月球重力异常特征与三维密度成像研究
摘要
“嫦娥工程”总体目标之一是研究月球的起源和演化,特别是月球内部层圈结构的形成和演化。以新近的高分辨率高精度的月球卫星重力、地形地貌以及其它月球物理、月球化学探测资料为基础,通过分析和反演月球重力异常,可以更进一步地刻画月球内部结构,为研究月球演化提供依据。论文旨在利用嫦娥一号探测成果,采用新的方法获取月球全球布格重力异常,依据月球重力场特征,分析与识别月球质量瘤,并通过实现月球全球重力异常三维反演,探讨月球撞击盆地演化以及月陆、月海壳幔结构特征等科学问题,为实现我国“嫦娥工程”科学目标提供资料和知识积累。本文采用地球物理反演理论与行星地质科学问题相结合的思路,基于我国嫦娥一号地形模型CLTM-s01和日本SELENE最新月球重力模型SGM100h,研究探讨了月球内部结构及演化问题。
论文首先从月球布格重力异常特征分析着手,根据布格异常的定义,运用球坐标系地形引力效应计算方法,进行了全球地形校正计算,获得了月球全球布格重力异常。通过分析对比质量瘤的异常特征,提出了用布格重力异常识别质量瘤的思想,认为Hertzsprung和Korolev撞击盆地并不具备质量瘤的特点,推断质量瘤撞击盆地高密度物质可能有不同的成因。统计显示,质量瘤盆地可分为平原类型和高地类型,面积较小的高地型质量瘤盆地的高密度物质主要分布在浅部,为充填的高密度玄武岩质岩石；平原型质量瘤盆地的高密度物质主要分布在深部,为上隆的高密度月幔物质。南极Aitken盆地存在与雨海类似的布格重力异常特征,因此本文将其列为月球最大的平原型质量瘤盆地。
论文在分析目前国内外位场反演成像方法的基础上,系统地讨论了球坐标系统中位场反演问题,尤其是模型加权函数问题。依据Backus-Gilbert模型评价理论,给出了新的全球密度成像模型目标函数,通过分析直角坐标系统中模型深度加权函数,推导出了基于球坐标系统的模型深度加权函数,并成功地构建了全球卫星重力异常密度反演算法的技术流程；通过模型约束和评价来压制降低反演的非唯一性,获得了可信的密度成像结果。理论模型密度成像结果表明,算法稳定收敛。
论文根据上述方法所得到月球布格重力异常,首先对雨海、澄海和东方海三个典型质量瘤撞击盆地的重力异常进行了反演成像,结果表明,质量瘤的异常源主要位于20-50km深度之间。其次,全球三维密度成像结果印证了局部密度成像结果,说明全球密度成像方法能获得合理的密度结构,且异常源之间有微弱连结。南极Aitken盆地下方的密度结构与正面质量瘤盆地类似,高密度物质同样集中在20-50km深度；在月球背面斜长岩高地区域,月球内部的径向密度极小值分布在10-50km深度。可以推测在50km深度之上,月球内部物质在球面和径向分布不均匀；而在50km之下,物质密度分布较均匀,斜长岩高地的月壳厚度可能达不到此前认为的100km。
论文所采用的月球卫星重力异常反演和分析方法,为月球内部结构研究提供了定量化的手段,所提出的球坐标三维密度成像方法,可用于球体内部三维结构分析,为行星内部结构及演化研究提供了新的途径。
One of the objectives in "Chang'E project" is to study the origination and evolution of the Moon, especially the interior layered structures. Current satellite gravity and topography of the Moon, in presence of high resolution and accuracy, and other data from lunar physical or chemical investigation have provided useful information to interpreate the lunar internal structure. Gravity field is currently the best data set to study the planetary interior structures. The lunar gravity anomaly reveals the lateral heterogeneities of surface and interior substance. Gravity inversion is a valid method to investigate the density structure in the lunar interior. In this thesis, the lunar Bouguer gravity anomaly was calculated by using a method of terrain correction in spherical coordinates system. Inversion of lunar gravity data can be used to analyze the density distribution and origination of the mascons, and then to study the evolution of lunar impact basins and the crust-mantle structures.
By applying the geophysical inversion theory to solve the planetary science problem, I firstly studied and discussed the inner structure of the Moon based on the Chang'E-1 topography model, CLTM-s01, and the Japanese SELENE's newly gravity field model, SGM100h. Thesis proposed the different views of the mascons formation from the lunar Bouguer gravity anomaly and the classification of mascons. Secondary, in order to quantitatively interpret the Bouguer anomaly, I constructed a new density imaging method used in spherical coordinates. The synthetic models demonstrated that this method is feasible to the inversion of the gravity data in small area or in global scale. Then, I applied it to lunar gravity data and retrieved the global 3-D density structures of the Moon.
I proposed that the masons should be identified from Bouguer gravity anomaly. In this study, the terrain correction for lunar free-air gravity anomaly is calculated in spherical coordinates based on the global topography data detected by the laser altimeter on Chang'E-1. According to the Bouguer gravity anomaly of the Moon, two impact basins, Hertzsprung and Korolev are lack of mascon features. The mascon basins seem to be classified into two types, Type Highland and Type Plain. For the mascon basins of Type Highland the dense materials mainly come from the shallow crust, which are associated with the basalt deposits. The other type, Type Plain, includes mascon basins whose major dense materials may be located deep at the litho-sphere, corresponding to the uplifted mantle. Further, the South Pole-Aitken (SPA) basin is considered the largest mascon basin on the Moon, and the feature of BGA in the basin implies the impacting direction.
This study addressed the inversion issues in spherical coordinates system, especially the key one of weighting function. I derived a new model objective function in the light of the Backus-Gilbert model appraisal theory in geophysical inversion. Furthermore, the correct depth weighting function was also derived because the previous function was not applicable to spherical coordinates system. The new method can directly solve the inversion problem of global satellite gravity data. Reliable results of density imaging were obtained and the non-uniqueness was suppressed by using model constraints and Tikhonov curves.
Lunar interior density distribution was retrieved by applying the new 3-D density imaging method. On the one hand, results from three mascons'gravity inversion indicated that the high density anomalies concentrated at the depth of 20-50km beneath the mascon basins. Their residual densities were larger than 0.3g/cm3 which are close to the density difference between lunar mantle and crust. Density structures along radial direction also demonstrated that the uplifted mantle dominates the origin of mascons'gravity anomalies. On the other hand, the global density imaging down to 100km depth of the Moon showed the similar features, which illustrated again that the lateral heterogeneities of interior density structures are mainly located above the depth of 50km.
论文首先从月球布格重力异常特征分析着手,根据布格异常的定义,运用球坐标系地形引力效应计算方法,进行了全球地形校正计算,获得了月球全球布格重力异常。通过分析对比质量瘤的异常特征,提出了用布格重力异常识别质量瘤的思想,认为Hertzsprung和Korolev撞击盆地并不具备质量瘤的特点,推断质量瘤撞击盆地高密度物质可能有不同的成因。统计显示,质量瘤盆地可分为平原类型和高地类型,面积较小的高地型质量瘤盆地的高密度物质主要分布在浅部,为充填的高密度玄武岩质岩石；平原型质量瘤盆地的高密度物质主要分布在深部,为上隆的高密度月幔物质。南极Aitken盆地存在与雨海类似的布格重力异常特征,因此本文将其列为月球最大的平原型质量瘤盆地。
论文在分析目前国内外位场反演成像方法的基础上,系统地讨论了球坐标系统中位场反演问题,尤其是模型加权函数问题。依据Backus-Gilbert模型评价理论,给出了新的全球密度成像模型目标函数,通过分析直角坐标系统中模型深度加权函数,推导出了基于球坐标系统的模型深度加权函数,并成功地构建了全球卫星重力异常密度反演算法的技术流程；通过模型约束和评价来压制降低反演的非唯一性,获得了可信的密度成像结果。理论模型密度成像结果表明,算法稳定收敛。
论文根据上述方法所得到月球布格重力异常,首先对雨海、澄海和东方海三个典型质量瘤撞击盆地的重力异常进行了反演成像,结果表明,质量瘤的异常源主要位于20-50km深度之间。其次,全球三维密度成像结果印证了局部密度成像结果,说明全球密度成像方法能获得合理的密度结构,且异常源之间有微弱连结。南极Aitken盆地下方的密度结构与正面质量瘤盆地类似,高密度物质同样集中在20-50km深度；在月球背面斜长岩高地区域,月球内部的径向密度极小值分布在10-50km深度。可以推测在50km深度之上,月球内部物质在球面和径向分布不均匀；而在50km之下,物质密度分布较均匀,斜长岩高地的月壳厚度可能达不到此前认为的100km。
论文所采用的月球卫星重力异常反演和分析方法,为月球内部结构研究提供了定量化的手段,所提出的球坐标三维密度成像方法,可用于球体内部三维结构分析,为行星内部结构及演化研究提供了新的途径。
One of the objectives in "Chang'E project" is to study the origination and evolution of the Moon, especially the interior layered structures. Current satellite gravity and topography of the Moon, in presence of high resolution and accuracy, and other data from lunar physical or chemical investigation have provided useful information to interpreate the lunar internal structure. Gravity field is currently the best data set to study the planetary interior structures. The lunar gravity anomaly reveals the lateral heterogeneities of surface and interior substance. Gravity inversion is a valid method to investigate the density structure in the lunar interior. In this thesis, the lunar Bouguer gravity anomaly was calculated by using a method of terrain correction in spherical coordinates system. Inversion of lunar gravity data can be used to analyze the density distribution and origination of the mascons, and then to study the evolution of lunar impact basins and the crust-mantle structures.
By applying the geophysical inversion theory to solve the planetary science problem, I firstly studied and discussed the inner structure of the Moon based on the Chang'E-1 topography model, CLTM-s01, and the Japanese SELENE's newly gravity field model, SGM100h. Thesis proposed the different views of the mascons formation from the lunar Bouguer gravity anomaly and the classification of mascons. Secondary, in order to quantitatively interpret the Bouguer anomaly, I constructed a new density imaging method used in spherical coordinates. The synthetic models demonstrated that this method is feasible to the inversion of the gravity data in small area or in global scale. Then, I applied it to lunar gravity data and retrieved the global 3-D density structures of the Moon.
I proposed that the masons should be identified from Bouguer gravity anomaly. In this study, the terrain correction for lunar free-air gravity anomaly is calculated in spherical coordinates based on the global topography data detected by the laser altimeter on Chang'E-1. According to the Bouguer gravity anomaly of the Moon, two impact basins, Hertzsprung and Korolev are lack of mascon features. The mascon basins seem to be classified into two types, Type Highland and Type Plain. For the mascon basins of Type Highland the dense materials mainly come from the shallow crust, which are associated with the basalt deposits. The other type, Type Plain, includes mascon basins whose major dense materials may be located deep at the litho-sphere, corresponding to the uplifted mantle. Further, the South Pole-Aitken (SPA) basin is considered the largest mascon basin on the Moon, and the feature of BGA in the basin implies the impacting direction.
This study addressed the inversion issues in spherical coordinates system, especially the key one of weighting function. I derived a new model objective function in the light of the Backus-Gilbert model appraisal theory in geophysical inversion. Furthermore, the correct depth weighting function was also derived because the previous function was not applicable to spherical coordinates system. The new method can directly solve the inversion problem of global satellite gravity data. Reliable results of density imaging were obtained and the non-uniqueness was suppressed by using model constraints and Tikhonov curves.
Lunar interior density distribution was retrieved by applying the new 3-D density imaging method. On the one hand, results from three mascons'gravity inversion indicated that the high density anomalies concentrated at the depth of 20-50km beneath the mascon basins. Their residual densities were larger than 0.3g/cm3 which are close to the density difference between lunar mantle and crust. Density structures along radial direction also demonstrated that the uplifted mantle dominates the origin of mascons'gravity anomalies. On the other hand, the global density imaging down to 100km depth of the Moon showed the similar features, which illustrated again that the lateral heterogeneities of interior density structures are mainly located above the depth of 50km.
引文
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