This paper investigates the relationship between the frequency features of the directional spectrum of ocean waves (cutoff frequency and peak frequency of wind waves, frequency of quasi-monochromatic swell) and the properties of the spectrum of the sea echo obtained by HF Doppler radar. A theoretical analysis is performed to check the validity of a simple result that states that at upper HF, a long-wave spectral feature at frequency F o affects the radar echo at frequencies +-fB +-Fo on either side of the Bragg lines at +_fB corresponding to resonant backscattering of radio waves with a given wavelength by half-wavelength ocean waves. An experiment using both radar and standard in situ measurements for several weeks at different times of the year shows that this relationship can be used to formulate a method for estimating the frequency features of the sea with suitable accuracy. 1. INTRODUCTION More than 20 years ago, the special spectral properties of high-frequency electromagnetic waves backscattered by the surface of the sea suggested that it might be possible to use HF radar to investigate wave fields on the surface of the ocean [Crombie, 1955]. There is indeed a correlation, because of the interaction of electromagnetic waves and ocean surface waves, between the Doppler spectrum of the radar echo and the directional spectrum of the sea. This directional spectrum can be fully extracted by the complete inversion of the radar echo, although with some difficulty [Lipa, 1978]. Nevertheless, many users who cannot operate standard in situ sensors (buoys, etc.) because of technical or economic constraints need some overall parameters of the sea state, and therefore it is of interest to study specific ways of estimating these parameters: wind direction [Long and Trizna, 1973; Stewart and Barnum, 1975; Broche, 1979], significant wave height and dominant period [Barrick, 1977a], swell characteristics [Tyler et al., 1972; Lipa and Barrick, 1980], and surface currems [Stewart and Joy, 1974; Barrick et al., 1977]. This paper deals with estimating the main fre-Copyright ¸ 1981 by the American Geophysical Union. quency-characteristic features of the sea spectrum, i.e., the cutoff and dominant frequency of wind waves and the frequency of swell. The general appearance of the Doppler spectra observed (Figure 3) is correctly described by current models of the interaction between the sea surface and HF electromagnetic waves, and especially by the models developed by Barrick [1972]. This appearance can be expressed by E(fa) = E(')(fa) + E(2)(fa) in which fa is the Doppler shift between the frequency of the radio wave received and that of the wave transmitted. E(I) (fa) represents the so-called 'first-order' echo which occurs in the form of two quasi-monochromatic lines ('Bragg lines') whose positions, which are symmetrical in relation to zero frequency, are given by fa = ---fB = -+(2gki)•/2/2• where g is the acceleration of gravity and k i the wave number of the incident electromagnetic waves. E(2)(fa) represents the so-called '...

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Fontanel, A., G. Grau, 1971, Corrélation optique en lumière cohérente, Geophysical Prospecting 19, 98–117. This paper describes a general bidimensional two‐step method of correlation (or convolution) making use of the theory of holography. In the first step the light diffracted by one of the two plane transparent objects to be correlated interferes with the light diffracted by the other one. The hologram thus generated is photographed in the focal image plane of a convergent lens. Owing to the quadratic detection property of the photographic emulsion, the square of the modulus of the product of the spectra of the two objects considered is recorded on the photographic plate. In the second step the convolution product of the two objects appears when the hologram is illuminated with a beam of coherent light. In its geophysical application this optical method of convolution makes it easy for us to obtain the autocorrelogram of a seismic cross‐section. This method also makes it possible to correlate each of the seismic traces by special precalculated optically‐recorded filters.

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