Space-borne high frequency (HF) radar sounder is an effective tool for investigation of lunar subsurface structure in lunar exploration. The primary strategy of radar sounder technology for subsurface structure detection is utilization of the nadir echoes time delay and intensity difference from the lunar surface and subsurface. It is important to fully understand electromagnetic wave propagation, scattering, and attenuation through the lunar media in order to retrieve information of lunar layering structure from weak nadir echoes of the subsurface, which is simultaneously interfered by strong off-nadir surface clutters. Based on the Kirchhoff approximation (KA) of rough surface scattering and the ray tracing of geometric optics, a numerical simulation of radar echoes from lunar layering structures is developed. According to the lunar surface feature, the topography of mare and highland surfaces is numerically generated, and the triangulated network is employed to make digital elevations of the whole lunar surface. Scattering from the lunar surface and subsurface is numerically calculated using KA approach. Radar echoes and its range images are numerically simulated, and their dependence on the parameters of lunar layering interfaces is discussed. The approach of this paper can also be utilized to investigate subsurface structures in Mars and other planetary exploration.
混合势积分方程(mixed-potential electric field integral equation,MPIE)由于其Green函数的低阶奇异性是矩量法(MoM)等数值方法求解散射问题的主要方程.在跨界面目标的散射问题中,MPIE中的矢量势和标量势Green函数包含Sommerfeld类型的谱域积分,利用离散复镜像法(discrete compleximage method,DCIM)和Sommerfeld恒等式,将其转化为有限项复镜像Green函数的求和运算,避免了烦杂的谱域积分运算.当场点和源点位于分界面同侧时,谱函数g^(kzi)与场源位置都无关,其复指数参量可一次拟合获得,用广义函数束方法(general pencil of functions,GPOF)进行拟合.然而,当场点和源点位于分界面两侧时,谱函数与场点和源点的纵向位置(z和z′)有关.提出双重GPOF拟合方法,即将谱函数~g(kzi)对场点z分离,对有限个源区离散点z′l的谱函数用GPOF方法拟合其复镜像参量,再次使用GPOF方法拟合这些复镜像参量随z′的函数关系,则任意z′位置的复镜像参量可由函数计算直接得到,无需逐点拟合求解.对两层介质半空间环境利用双重GPOF方法、逐点GPOF方法和Sommerfeld精确积分方法分别计算,说明双重GPOF方法的有效性和准确性.本文将双重GPOF/DCIM计算跨介质分界面的理想导体球目标的散射,数值地讨论了分界面对体目标感应电流及散射的影响.
用数值模式匹配法(Numerical Mode Match,NMM)求解空间随机分布的二维任意形状导体柱目标的复合散射。每个目标的散射场在各自局部坐标系中用柱面波函数展开,外部空间的散射场由所有目标散射场的叠加共同贡献。在每个导体目标表面选取若干离散点数值匹配边界条件,得到关于展开系数的超定矩阵方程,用奇异值分解(Singular Value Decomposition,SVD)或最小二乘法获得其最佳逼近解。这样,空间的散射场可由级数展开解析计算。数值分析了展开级数的截断问题,与矩量法(Method of Moment,MoM)数值计算的结果比较和误差分析获得不同形状和不同尺寸目标的展开项数,并用多项式拟合了简单的函数式。最后,针对不同形状组合的多导体柱复合散射模型分析其双站散射计算,与MoM方法的结果比较表明:数值模式匹配法能快速准确地分析任意尺寸任意位置任意形状复合目标的散射计算。
