1:45 PM - 3:15 PM
[SSS09-P05] A study on estimating the arrival direction of microtremors from arrays of simple geometry
Keywords:Microtremor, Rayleigh wave, FK spectrum, Array observation
A method was developed to estimate Quasi-frequency-wavenumber spectrum (Quasi-FK spectrum), which has similar characteristics to Frequency-wavenumber spectrum (FK spectrum), from simultaneous observation records of the vertical component of microtremor from an array consists of relatively freely arranged three receivers.
This method is distinctive in that it uses particle swarm optimization (PSO), one of the metaheuristic methods, which allows for a relatively free arrangement of the receivers and provides a wealth of information on the back azimuth of waves despite the small number of receivers. In addition, the proposed method allows the intensity distribution of microtremors with respect to back azimuth to be determined specifically. In contrast to the FK spectrum, the Quasi-FK spectrum can be expressed as a one-variable function with only azimuth as an argument rather than a two-variable function at a certain frequency because it is an effective mode representation of the FK spectrum. Thus, an approximate model of the Quasi-FK spectrum can be considered with fewer parameters than to create that of the FK spectrum. We therefore assume a functional form of the Quasi-FK spectrum with some parameters and identified their value by the information obtained from observations using the PSO. However, due to the limited number of parameters that can be identified, complex functional forms cannot be assumed, and only unimodal, symmetric-shaped functions were considered.
The proposed method was applied to ideal synthetic data and actual field data to confirm its validity and effectiveness. Verification using the synthetic data confirms that the mean arrival direction and the degree of concentration of intensity distribution can be estimated correctly as long as the wavefield is not isotropic. Moreover, it was found that results obtained using a flattened-shaped array were not much different from those obtained using an array of an equilateral triangle. In the analysis of the field data, the FK method (Capon 1969), which is a typical method for obtaining information on the arrival direction of the waves, was also applied. As a result, it was shown that the Quasi-FK spectrum obtained by the proposed method was approximately consistent with the Capon’s FK spectrum in the frequency range where single mode dominates and the intensity distribution can be regarded as unimodal, symmetric-shaped function.
This method is distinctive in that it uses particle swarm optimization (PSO), one of the metaheuristic methods, which allows for a relatively free arrangement of the receivers and provides a wealth of information on the back azimuth of waves despite the small number of receivers. In addition, the proposed method allows the intensity distribution of microtremors with respect to back azimuth to be determined specifically. In contrast to the FK spectrum, the Quasi-FK spectrum can be expressed as a one-variable function with only azimuth as an argument rather than a two-variable function at a certain frequency because it is an effective mode representation of the FK spectrum. Thus, an approximate model of the Quasi-FK spectrum can be considered with fewer parameters than to create that of the FK spectrum. We therefore assume a functional form of the Quasi-FK spectrum with some parameters and identified their value by the information obtained from observations using the PSO. However, due to the limited number of parameters that can be identified, complex functional forms cannot be assumed, and only unimodal, symmetric-shaped functions were considered.
The proposed method was applied to ideal synthetic data and actual field data to confirm its validity and effectiveness. Verification using the synthetic data confirms that the mean arrival direction and the degree of concentration of intensity distribution can be estimated correctly as long as the wavefield is not isotropic. Moreover, it was found that results obtained using a flattened-shaped array were not much different from those obtained using an array of an equilateral triangle. In the analysis of the field data, the FK method (Capon 1969), which is a typical method for obtaining information on the arrival direction of the waves, was also applied. As a result, it was shown that the Quasi-FK spectrum obtained by the proposed method was approximately consistent with the Capon’s FK spectrum in the frequency range where single mode dominates and the intensity distribution can be regarded as unimodal, symmetric-shaped function.