中国及邻区模拟大地水准面的研究
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摘要
论文主要讨论了利用实际的地球物理资料，模拟正演了大地水准面的短波部分，并利用了地球重力场模型的低阶项计算出中长波部分，叠加得到模拟大地水准面。利用实际数据讨论了各种资料对大地水准面的影响，分析了它们的影响范围，确定了计算时的积分半径。利用GPS水准对模拟大地水准面进行约束，采用“移去——恢复”技术和多面函数法进行拟合内插，得到转换后的大地水准面。
大地水准面是地球内部密度分布的直接反映，其频谱结构是长波占优，反映地球深部或地幔的密度异常分布，而大地水准面起伏的中短波部分与岩石圈内部负荷及地形有很强的相关性。因此，如果知道了地球内部结构和动力学过程，我们可以唯一准确地确定大地水准面。理论上，大地水准面的模拟除去考虑地形、地壳内密度分布不均匀的影响外，还应考虑地幔的影响，通常可用地幔的波速异常转换为密度异常，再根据内部负荷的响应理论推算出地表的大地水准面。但是，不同的地幔粘滞度结构将对结果的不确定性带来较大的影响，并且还要考虑在地幔对流环境中内部负荷的动力学效应，同时涉及理论复杂，计算量大。利用现有的全球重力场模型(如EGM96)的长中波长部分来顾及地幔部分的影响，而用地形、界面起伏及横向密度不均匀等实际资料来模拟重力场短波部分的局部影响，最后迭加得到理论模拟大地水准面。
由于各物质界面处于不同的深度，考虑它们对大地水准面的影响不能采用同样的积分范围，而且由于本文直接使用位函数，其收敛速度很慢，就影响的绝对值而言，必须考虑全球积分。这一方面要求顾及地球弯曲的影响，另一方面对资料的要求也比较高，而且计算工作量也很大。论文中提出了利用柱体积分时采用移动坐标系来顾及地球弯曲的影响，并利用差分的概念，设想离计算区域到一定距离后，流动点对计算区域内的中心点和边缘点的影响之差为一常数，并用试验的方法，统计分析了它们对大地水准面的有效积分拓展范围。
由于模拟大地水准面得到的只是各点之间的差值关系，与实际大地水准面之间可能存在系统差，由于GPS水准能够提供高精度的大地水准面起伏，为此我们利用GPS水准资料对其进行约束。在转换过程中，为了提高精度，采用了“移去——恢复”技术和多面函数法进行拟合内插，并用模拟大地水准面对某地区的高程进行了拟合，与已知数据相比，比以往的结果有一定程度的改善。
In this thesis, the short waves of the geoid are calculated by observed geophysical data, and the middle- and long-waves of geoid are calculated by low orders of the earth gravity model (such as EGM96), then their superposition is the simulated geoid obtained. The effects on the determination of geoid of individual geophysical data are discussed and the reasonable integration ranges are proposed. The GPS-levelling is used to add constraints on the simulated geoid, and the "remove-restore" method and the multi-quadric function method are used to interpolation, so as to obtain the refined geoid.
The geoid undulations are the direct reflection of the earth internal density distributions. The long-wave parts are prominent in frequency domain of the geoid undulations. They reflect the abnormal density distribution in the deep earth or the mantle. The short waves of the geoid are strong related with the lithosphere loading and ground topography. So if we know the earth internal structures and its geodynamic processes, we can determine a unique geoid. Theoretically, in the simulation of the geoid, not only the effects of topography and the density distribution in the crust, but also the effects of the mantle abnormal density should be taken into consideration. The density of the mantle can be calculated by the velocities of seismic waves, and then their effects on the geoid can be calculated by internal loading theory. But the viscosity structures of the mantle bring a large uncertainty of the geoid, in addition, the dynamical effects of the mantle convection are also need to be considered. However
, the relevant theoretical problems are complex and the computation loading is very heavy. By using the middle- and long-wave parts of the recent earth gravity model (such as EGM96), the effects of the mantle are calculated. And the topographical data, the interface undulation data, and the lateral heterogeneous density distribution data, are then used to simulate the short-wave parts of the earth gravity model. The superposition of the two parts gives the theoretical simulated geoid.
As the interface in the earth located in different depth, so when their effects on the geoid are calculated, different integration range should be used. However, as we use potential functions directly in our study, the convergent speed of the calculation is very slow, the global integration must be taken. So we need consider the effects of the earth curvature. In global integration, the requirement of the data coverage and the computation are comparative high. In this thesis, a moving coordinate system is used to overcome the effects of the earth curvature. And a differential calculation concept is proposed that assumes the difference of geoid calculated between the central point and its marginal point is constant when the integration area is far away from the central point. An experimental method is developed to statistic the efficient
integration range for geoid calculation.
Because the simulated geoid only reflects the differences of the real geoid, their values may have a systematic error, so GPS-levelling data are used to constrain the geoid interpolations. For improving the accuracy of the geoid conversion, the "remove-restore" method and the multi-quadric function method are used to geoid interpolation. Through comparing with the geoid values of known points, our method has some significant improvements on the geoid determination method used before.
大地水准面是地球内部密度分布的直接反映，其频谱结构是长波占优，反映地球深部或地幔的密度异常分布，而大地水准面起伏的中短波部分与岩石圈内部负荷及地形有很强的相关性。因此，如果知道了地球内部结构和动力学过程，我们可以唯一准确地确定大地水准面。理论上，大地水准面的模拟除去考虑地形、地壳内密度分布不均匀的影响外，还应考虑地幔的影响，通常可用地幔的波速异常转换为密度异常，再根据内部负荷的响应理论推算出地表的大地水准面。但是，不同的地幔粘滞度结构将对结果的不确定性带来较大的影响，并且还要考虑在地幔对流环境中内部负荷的动力学效应，同时涉及理论复杂，计算量大。利用现有的全球重力场模型(如EGM96)的长中波长部分来顾及地幔部分的影响，而用地形、界面起伏及横向密度不均匀等实际资料来模拟重力场短波部分的局部影响，最后迭加得到理论模拟大地水准面。
由于各物质界面处于不同的深度，考虑它们对大地水准面的影响不能采用同样的积分范围，而且由于本文直接使用位函数，其收敛速度很慢，就影响的绝对值而言，必须考虑全球积分。这一方面要求顾及地球弯曲的影响，另一方面对资料的要求也比较高，而且计算工作量也很大。论文中提出了利用柱体积分时采用移动坐标系来顾及地球弯曲的影响，并利用差分的概念，设想离计算区域到一定距离后，流动点对计算区域内的中心点和边缘点的影响之差为一常数，并用试验的方法，统计分析了它们对大地水准面的有效积分拓展范围。
由于模拟大地水准面得到的只是各点之间的差值关系，与实际大地水准面之间可能存在系统差，由于GPS水准能够提供高精度的大地水准面起伏，为此我们利用GPS水准资料对其进行约束。在转换过程中，为了提高精度，采用了“移去——恢复”技术和多面函数法进行拟合内插，并用模拟大地水准面对某地区的高程进行了拟合，与已知数据相比，比以往的结果有一定程度的改善。
In this thesis, the short waves of the geoid are calculated by observed geophysical data, and the middle- and long-waves of geoid are calculated by low orders of the earth gravity model (such as EGM96), then their superposition is the simulated geoid obtained. The effects on the determination of geoid of individual geophysical data are discussed and the reasonable integration ranges are proposed. The GPS-levelling is used to add constraints on the simulated geoid, and the "remove-restore" method and the multi-quadric function method are used to interpolation, so as to obtain the refined geoid.
The geoid undulations are the direct reflection of the earth internal density distributions. The long-wave parts are prominent in frequency domain of the geoid undulations. They reflect the abnormal density distribution in the deep earth or the mantle. The short waves of the geoid are strong related with the lithosphere loading and ground topography. So if we know the earth internal structures and its geodynamic processes, we can determine a unique geoid. Theoretically, in the simulation of the geoid, not only the effects of topography and the density distribution in the crust, but also the effects of the mantle abnormal density should be taken into consideration. The density of the mantle can be calculated by the velocities of seismic waves, and then their effects on the geoid can be calculated by internal loading theory. But the viscosity structures of the mantle bring a large uncertainty of the geoid, in addition, the dynamical effects of the mantle convection are also need to be considered. However
, the relevant theoretical problems are complex and the computation loading is very heavy. By using the middle- and long-wave parts of the recent earth gravity model (such as EGM96), the effects of the mantle are calculated. And the topographical data, the interface undulation data, and the lateral heterogeneous density distribution data, are then used to simulate the short-wave parts of the earth gravity model. The superposition of the two parts gives the theoretical simulated geoid.
As the interface in the earth located in different depth, so when their effects on the geoid are calculated, different integration range should be used. However, as we use potential functions directly in our study, the convergent speed of the calculation is very slow, the global integration must be taken. So we need consider the effects of the earth curvature. In global integration, the requirement of the data coverage and the computation are comparative high. In this thesis, a moving coordinate system is used to overcome the effects of the earth curvature. And a differential calculation concept is proposed that assumes the difference of geoid calculated between the central point and its marginal point is constant when the integration area is far away from the central point. An experimental method is developed to statistic the efficient
integration range for geoid calculation.
Because the simulated geoid only reflects the differences of the real geoid, their values may have a systematic error, so GPS-levelling data are used to constrain the geoid interpolations. For improving the accuracy of the geoid conversion, the "remove-restore" method and the multi-quadric function method are used to geoid interpolation. Through comparing with the geoid values of known points, our method has some significant improvements on the geoid determination method used before.
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