基于平滑因子和勒让德多项式展开的月坑地形模型

A Model of Lunar Crater Section Topography Based on Smooth Factor and Legendre Polynomials

提出引入平滑因子的月坑模型,使其接近月坑真实的碗状模型,以利于吉布斯现象的抑制.考虑月坑旋转体模型的对称性,仅对模型剖面进行建模,使用勒让德多项式进行展开,可有效地简化运算.结果表明:平滑因子的引入使得月坑理论模型的边界更加平滑,有效地避免了吉布斯现象中杂波的产生.对勒让德展开系数求解的两类方法REC和ASY进行比较分析,发现基于渐近公式的ASY算法更加稳定,特别是超高阶展开系数的求解.研究可为月坑区域有效弹性厚度的估计提供参考.

We propose a theoretical model of lunar crater to suppress Gibbs phenomenon by introducing a smooth-factor.The model makes crater close to its real morphology of a bowl.Considering revolving symmetry,we model merely its section topography and expand it in Legendre polynomials for simplification.It shows that the smooth-factor smoothes crater’s boundary and avoids generation of oscillations in Gibbs phenomenon.For estimation of expansion coefficients,ASY shows advantage of stability than REC,particularly at super-high degrees.It provides a reference for selenophysical parameters estimation,especially for effective elastic thickness over craters.