地球内部重力势理论及全球动力学扁率研究
文献类型：学位论文
| 作者 | 刘宇 |
| 学位类别 | 博士 |
| 答辩日期 | 2008-06-16 |
| 授予单位 | 中国科学院上海天文台 |
| 授予地点 | 上海天文台 |
| 导师 | 黄乘利 |
| 关键词 | 地球动力学扁率 地球内部重力 地球内部物理 地球平衡形状 |
| 其他题名 | The Study Of The Gravity Potential Theory Of The Earth Interior And The Global Dynamical Flattening |
| 中文摘要 | The global dynamic flattening ($H$) is an important quantity in research of global geophysics, geodynamics and astronomy. It relates with the luni-solar precession, nutation(18.6 yr terms), tilt-over mode and so on. From observations, the value of H is about 1/305.5 with very high accuracy. But the calculated value of H from PREM model is about 1/308.8 at the first order accuracy. There is about 1\% difference between them, which is an interesting question and attracted many researches since 1980s. But, there is not any certain conclusion about it till now. At first, we recalculate the geometrical flattening ($f$) profile, which is rotating symmetric,from PREM Earth model from potential theory in hydrostatic equilibrium (HSE). Higher accuracy and more pivotal points are adopted in this work, and we get finer flattening profile than before. By using of the finer flattening profile, we get the dynamic flattening of PREM ($H_{PREM}$), which is a little closer to the observed value than before. But the change is so little that no matter how many points and how high the accuracy we adopt, the 1\% difference can not be interpretted. In order to study this 1\% difference, we replace the homogenous uppest crust and ocean layers in PREM with some real surface layers model. According to the depth range of each model, we construct three Earth models as following: \begin{itemize} \item Model1: PREM without 5.615 km depth surface layer(PREM\_NS\_5) + real ocean data(ECCO) + real topograph data (GTOPO30); \item Model2: PREM without 10.376 km depth surface layer(PREM\_NS\_10) + real ocean and topograph data (ETOPO5); \item Model3: PREM without 70.137 km depth surface layer(PREM\_NS\_70) + real crustal data (CRUST2). \end{itemize} The moments of inertia of these differ from uniform one in PREM. The effect on $H$ from this is called direct effect. From our calculation, the real Earth surface layer can directly change $H$ largely by 3\%, while its mass is less than 0.2\% of the whole Earth. The discussion on these results are made, and our results provide an indirect evidence for the theory of isostasy. The internal gravitational field produced by real surface layers is no longer symmetrical as PREM. This can change the figure of the equi-potential surfaces of the Earth interior and therefor changes $H$, and we call this as indirect effect. We derivate, for the first time, a set of equations to calculate the parameters of the figure of internal equi-potential surface which is non-symmetric and more general, and the program code is completed. The figure profile calculated from this set of equations and from PREM model is coincided with that obtained before. The results of the above models show that the indirect effect is also large to 3\% approximately. When we replace the volume from surface to 5.615 kilometers depth only as in model 1, the indirect effect make $H$ deviate more from $H_{PREM}$; when we go further to 10.376 kilometers depth as in model 2,the situation becomes more serious. But when we reach 70.137 kilometers depth, the indirect effect drag back $H$ from the deviation of the direct effect. The value of $H$ of model 3 with both direct and indirect effects is 1/306.68, that is to say, the total effect of the mass distribution of the volume from the surface of the Earth to 70km depth reduce the diferrence of $H_{PREM}$ and $H_{obs}$ from 1\% to 0.38\%. Our calculation shows that the indirect effect which is calculated first time is very notable, while it has not been discussed before. Some discussion of these results and its related theory of isostasy are also presented. |
| 英文摘要 | 全球动力学扁率（$H$）是研究地球旋转的一个重要物理量。 日月岁差、主章动（18.6年项）和倾斜模（tilt-over mode）等都与其密切相关。 由高精度天文岁差观测，$H$ 的值约为1/305.5，但在一阶扁率精度下，由PREM地球模型计算得到的$H$值约为1/308.8。 围绕两者间这$1\%$的差别，自上世纪八十年代初以来，众多学者展开了大量的研究，但都没有直接而令人信服的结论。 本文首先重复了由地球内部密度分布求取旋转对称地球内部几何扁率剖面的工作。 在这个工作中，本文采用了更高的计算精度并选取了更密集的计算点，取得了更为精细的PREM模型内部扁率剖面。 利用这更为精细的PREM模型内部扁率剖面，本文得到的全球动力学扁率较其他人的同类工作结果略有接近观测值。 但这个改善是非常有限的，即便采用再高的精度和再密集的计算点也远远不能解释那$\,1\%\,$的差别。 为了研究真实地球表层质量分布对全球动力学扁率的影响，本文选取了数个真实地球表层数据，并按其各自的覆盖深度与PREM模型构建了如下三个组合模型： \begin{itemize} \item 模型1：PREM 去除 5.615 km深表层(PREM\_NS\_5) + 真实海洋数据(ECCO) + 真实地形数据 (GTOPO30); \item 模型2：PREM 去除 10.376 km深表层(PREM\_NS\_10) + 真实海洋及地形数据(ETOPO5); \item 模型3： PREM 去除 70.137 km深表层(PREM\_NS\_70) + 真实地壳数据(CRUST2.0). \end{itemize} 首先本文计算了真实地球表层质量分布对全球动力学扁率的直接贡献即其自身的转动惯量不同于PREM模型相应地层而造成的影响。 由所构建三个模型的计算结果可以看到，真实地球表层的质量虽不足全球质量的$0.2\%$，但其对全球动力学扁率的直接影响达$3\%$。 另外，三个模型的结果互比较还为地壳均衡学说提供了间接证据。 为了研究真实地球表层质量的不均匀分布对全球动力学扁率的间接影响（由这些表层质量引起的地球内部其它部分等重力势面形状的变化），本文首次推导完成了一般形状地球的内部形状计算公式，并独立完成了数值实现工作。 这组计算公式将可计算的地球内部形状由先前的旋转对称扩展至一般形状。 经检验，其用于PREM模型的结果与前面工作结果一致。 对所构建的三个模型的计算表明，真实地球表层对全球动力学扁率的间接影响同样很大，可达$3\%$。 在所构建的模型1及模型2中，全球动力学扁率计算值均进一步偏离观测值，而模型3的全球动力学扁率计算值有明显的回归。 考虑直接及间接影响后，模型3的$H$计算值为$1/306.68$。 即深至70千米处的地球表层质量不均匀分布可以解释上述$1\%$差别中的约$2/3$。 其中的间接影响虽在以前从未被讨论过，但本文的计算结果表明该影响非常显著。 对以上结果做了比较与分析后，认为三个模型的结果再次为地壳均衡学说提供了间接证据。 |
| 语种 | 中文 |
| 公开日期 | 2011-07-01 |
| 页码 | 146 |
| 源URL | [http://119.78.226.72//handle/331011/14624]  |
| 专题 | 上海天文台_中国科学院上海天文台学位论文 |
| 推荐引用方式 GB/T 7714 | 刘宇. 地球内部重力势理论及全球动力学扁率研究[D]. 上海天文台. 中国科学院上海天文台. 2008. |
入库方式： OAI收割
来源：上海天文台
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