A theory for sea scatter at large incident angles (0 _> 30 ø) is developed by using a two-scale roughness model. The small-scale waves are assumed to satisfy the small perturbation assumptions, and the largescale waves to satisfy the physical optics approximations. Measured sea surface slope density and sea spectra reported by oceanographers are incorporated into the theory to explain effects of incident angle, polarization, frequency, wind speed, and anisotropic characteristics of the sea surface. It is observed that the increase of the backscattering coefficients with the wind is due primarily to the growth of the sea spectrum and, to a lesser extent, to the interaction between the two scales of roughness. This interaction effect is also the cause of the shift of the minimum of the scattering coefficient around the crosswind direction toward the downwind direction. The difference between the upwind and crosswind observations is the result of the anisotropic characteristics in the sea spectrum generated by the difference between the upwind and crosswind slope variances. The difference between the upwind and downwind observations is the consequence of the skewness in the slope probability density function of the large-scale waves defined with respect to the plane perpendicular to the look direction. Comparison with some experimental data shows satisfactory agreement.

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Equations (9) and (10) are the general design equations. Computer program SCOTTY (available from the author) solves these equations for any required boundary conditions. Abstract-To study the angular behavior of the usual backscattering integral, a numerical example is given and the integral is evaluated without approximating the surface correlation function. Results obtained are compared with approximate analytic evaluations. It isshown that either one of the two possible approximations may be acceptable, depending upon the incident frequency.

The backscattering characteristics of a computer‐generated known one‐dimensional random surface are studied by computing first the exact surface current distribution over the illuminated area (using four or more points per wavelength) by the moment methods and then calculating the backscattered field by the gaussian quadrature technique. These computations are repeated 40 to 65 times (depending on the incident frequency) over different surface segments to obtain enough scattered field samples to estimate the average scattered power. If the surface current distribution over the surface segment is estimated by the Kirchhoff approximation, the above calculations may be repeated to obtain the average scattered power under the Kirchhoff approximation. By comparing these two average scattered powers at different frequencies, it was found that (1) the two averaged powers can agree to within 2 dB over a range of frequencies in the incident angular range 0° ≤ θ ≤ 40°; (2) within the range of agreement specified in (1), the average backscattered power need not be proportional to the slope distribution of the random surface; and (3) further study is needed to establish the range of validity of the Kirchhoff approximation. Comparisons were also made between existing approximations to the Kirchhoff integral representing the average backscattered power and the numerically computed backscattered power under the Kirchhoff approximation. It was found that the choice of approximations depends upon the incident frequency and the shape of the surface correlation function.

While the present analysis is highly idealized, we have indicated that the diffusion approximation, which ignores displacement currents is adequate, in certain cases, for predicting the transient response waveform in a conducting medium. As expected, the discrepancies occur at, small times. Also, it is important to realize that the diffusion analysis does not provide any information about the wavefront of the signal at the arrival time t = ta. Finally, we should stress that in this investigation we have assumed the medium constants u and e are independent of frequency. This, in itself, can only be an approximation for a finite range of frequencies. Further work, now in progress, on this subject is concerned with realistic dispersion models for the electrical characteristics of the medium. JAMES R. W m KENNETE P. SPIES Cooperative Inst. for Rps. in Environmental Sci. University of Colorado Boulder, Colo. 80302 REFEREKCES [l] J. R. Wait. "-4 transient magnetic dipole source in a dispersive 121 B. E. Bhattacharya, PropaiaJi6n of an electric pulse through a medium." J.