基于平滑因子和勒让德多项式展开的月坑地形模型

doi:10.19596/j.cnki.1001-246x.7946

计算物理 ›› 2019, Vol. 36 ›› Issue (6): 726-732.DOI: 10.19596/j.cnki.1001-246x.7946

基于平滑因子和勒让德多项式展开的月坑地形模型

钟振^1,2,3, 张腾^1,2, 雷良建¹

1. 贵州师范大学物理与电子科学学院, 贵州贵阳 550001;
2. 贵州省射电天文数据处理重点实验室, 贵州贵阳 550025;
3. 武汉大学测绘遥感信息工程国家重点实验室, 湖北武汉 430079

收稿日期:2018-08-20 修回日期:2018-09-29 出版日期:2019-11-25 发布日期:2019-11-25
作者简介:钟振(1982-),男,博士,副教授,从事月球重力场和月球内部结构研究,E-mail:zhenzhongmail@163.com
基金资助:
国家自然科学基金（41864001，41404021）、武汉大学测绘遥感信息工程国家重点实验室开放基金（17P03）及贵州师范大学博士科研资助项目

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

ZHONG Zhen^1,2,3, ZHANG Teng^1,2, LEI Liangjian¹

1. School of Physics and Electronic Science, Guizhou Normal University, Guiyang, Guizhou 550001, China;
2. Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University, Guiyang, Guizhou 550025, China;
3. State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, Hubei 430079, China

Received:2018-08-20 Revised:2018-09-29 Online:2019-11-25 Published:2019-11-25

摘要/Abstract

摘要： 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.

关键词: 月坑地形, 勒让德多项式展开, 高斯-勒让德积分, 渐近展开

Abstract: 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.

Key words: crater topography, Legendre polynomial expansion, Gauss-Legendre quadrature, asymptotic expansion

中图分类号:

P223

钟振, 张腾, 雷良建. 基于平滑因子和勒让德多项式展开的月坑地形模型[J]. 计算物理, 2019, 36(6): 726-732.

ZHONG Zhen, ZHANG Teng, LEI Liangjian. A Model of Lunar Crater Section Topography Based on Smooth Factor and Legendre Polynomials[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(6): 726-732.

参考文献

[1] TURCOTTE D L, HAXBY W F, NORBERRY J. Role of membrane stresses in the support of planetary topography[J]. Journal of Geophysical Research Solid Earth, 1981, 86(B5):3951-3959.
[2] ARKANI-HAMED JAFAR. The lunar mascons revisited[J]. Journal of Geophysical Research Planets, 1998, 103(E2):3709-3739.
[3] SUGANO T, HEKI K. Isostasy of the Moon from high-resolution gravity and topography data:Implication for its thermal history[J]. Geophysical Research Letters, 2004, 31(24):1183-1186.
[4] CROSBY A, MCKENZIE D. Measurements of the elastic thickness under ancient lunar terrain[J]. ICARUS, 2005, 173(1):100-107.
[5] HUANG Q, WIECZOREK M A. Density and porosity of the lunar crust from gravity and topography[J]. Journal of Geophysical Research Planets, 2012, 117(E05003):1-9.
[6] ZHONG Z, LI F, YAN J, et al. Lunar geophysical parameters inversion based on gravity/topography admittance and particle swarm optimization[J] Advances in Space Research, 2014, 54(4):770-779.
[7] ZHONG Z, JIANGUO Y, RODRIGUEZ J,et al. Ancient selenophysical structure of the Grimaldi basin:Constraints from GRAIL gravity and LOLA topography[J]. ICARUS, 2018, 309, 411-421.
[8] WILLIAMS D E, MCCAULEY J F, TRASK N J. The geologic history of the moon[R]. US Geol Survey Prof Paper, 1348.
[9] CINTALA M J, WOOD C A, HEAD J W, et al. The effets of target characteristics on fresh crater morphyology-Preliminary results for the moon and Mercury[C]//Lunar & Planetary Science Conference, 1979, 9:3803-3830.
[10] ARTEMIEVA N A, IVANOV B A. Numerical simulation of oblique impacts:Impact melt and transient cavity size[C]//Lunar & Planetary Science Conference, 2001, 32.
[11] GOLUB G H, WELSCH J H. Calculation of Gauss quadrature rules[J]. Mathematics of Computation, 1969, 23(23):221-230.
[12] BAILEY D, JEYABALAN K, XIAOYE L S. A comparison of three high-precision quadrature schemes[J]. Experimental Mathematics, 2005, 14(3):317-329.
[13] HALE N, TOWNSEND A. Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights[J]. 2012, 35(35):652-674.
[14] BOGAERT I. Iteratin-free computation of Gauss-legendre quadrature nodes and weights[J]. Siam Journal on Scientific Computing, 2014, 36(3):1008-1026.
[15] GIBBS J W. Fourier's series[J]. Nature, 2010, 59(1522):200-200.
[16] WILLIAMS K K, ZUBER M T. Measurement and analysis of lunar basin depths from Clementine altimetry[J]. Icarus, 1998, 131(1):107-122
[17] 姚端正,梁家宝. 数学物理方法[M]. 北京:科学出版社, 2010.
[18] WIECZOREK M A, NEUMANN G A, NIMMO F, et al. The crust of the moon as seen by GRAIL[J]. Science, 2013, 339(6120):671-675.
[19] 李庆杨,王能超,易大义. 数值分析[M]. 北京:清华大学出版社, 2014.
[20] 程乾生. 数字信号处理[M]. 北京:北京大学出版社, 2010.

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

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