The purpose of this paper is to make clear the multi-dimensional propagation phenomena of seismic waves in soil by means of statistical analyses. In the analyses are discussed the characteristics of the coherences in time and frequency domains and of the transfer functions between not only a single component but also three components of seismic motions. The sample records used for the statistical analyses are 18 earthquakes observed by a set of vertically located instruments. The correlation functions between orthogonal horizontal components as well as between the corresponding components are high for the time lags that are almost equal to the travel times of vertical incident and reflect shear waves. It is shown that the amplitudes of the transfer functions for orthogonal components reveal peaks at about the natural frequencies of shear wave soil models by estimating the transfer functions fo 3-dimensional seismic motion vector for 3-inputs-3-outputs systems. The results indcate that seismic shear waves propagate multi-dimensionally. It is concluded that seismic shear waves propagate vertically in soil with changing the directions of motion. This change can be explained in terms of the irregularities of soil structure.
