ON THE THEORY OF DELTA-K RADAR OBSERVATIONS OF OCEAN SURFACE-WAVES

We consider the theory of waves scattered from a moving, rough, and di spersive surface in the small perturbation limit, The first-order scat tered field for a time-dependent surface is obtained in the far zone o f scattering in terms of the two-dimensional spectral amplitude of the surface and its dispersion relation, We develop a rigorous Delta k ra dar theory and show that the nonzero output of a Delta k radar occurs only when the Bragg condition for each signal component is satisfied s eparately, The frequency correlation function of the scattered field i s then proportional to the mean value of the product of the spectral a mplitudes of the surface at the corresponding Bragg wavenumbers. The m ean value of this product is nonzero only for surfaces that have a loc ally varying spectrum and is proportional to the Fourier transform (wi th the argument Delta k) of the variation of the local spectrum with r espect to the pattern position, Such variations may be caused by eithe r amplitude or phase modulation of the surface structure, In the forme r case, our results are similar to the results of existing theory. The latter case of phase modulation of the surface (for example, internal waves interacting with capillary waves) cannot be explained by previo us theory.