二维随机粗糙面的fBm模拟及其统计特性

数值模拟在物理建模中具有相当重要的地位。本文基于对二维分形布朗运动（ｆＢｍ）的研究，根据ｆＢｍ的特征，阐述了用二维ｆＢｍ函数模拟随机粗糙面的方法。由于很多电磁散射问题与粗糙面的各阶矩有很大的关系，我们导出了二维随机粗糙面的统计参量与分维Ｄ的关系。基于对二维ｆＢｍ的小波分析，提出了在时－频相空间估计分维Ｄ的方法。这种方法比较简单而切实可行，不但适合于粗糙面整体分维的计算，更适合于局部分数维的计算。所

fBm Simulate of Two-dimensional Rough Sarface and Its Statistic Characteristic

Numerical simulation plays a great role in physical model. In this paper, based on the analysis of two-dimension fractional Bron motion (fBm) and according to theory of fractional Brown motion (fBm), fBm simulation of two-dimension rough surface is presented. As many problems of electromagnetic scattering are related to each orders of rough surface, the relationship between the statistic parameter of rough surface and fractal dimension D is derived. According to mulitdimension wavelet theory, the esteormating of fractal dimension of rough surface is put forward in time-frequency domain, which is simple and practicable. This method not only adapts to predicting the whole fractal dimension of rough surface, but also adapts to estimating local fractal dimension. All results have been vert fed by computational simulation.