CROSS CORRELATIONS AND CROSS SPECTRA FOR SPACED ANTENNA WIND PROFILERS .1. THEORETICAL-ANALYSIS

The presented theory ties the properties of a turbulently advected sca ttering medium to the cross correlation and cross spectrum of signals in a general configuration of receiving and transmitting antennas. The correlation length of Bragg scatterers and antenna diameter are the s ignificant parameters determining the diffraction pattern's correlatio n length. We examine how vertical anisotropy of the scattering medium affects the diffraction pattern's correlation length. We demonstrate t hat the cross spectrum can be formulated in terms of a pair of spectra l sampling functions (a one-dimensional Doppler and a three-dimensiona l wavenumber function), and closed form solutions are obtained. We giv e the conditions under which the scattering medium's statistical prope rties can be represented by a Gaussian correlation or spectral model, and the distance over which the diffraction pattern simply advects wit hout significant change. We show that the diffraction pattern of a pai r of scatterers can translate at the speed of the scatterers, not twic e their speed as is commonly thought.