The effect of bandwidth on the interpretation of the cross spectra of wave recordings from spatially separated sites

It is argued that the coherence between records from a triangle of stations can be used to deduce not only the effective beamwidths of gravity wave patterns but can also be used to obtain their velocity bandwidth throughout the wave spectrum and its effect on the apparent velocity of propagation. Relationships between the apparent velocity of wave propagation and the velocity bandwidth are derived; they are analogous to the cross correlation approach of Briggs, Phillips, and Shinn but are herein generalized to include the frequency domain. The significance of the similarity hypothesis which is essential to the Briggs, Phillips and Shinn approach is discussed. The effect of the frequency bandwidth corresponding to the sampling rate and digital methods of analysis is considered in relation to the apparent phase velocity. The analytical results are applied to experimental data on gravity wave motions in the D region of the ionosphere.