six ground systems at TEST site. The 1 st ground system consists of one upper layer overlying half-space, the 2nd ground system consists of two layers overlying half-space, and so on. The Rayleigh-wave dispersion curve from the vertical components of simulated ambient vibrations of the triangular array for each ground system was calculated using the high resolution f-k spectral method. According to results using simulated ambient vibrations at the fictitious TEST site, two conclusions could be given. First, there would be direct relation between the predominant frequency of the H/V spectral ratio and the lowest asymptotic frequency of Rayleigh-wave dispersion curve. Second, the estimation of deeper layers using Rayleigh-wave dispersion curve would have some limitation if the Rayleigh-wave does not have strong influence in these layers. Key-Words: - Rayleigh-wave dispersion, Simulated ambient vibration, High resolution f-k spectral method, H/V spectral ratio, Pseudo-Dirac source, Predominant frequency, Critical frequency range. 1 Introduction Nowadays, the use of ambient vibrations for estimating the shear wave profile (Vs) of a site is increasing as high performance technology is being developing for in-situ measurements and computers as well. As it is known, the shear wave velocity and the thickness of layers are important soil parameters for assessing the dynamic behavior of a site during earthquakes for seismic microzonation purposes. The usual method of obtaining the Vs profile is the PS logging, which is normally considered reliable but expensive. As a less expensive and non-destructive technique, the use of Rayleigh-wave dispersion characteristics for estimating Vs is being explored by many researchers all over the world since the 1980 s. There are several methods for this purpose, e.g., the f-k spectral method, the SAC or SPAC method, the SASW method, etc. However, there are few papers discussing on the possible limitations and/or potentials of Rayleigh-wave dispersion curve obtained from observed ambient vibrations. One way for exploring and for discussing its limitations and/or potentials is the computer simulation of ambient vibrations (synthetic ambient vibrations) using some fictitious Vs soil profiles. This paper presents some discussions on the limitations and/or potentials of Rayleigh-wave dispersion characteristics obtained by the f-k spectral method at a fictitious TEST site. 2 Simulation of ambient vibrations at TEST situ The ground model of this fictitious site is a horizontally layered half-space, which number of layers increases with the depth (Table 1). Simulated ambient vibrations for six ground systems at TEST site were calculated. The 1 st ground system consists of one upper layer overlying half-space, the 2nd ground system consists of two layers overlying half-space, and so on. These simulated ambient vibrations are calculated using the same method proposed in previous paper by Tokeshi et al. [1]. Figure 1 shows the ground surface of this model, which is a square of 1250m side divided into 10,000 square elements (12.50m side). Seven fictitious stations in triangular array were set on the surface (see Fig. 1). Figure 2 ISSN: Page 26 ISBN:

2 Table 1 Summary of physical parameters assigned to the fictitious TEST site. Layer Thickness Density (m) (t/m 3 ) V P (m/s) V S (m/s) Q P & Q S Half-space Infinite shows an example of the pseudo-dirac source, which 3 components are defined in equations (1). Qx = Qh cosφ Qy = Qh sinφ Qz = Qv (1) where, φ is the random direction of Qh measured clockwise from the line parallel to the X-axis at the station. A relation of forces (R F = 1), meaning that the ratio between horizontal (Qh) and vertical (Qv) input forces is the unity, was used for all sources. I.e., the value of the magnitude for Qh and Qv was the unity, respectively. Around 409,600 tri-directional sources of pseudo-dirac type with a constant amplitude (R F = 1), are applied randomly at the center of any of the 10,000 elements at a random time between 0 and 81.91s. Only the sources activated within a radius of 300m measured from each of the 7 stations were considered for computing the 3 components simulated ambient vibrations (two horizontal components parallel to X and Y axes and one vertical component parallel to the Z axis). 3 Comparison of theoretical and synthetic Rayleigh-wave dispersions The Rayleigh-wave dispersion curve from the vertical components of simulated ambient vibrations of the triangular array for each ground system was calculated using the high resolution f-k spectral method [2]. Figure 3 presents a comparison of the theoretical and the synthetic Rayleigh-wave dispersion curves obtained from the simulated ambient vibration for the 3 rd system, 4 th system, 5 th system and 6 th system. No clear synthetic Rayleigh-wave dispersion curves for the 1 st and the 2 nd ground systems were obtained due to low impedance contrasts. The synthetic Rayleigh-wave dispersion curve for the 3 rd ground system shows bad fitting with the corresponding theoretical one in the frequency range of Hz, even though, there is high impedance contrast between the 3 rd and the 4 th layer (half-space) (see Fig. 3). These Rayleigh-wave dispersion curves tend to better fittings as deeper layers are added. The synthetic and theoretical Rayleigh-wave dispersion curve for the 6 th ground system show good fitting maybe due to high reflectivity characteristics of deepest hard half-space. 4 H/V spectral ratio of simulated ambient vibrations Synthetic ambient vibrations for the 3 components (two horizontal components parallel to X and Y axes and one vertical component parallel to the Z axis) were calculated for each of the 7 stations of the fictitious triangular array at TEST site. Figure 4 presents the average H/V spectral ratio of 7 stations (without smoothing) obtained for the 3 rd system, 4 th system, 5 th system and 6 th system. Little difference of H/V spectral ratio for the 3 rd ground system (black line in Fig. 4) and higher systems was obtained. Sharp predominant peaks around the red segmented circle were obtained for all these ground systems. The values of frequency for these peaks are quite close to the frequency where the Rayleigh dispersion curve appears asymptotic. The relationship between the value of frequency around the peak of H/V spectral ratio and the value of frequency where the Rayleigh dispersion curve appears asymptotic has been confirmed. Bonnefoy et al. [3] found similar results. However, the above frequency range (called here as «critical frequency range») shows high deviation of Rayleigh-wave dispersion characteristics, giving uncertainty on its actual characteristics. ISSN: Page 27 ISBN:

3 300 m Figure 1 Triangular array of 7 stations used to simulate ambient vibrations at TEST site. Source location Station location 1 7 Y Q y Qh Q Z Q x Z X Figure 2 Uni-directional forces Qx, Qy and Qz in Cartesian coordinates at a typical source location and its spatial relation with the station locations (red points). ISSN: Page 28 ISBN:

4 Figure 3 Comparison of the theoretical and the synthetic Rayleigh wave dispersion curves obtained from the simulated ambient vibration. Figure 4 Average H/V spectral ratios of 7 stations at fictitious TEST site. ISSN: Page 29 ISBN:

5 5 Conclusions From the results obtained from the comparison of theoretical and the synthetic Rayleigh-wave dispersion curve from simulated ambient vibrations at the fictitious TEST site, as well as, from the H/V spectral ratio of simulated ambient vibrations, two conclusions could be given: 1. There would be direct relation between the predominant frequency of the H/V spectral ratio and the lowest asymptotic frequency of Rayleigh-wave dispersion curve. 2. The estimation of deeper layers using Rayleigh-wave dispersion curve would have some limitation if the Rayleigh-wave does not have strong influence in these layers. Acknowledgements This work has been supported by Grants-in-Aid for the Scientific Research (No ) from the Japan Society for the Promotion of Science (JSPS). References: [1] Tokeshi J.C., Sugimura Y., Karkee M.B., Parametric study on simulated microtremors and its application to interpretation of microtremor records. J. Struct. Constr. Eng., AIJ, No. 535, 2000, pp [2] Capon J., High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE, Vol. 57, 1969, pp [3] Bonnefoy-Claudet A., Cornou C., Bard P.Y., Cotton F., Moczo P., Kristek J. and Fah D., H/V ratio: a tool for site effects evaluation. Results from 1-D noise simulations. Geophys. J. Int., Vol. 167, 2006, pp ISSN: Page 30 ISBN: