二维改进分形海面电磁散射分形规律分析

摘要

Aiming at the problem that the power spectrum of fractal sea surface model cannot satisfy the positive power law when the spatial wave numbers are smaller than the fundamental wave numbers, we propose a 2-D sea surface model which combines the statistical model with the normali-sation band-limited Weierstrass fractal model.It determines the closed-form solutions of surface power spectrum and directional distribution function, and compares the data of surface power spectrum with the data in related literatures .The closed-form solution of the electromagnetic scattering coef-ficient of the model is deduced under the condition of Kirchhoff approximation.The real and imaginary parts of Hurst exponents of the scattering co-efficient which varying along with the time are calculated as well, its fractal dimensionality is then further derived.From the results of simulation it is known that the surface power spectrum fits well with the common spectrum of Pierson-Moskowitz (PM), this validates the effectiveness of the model.The scattered signal maintains some of the fractal characteristics of the fractal sea surface, and its fractal dimensionality equals to the fractal dimensionality of the sea surface minus 1, this provides a new assessment for the detection of sea surface targets .%针对分形海面模型的功率谱在空间波数小于基波波数时不能满足正幂律的问题，提出一种统计模型和归一化带限Weierstrass分形模型相结合的二维海面模型，确定了表面功率谱和方向分布函数的闭式解进行了表面功率谱和有关文献的数据的对比。在满足Kirchhoff近似的条件下推导该模型电磁散射系数的闭式解，计算了散射系数随时间变化的实部和虚部的Hurst指数，进而求得其分形维数。从数值仿真结果可知表面功率谱和PM谱都拟合的很好，验证了模型的有效性。散射信号保持着分形海表面的一些分形特性，并且其分形维数为海表面的分形维数减1，这为海面目标检测提供了新的评估。