基于背向散射脉冲传播时间统计特性的随机界面参数反演研究

研究了利用背向散射脉冲传播时间统计特性反演随机界面参数的问题.首先扩展了Fuks & Godin关于随机界面背向散射脉冲传播时间统计特性理论，给出了当随机界面高度-斜率统计相关情形下，最早返回的两个脉冲传播时间及其时延的概率密度函数（PDF）表达式.进而提出了一种基于背向散射脉冲传播时间统计特性的随机界面参数反演算法：采用遗传算法匹配前两个背向散射脉冲传播时间及其时延的PDF实现随机界面高度—斜率相关系数的绝对值|ρ|和无量纲参数T的反演.最后利用参数的后验概率分析反演结果的不确定性.数值模拟结果表明：该算法可有效反演随机界面的参数，参数|ρ|相对于T反演精度较高；|ρ|和T之间存在较强的参数耦合.与前人认为可忽略高度—斜率相关性（|ρ|）的观点不同：此类反演问题中应同时考虑|ρ|和T.

Inversion of rough surface parameters based on travel-time statistics of backscattered pulses

The inverse problem of rough surface parameters estimation from travel-time statistics of backscattered pulses is studied in this paper. We extend the theoretical results of Fuks and Godin on travel time statistics of backscattered pulses from a random surface to the case of surface elevation slope correlation, and obtain explicitly the probability density functions (PDF) of the travel times of the first and second backscattered pulses and the time delay between them. And a genetic algorithm based matched PDF inversion algorithm is proposed, which may be applied to estimate the elevation slope correlation |ρ| and a dimensionless parameter T of random surface from travel time statistics of backscattered pulses. The uncertainties of the parameter estimation are analysed in terms of the posterior probability distributions of inversion results. Numerical simulation illustrates that the algorithm is effective to inverse the parameters of random surface and the inversion result of |ρ| being a higher accuracy with respect to T. It is suggested that the elevation slope correlation (|ρ|) cannot be neglected as other previous authors, both |ρ| and T should be considered at the same foot in this kind of inversion problem.