Abstract
We present general formulation that can compose various methods to determine phase velocities, arriving directions of Rayleigh and Love waves, and particle motions of Rayleigh waves, by using a circular array data set of three-component microtremors. We also present formulas to examine the effects of both the number of sensors consisting of a seismic array and the presence of noise on the analysis results. In the formulation, we postulate that a wavefield of microtremors is a set of plane waves propagating in a 2D plane, polarized in the horizontal directions, and that each wave is not correlated with others. Our formulation is valid under general situations where plane waves arrive from different directions with different intensities.
The data processing procedure to apply our formulation is as follows. Horizontal-component waveforms provided from a circular array are compiled into two kinds of data sets of waveforms: radial and tangential components with respect to the circular array. Respective component waveforms are Fourier-expanded with regard to the angular-axis at each time, so that the resulting Fourier coefficients form complex time histories. Those time histories are used to estimate either cross or power spectral densities, from which we extract the information of interests, such as phase velocities, arriving directions, and particle motions. The formulations presented in this study describe the relation between the spectral densities and those quantities.
