非线性随机表面Kirchhoff散射模式

自从Longuet-Higgins(1963)根据非线性作用导出较正态分布为准确的波面高度分布以来，高阶矩在军事、高科技等很多方面得到了应用。Huang等(1980)曾检验了高阶非线性分布，他们发现当波高概率分布中包含直至四阶项时与观测结果相符，但如果考虑更高阶不但效果不好，反而更差。尽管非线性随机过程在海浪理论中获得了广泛的应用，但对海面雷达散射研究仅讨论到三阶矩的影响(Fung et al.，1991；Chen et al.，1992)。电磁随机表面散射理论有适应大尺度随机起伏的粗糙面的Kirchhoff散射模式、轻度粗糙表面的微扰散射模式、大小尺度独立叠加的双尺度散射模式、全波散射模式(Bahar，1987)和积分方程散射模式(Chen et al.，1992)等。对随机粗糙Kirchhoff表面电磁波散射问题，尽管几十年来许多科学家已经进行了大量研究(Fung et al.，1991； Ulaby et al.，1982；Wu et al.，1988)，Eom等(1983)曾对Gaussian面和非 Gaussian面的散射特性进行了比较研究，Fung等(1991)将Kirchhoff散射模式推广应用到三阶粗糙随机表面，然而更高阶矩对散射截面的影响还未见报道。本文在Fung等(1991)的基础上将Kirchhoff散射模式推广应用到四阶项，并对模式的应用进行了分析和讨论。

A KIRCHHOFF SCATTERING MODEL FOR NONLINEAR RANDOM SURFACES

According to two-dimensional nonlinear ocean wave model, the standard Kirchhoff surface scattering model is extended to include the forth order surface statistics. The bistatic radar scatterting coefficient, which includes the surface correlation function, the surface skewness function and the surface kurtosis function, is derived. The radar backscattering cross section is calculated and the effects of the surface skewness function and the surface kurtosis function are also discussed. Conclusions can be drawn as follows: (1) the effect of the surface correlation function is dominant for the radar backscattering cross section, (2)the effect of the surface skewness function is the largest at the direction of surface tilt, (3)the larger the incidence angle is, the larger the effect of the surface kurtosis function on the radar backscatter cross section.