Method for estimating azimuthal intensity distribution of microtremors using simple arrays

Abstract

SUMMARY In this paper, a method is proposed for estimating the intensity distribution of microtremors for the arrival direction, from simultaneous observations of vertical motion, using an array of simple geometry consisting of only three receivers. This method is based on the fact that the complex coherence function, which is defined as the normalized cross-spectrum of microtremor recordings observed at two sites, contains information about the azimuthal intensity distribution of the microtremor field. To obtain the azimuthal intensity distribution from a limited number of conditions, the functional form of the azimuthal intensity distribution of the microtremor field was assumed and its parameters were estimated. Information on the arrival direction of the microtremor field was specifically obtained using particle swarm optimization (PSO), one of the metaheuristic methods, and then employed to identify the parameters. The proposed method was applied to ideal synthetic data to clarify the potential problems that may arise from using PSO as the core algorithm. Despite PSO-induced errors, the proposed method was able to accurately infer directional information over a wide frequency range. The proposed method was also applied to actual field data to verify its effectiveness and applicability. The results indicate that the proposed method can provide similar results to the frequency–wavenumber (FK) method in a wide frequency range. The quasi-FK spectrum, an effective mode representation of the FK spectrum, was displayed to visualize the directionality.