Dual-frequency dual-wavenumber cross-coherence of nonstationary and inhomogeneous harmonizable random fields

We present a definition of a dual-frequency dual-wavenumber cross-spectrum of two nonstationary and inhomogeneous harmonizable random fields, which is in fact a generalization of the Loeve (dual-frequency) cross-spectrum of two random processes. Furthermore, a geometric argument shows that a proper normalization yields a natural measure of cross-coherence, and application of Cauchy-Schwarz´s inequality results in a necessary and sufficient condition for full cross-coherence. Finally, estimators of the cross-spectrum and the cross-coherence based on the multitaper approach are suggested, and tested on simulated data.