3:30 PM - 3:45 PM
[SSS10-07] Dependence of effective phase velocity on inter-station distance in Rayleigh wave fields dominated by multiple modes
Keywords:Microtremor, Spatial autocorrelation (SPAC) method, Higher modes, Effective phase velocity, Multimode analysis
The spatial autocorrelation (SPAC) method, one of the most effective methods for estimating surface wave dispersion curves that provide strong constraints to the inverse estimation of velocity structure, yields an effective dispersion curve when applied to a Rayleigh wave field dominated by multiple modes. The concept of an effective dispersion curve has become well-recognized in recent years, while some researchers still assume single-mode dominance. This situation partly stems from the fact that the properties of the effective dispersion curve have not been clarified sufficiently.
The effective dispersion curve is clearly a quantity that depends on the distance between observation points by its definition (Ikeda et al. 2012). However, many researchers do not seem to pay sufficient attention to this fact. The SPAC method requires an array of receivers with many inter-station distances to obtain dispersion curves over a wide frequency range. Generally, the dispersion curves obtained from each array are collected to construct a single dispersion curve for subsequent inverse estimation of the velocity structure. This procedure is correct for wave fields dominated by single mode but not for ones dominated by multiple modes because the effective dispersion curves obtained from different sizes of arrays should not be joined together. Therefore, the dependence of the effective dispersion curve on the array size should be extensively investigated and familiarised in more detail.
We simulated Rayleigh wave fields with multiple-mode dominance as ergodic stationary stochastic processes to clarify the relation between the effective dispersion curves and the array size employed for the observation. The synthetic data were prepared as time series to simulate actual observations of the wave field. Consequently, The effects of noise in the observations and the finiteness of the obtainable sample paths are taken into account. The power spectrum for generating the wave field is constructed by the dispersion curves and medium responses calculated from the subjected ground structure model (Tokimatsu et al. 1992).
The results show that the dependence of the effective dispersion curve on the distance between the observation points is not negligible, depending on the wave field of interest. In this regard, the direct fitting method of the SPAC coefficients (Ikeda et al. 2012) would be preferable in wave fields where higher-order modes dominate compared to the conventional methods of inversion via dispersion curves. Furthermore, the results imply that investigating the dependence of the effective dispersion curve on the inter-station distance would help to identify the presence or absence of excitation of higher-order modes.
The effective dispersion curve is clearly a quantity that depends on the distance between observation points by its definition (Ikeda et al. 2012). However, many researchers do not seem to pay sufficient attention to this fact. The SPAC method requires an array of receivers with many inter-station distances to obtain dispersion curves over a wide frequency range. Generally, the dispersion curves obtained from each array are collected to construct a single dispersion curve for subsequent inverse estimation of the velocity structure. This procedure is correct for wave fields dominated by single mode but not for ones dominated by multiple modes because the effective dispersion curves obtained from different sizes of arrays should not be joined together. Therefore, the dependence of the effective dispersion curve on the array size should be extensively investigated and familiarised in more detail.
We simulated Rayleigh wave fields with multiple-mode dominance as ergodic stationary stochastic processes to clarify the relation between the effective dispersion curves and the array size employed for the observation. The synthetic data were prepared as time series to simulate actual observations of the wave field. Consequently, The effects of noise in the observations and the finiteness of the obtainable sample paths are taken into account. The power spectrum for generating the wave field is constructed by the dispersion curves and medium responses calculated from the subjected ground structure model (Tokimatsu et al. 1992).
The results show that the dependence of the effective dispersion curve on the distance between the observation points is not negligible, depending on the wave field of interest. In this regard, the direct fitting method of the SPAC coefficients (Ikeda et al. 2012) would be preferable in wave fields where higher-order modes dominate compared to the conventional methods of inversion via dispersion curves. Furthermore, the results imply that investigating the dependence of the effective dispersion curve on the inter-station distance would help to identify the presence or absence of excitation of higher-order modes.