基于重力/地形导纳的月球物理参数反演和月球热模型研究
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摘要
目前主要月球重力场模型已经实现了月球的全球覆盖,全球有效阶次已得到显著地提高,月球地形模型的有效阶次已达历史之最,可以满足月球物理研究的需求。由于月震数据有限,且月震台站分布不均,无法利用月震数据分析月球的全球特征,因此,利用重力和地形数据分析月球物理参数的全球特征已成为可能,利用重力/地形导纳求解月壳厚度、岩石圈弹性厚度、月球表面热流密度已成为当前的主要手段。LLR数据表明月-地间距在不断地增大,早期月-地间距较小,月球所受潮汐力较大,利用重力/地形导纳求解岩石圈的弹性厚度,可以探究早期潮汐效应对月球热演化的影响。本文所做的工作如下：
1.利用球面函数对主要月球重力场模型进行了局部谱分析,同时利用GEODYN-Ⅱ定轨软件仿真分析了不同轨道特征的探月卫星对月球重力场模型的改进。结果表明CEGM02较适合于作月球物理解释,SGM150j较适合于作探月卫星精密定轨。综合以往探月卫星如嫦娥一号、嫦娥二号、SELENE、LP、Clementine、 Lunar Orbiters、GRAIL等探月卫星轨道跟踪数据,并对数据基准进行统一,采用最优化的数据融合方案和Kaula约束准则,可进一步解算高精度的月球重力场模型,为未来月球重力场模型的研制和月球物理参数的求定提供参考。
2.针对月震数据有限、月震台站分布不均、传统方法单独反演月球物理参数的不适宜性,提出联合月球重力/地形导纳和非线性反演方法粒子群PSO算法同时求解物理参数如载荷比、月壳厚度、月壳密度、岩石圈弹性厚度等,并分析了不同月球重力场模型参与重力/地形导纳和相关性分析的差异。结果表明主要月球重力场模型在月球正面较适合于作重力/地形导纳研究,CEGM02和SGM150j较适合于作月球背而重力/地形导纳分析；粒子群PSO算法能够同时反演月球物理参数的最优解,计算效率高于传统迭代方法。本文方法比较适合于月球物理参数多参数的反演,可为月球内部精细结构研究提供有宜的参考。
3.不同研究使用的数据不同,采用的数据处理方法也不同,计算得到的月核大小及其组成各异。由于各类信息的缺乏对月球深部结构的分析存在极大的不确定性,利用月球平均密度p和转动惯量因子I/MR2作为约束参数,采用六层月球分层模型研究了月核的大小及其密度组成。结果表明月核大小约为410km,相应的密度大约为5.768g/cm3,说明月核的组成成分可能为Fe-FeS的合金,与大多数学者的研究结果相似。计算求得的月球圈层结构及内部密度分布具有一定的参考价值。
4.针对早期月-地间距较近,月球所受潮汐力较大,利用变分基本引理将月球热演化的控制方程转换成相应的弱解形式,并对弱解形式进行无量纲处理。利用重力/地形导纳求解的弹性厚度进一步求解表而热流密度,并以此为约束条件,使用有限元方法研究了潮汐力在不同初始温度条件下对月球热演化的影响。结果表明潮汐效应会加快热对流的产生,促使月-地连线方向产生大尺度的对流柱,加速月球内部热量的释放。综合其它物理机制可能为月球不对称热演化、月壳二分性、玄武岩二分性、月岩剩磁等成因提供解释。
Gravity coefficients of most lunar gravity field models are becoming more valid globally. And the lunar topography model derived from LOLA data is even expressed to degree and order720. This makes lunar geophysical research thus become possible. Because of the selenographical limited extent of network, lunar geophysical parameters cannot be obtained globally just from limited seismic data. Another powerful method that can be used to probe the lunar subsurface structure globally is through the collaborative analysis of gravity and topography data. Then the lunar crustal thickness, lithosphere elastic thickness and surface heat flux can be obtained from gravity/topography admittance. Besides, LLR data indicates that the distance between the moon and the earth is increasing. This shows that the distance might be smaller in the early stage when the moon suffered a larger tidal force exerted by the earth. Tidal force should therefore be considered in the lunar thermal evolution. Using heat flux derived from elastic thickness as a constraint, the tidal effect on the thermal evolution can then be predicted. So this work in this thesis is as follows:
1. We analyzed degree RMS of various gravity field models by using localized spherical harmonic functions. The contribution of various orbits in the lunar gravity field model was also investigated through the orbit determination software GEODYN-Ⅱ. Results indicate that CEGM02takes an advantage in the lunar geophysical parameters estimation, but SGM150j is more suitable for the precision orbit determination. With the joint of data from Chang'E-1, Chang'E-2, SELENE, LP, Clementine, Lunar Orbiters and GRAIL, we can solve a more accurate lunar gravity field model, when considering new optimization methods and Kaula constraint. This research can provide a good reference for the production of new gravity field model and the estimation of lunar geophysical parameters.
2. Because of the limited lunar seismic data, the limited selenographical extent of network and the traditional methods failing in the best inversion solution, some lunar geophysical parameters such as load ratio, crustal thickness, crustal density and lithosphere elastic thickness can be simultaneously calculated with the joint of lunar gravity/topography admittance and nonlinear inversion method Particle Swarm Optimization namely PSO. Using this method, we also analyzed the admittance and correlation difference of various gravity field models. Results show that all the models are appropriate for gravity/topography admittance and correlation analysis on the nearside of the moon. But as to the farside, CEGM02and SGM150j show a superior advantage in such analysis. Moreover, through the algorithm PSO, all the parameters of the best-fit model can be calculated with a reducing calculation time. It can be concluded that multi-parameters inversion can be successful with the joint admittance and PSO, which is unquestionably beneficial for lunar internal structure investigation.
3. Separate data and approach often lead to a discrepancy in the size of the lunar core and its composition. And the lack of information about the interior structure often results in uncertainty. Up to now, the lunar average density and its inertia moment factor Ⅰ/MR2are widely used to place constraints on its interior structure. We modeled the moon as a sphere with six layers by using such method. Results show that the size of the lunar core is about410km and its corresponding density is approximately5.768g/cm3. This indicates that the core may be composed of Fe-FeS alloy, which is similar with other findings. Consequences concluded here could provide a useful reference for further studies.
4. The distance between the moon and the earth may be slight in the early stage, when the moon might suffer a larger tidal force exerted by the earth. This is why tidal force should be considered in the lunar thermal evolution, especially in its initial stage. We converted the governing equation of the thermal evolution into dimensionless weak form. Using the finite element method analysis, the thermal evolution of the moon was investigated with different initial temperatures when considering tidal effect on different stages. Results indicate that tidal force can speed up the generation of convection, and cause large-scale convection column in center-to-center direction from the moon to the earth, which accelerates the interior heat release. Consequences here could provide some interpretation for lunar asymmetric thermal evolution, crust dichotomy, basalt dichotomy and remanence in the rock with the combination of other physical mechanism.
1.利用球面函数对主要月球重力场模型进行了局部谱分析,同时利用GEODYN-Ⅱ定轨软件仿真分析了不同轨道特征的探月卫星对月球重力场模型的改进。结果表明CEGM02较适合于作月球物理解释,SGM150j较适合于作探月卫星精密定轨。综合以往探月卫星如嫦娥一号、嫦娥二号、SELENE、LP、Clementine、 Lunar Orbiters、GRAIL等探月卫星轨道跟踪数据,并对数据基准进行统一,采用最优化的数据融合方案和Kaula约束准则,可进一步解算高精度的月球重力场模型,为未来月球重力场模型的研制和月球物理参数的求定提供参考。
2.针对月震数据有限、月震台站分布不均、传统方法单独反演月球物理参数的不适宜性,提出联合月球重力/地形导纳和非线性反演方法粒子群PSO算法同时求解物理参数如载荷比、月壳厚度、月壳密度、岩石圈弹性厚度等,并分析了不同月球重力场模型参与重力/地形导纳和相关性分析的差异。结果表明主要月球重力场模型在月球正面较适合于作重力/地形导纳研究,CEGM02和SGM150j较适合于作月球背而重力/地形导纳分析；粒子群PSO算法能够同时反演月球物理参数的最优解,计算效率高于传统迭代方法。本文方法比较适合于月球物理参数多参数的反演,可为月球内部精细结构研究提供有宜的参考。
3.不同研究使用的数据不同,采用的数据处理方法也不同,计算得到的月核大小及其组成各异。由于各类信息的缺乏对月球深部结构的分析存在极大的不确定性,利用月球平均密度p和转动惯量因子I/MR2作为约束参数,采用六层月球分层模型研究了月核的大小及其密度组成。结果表明月核大小约为410km,相应的密度大约为5.768g/cm3,说明月核的组成成分可能为Fe-FeS的合金,与大多数学者的研究结果相似。计算求得的月球圈层结构及内部密度分布具有一定的参考价值。
4.针对早期月-地间距较近,月球所受潮汐力较大,利用变分基本引理将月球热演化的控制方程转换成相应的弱解形式,并对弱解形式进行无量纲处理。利用重力/地形导纳求解的弹性厚度进一步求解表而热流密度,并以此为约束条件,使用有限元方法研究了潮汐力在不同初始温度条件下对月球热演化的影响。结果表明潮汐效应会加快热对流的产生,促使月-地连线方向产生大尺度的对流柱,加速月球内部热量的释放。综合其它物理机制可能为月球不对称热演化、月壳二分性、玄武岩二分性、月岩剩磁等成因提供解释。
Gravity coefficients of most lunar gravity field models are becoming more valid globally. And the lunar topography model derived from LOLA data is even expressed to degree and order720. This makes lunar geophysical research thus become possible. Because of the selenographical limited extent of network, lunar geophysical parameters cannot be obtained globally just from limited seismic data. Another powerful method that can be used to probe the lunar subsurface structure globally is through the collaborative analysis of gravity and topography data. Then the lunar crustal thickness, lithosphere elastic thickness and surface heat flux can be obtained from gravity/topography admittance. Besides, LLR data indicates that the distance between the moon and the earth is increasing. This shows that the distance might be smaller in the early stage when the moon suffered a larger tidal force exerted by the earth. Tidal force should therefore be considered in the lunar thermal evolution. Using heat flux derived from elastic thickness as a constraint, the tidal effect on the thermal evolution can then be predicted. So this work in this thesis is as follows:
1. We analyzed degree RMS of various gravity field models by using localized spherical harmonic functions. The contribution of various orbits in the lunar gravity field model was also investigated through the orbit determination software GEODYN-Ⅱ. Results indicate that CEGM02takes an advantage in the lunar geophysical parameters estimation, but SGM150j is more suitable for the precision orbit determination. With the joint of data from Chang'E-1, Chang'E-2, SELENE, LP, Clementine, Lunar Orbiters and GRAIL, we can solve a more accurate lunar gravity field model, when considering new optimization methods and Kaula constraint. This research can provide a good reference for the production of new gravity field model and the estimation of lunar geophysical parameters.
2. Because of the limited lunar seismic data, the limited selenographical extent of network and the traditional methods failing in the best inversion solution, some lunar geophysical parameters such as load ratio, crustal thickness, crustal density and lithosphere elastic thickness can be simultaneously calculated with the joint of lunar gravity/topography admittance and nonlinear inversion method Particle Swarm Optimization namely PSO. Using this method, we also analyzed the admittance and correlation difference of various gravity field models. Results show that all the models are appropriate for gravity/topography admittance and correlation analysis on the nearside of the moon. But as to the farside, CEGM02and SGM150j show a superior advantage in such analysis. Moreover, through the algorithm PSO, all the parameters of the best-fit model can be calculated with a reducing calculation time. It can be concluded that multi-parameters inversion can be successful with the joint admittance and PSO, which is unquestionably beneficial for lunar internal structure investigation.
3. Separate data and approach often lead to a discrepancy in the size of the lunar core and its composition. And the lack of information about the interior structure often results in uncertainty. Up to now, the lunar average density and its inertia moment factor Ⅰ/MR2are widely used to place constraints on its interior structure. We modeled the moon as a sphere with six layers by using such method. Results show that the size of the lunar core is about410km and its corresponding density is approximately5.768g/cm3. This indicates that the core may be composed of Fe-FeS alloy, which is similar with other findings. Consequences concluded here could provide a useful reference for further studies.
4. The distance between the moon and the earth may be slight in the early stage, when the moon might suffer a larger tidal force exerted by the earth. This is why tidal force should be considered in the lunar thermal evolution, especially in its initial stage. We converted the governing equation of the thermal evolution into dimensionless weak form. Using the finite element method analysis, the thermal evolution of the moon was investigated with different initial temperatures when considering tidal effect on different stages. Results indicate that tidal force can speed up the generation of convection, and cause large-scale convection column in center-to-center direction from the moon to the earth, which accelerates the interior heat release. Consequences here could provide some interpretation for lunar asymmetric thermal evolution, crust dichotomy, basalt dichotomy and remanence in the rock with the combination of other physical mechanism.
引文
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