A theoretical study of the use of arrays for the analysis of seismic noise fields has been completed. The frequency-wavenumber power spectral density P(kx,ky,f) is defined and techniques for estimating it are given. The estimates require that the auto- and crosspower spectral densities be estimated for all elements in the array. Subject to certain asymptotic properties of these auto- and crosspower spectral density estimates, expressions for both the mean and variance of the estimates of P(kz,ky,f) have been obtained. It has been demonstrated that if P(kx,ky,f)is estimated by the Frequency Domain Beamforming Method, then the estimate has the same stability as the estimates of auto? and crosspower spectral density.
P(kx,ky,f)has been estimated from both long- and short-period noise recorded by the Large Aperture Seismic Array in Montana. At frequencies higher than 0.3 Hz, a compressional body-wave component which correlates with atmospheric disturbances over distant oceans has been detected. In the frequency range of 0.2 and 0.3 Hz both body waves and higher mode Rayleigh waves are observed. At frequencies below 0.15 Hz the organized vertical component of microseisms consists primarily of fundamental mode Rayleigh waves. Appreciable amounts of fundamental mode Love wave energy may also be present on horizontal instruments at these low frequencies.