Recently, microtremors are investigated for the application to earthquake engineering, and many of these studies pay much attention to power spectrum. But, power spectrum depends not only on the underground structure of the observation site but alse on the path of propagation and the source spectrum. It is therefore important to extract the quantities of microtremors which depend only on the under ground structure. One is the phase velocity of microtremors, and another is the linear relation between radial and vertical components, if microtremors are composed only of Rayleigh wave.
In the present paper, the quantities of microtremors are derived in a statistical way. It is demonstrated that the phase velocity of vertical component of microtremors can be obtained by means of frequency-wavenumber spectrum in the case of complex wave field, and by means of phase difference between two observation points in the case of simple wave field. But, the linear relation could not be obtained, because of complex constitution of horizontal components or coexistance body waves and/or higher mode Rayleigh waves with fundamental mode Rayleigh wave.