卫星测高反演海洋重力异常的精度分析

针对卫星测高技术中由于大地水准面取值受各项误差影响导致精度较低的问题,该文联合多源多代卫星测高数据,基于逆Vening-Meinesz公式确定海洋重力异常,进一步对海洋重力异常进行内部和外部检核。结果表明,卫星测高反演的海洋重力异常与EGM2008比较的精度为±7.116mgal;与船测重力异常比较的精度为7.417mgal,这与国际上对测高重力异常与船测重力异常比较精度一致。     

利用卫星测高数据反演海洋重力异常研究

全面研究了利用卫得测高数据反演海洋重力异常3种主要方法（即Stokes数据解析反解以及逆Vening-Meinesz公式）的技术特点，建立了3种算法的数学模型及其谱计算式，在以1440阶次位模型定义的标准场中完成了3种算法的数值比较和内部检核，通过仿真试验实现了3种算法的可靠性和稳定性检验，最后，本文利用卫得测高实测对南中国海地区的海洋重力异常进行了实际反演，并将反演结果同船测数据进行了比较。     

测高重力异常中央区奇异积分数值求积公式

为简化逆Stokes法和逆Vening-Meinesz法反演中央区重力异常计算过程,提高计算效率,本文采用数值求积公式,分别利用Simpson公式和Cotes公式对逆Stokes法和逆Vening-Meinesz法中的奇异积分问题进行了新的研究,系统地推导出了中央区重力异常普适数值积分计算公式.在大地水准面高和垂线偏差理论模型下的分析表明,此公式可直接利用格网节点处的大地水准面高和垂线偏差计算重力异常值,形式简单,计算效率高,计算精度与解析法计算结果精度相当,可以满足实际应用.研究结果可为高精度卫星测高反演重力异常提供基础理论依据.     

基于逆Vening-Meinesz公式的测高重力中央区效应精密计算

为提高利用逆Vening-Meinesz公式反演测高重力中央区效应的精度，视中央区为矩形域，将垂线偏差分量表示成双二次多项式插值形式，引入非奇异变换，推导出了重力异常的计算公式。以低纬度区域2'×2'的垂线偏差实际数据为背景场进行了计算，结果表明，当中央区包含4个网格时，传统公式与推导出的重力异常计算公式误差的最大值大于1 mGal。推导出的公式可为高精度测高重力中央区效应的计算提供理论依据。     

Geosat／GM波形重跟踪反演中国沿海区域重力异常

利用Geosat/GM测高波形数据,在中国海域内(117°E～129°E,21°N～41°N)比较了阈值法、Beta5和改进阈值法三种重跟踪算法.分析表明,改进阚值法优于其他两种重跟踪方法.由改进阈值法的测高数据.分别采用最小二乘法(least sqlilare collocation,LSC)和逆Vening-Meinesz(IVM)计算了卫星测高重力异常,并与船测重力数据进行了比较.结果显示,LSC的精度优于IVM.与KMS02和Sandwell & Smith V15两个重力场模型相比较,本文结果在东海优于这两个模型,在台湾海域结果稍差,需要融合ERS-1等其他数据进一步提高精度.     

基于EIGEN-6C4的区域重力异常插值方法

重力异常作为地球重力场的一种基本指标,广泛应用于大地测量、地球物理、地质、地震与海洋领域。为了快速获取高精度的未知点重力异常,本文基于EIGEN-6C4重力场模型解算某110 km×110 km区域内重力异常,构建5′×5′的重力异常格网模型,结合格网节点数据采用6种不同的插值算法拟合未知点的重力异常,最后使用外部检核的方法评价插值算法的精度。实验结果表明,6种插值算法的拟合精度均达到4 mgal以内,自然三次样条法和反距离加权插值法拟合精度最高,得到精度达到2.7 magl的重力异常。     

基于逆Stokes公式的测高重力反演中央区效应计算

为提高利用逆Stokes公式反演测高重力的精度,将中央区大地水准面高表示成双三次多项式插值形式,引入了非奇异变换,推导出了重力异常的计算公式。大地水准面高理论模型下的分析表明,该公式有较高的精度。以分辨率为2′×2′的大地水准面高数据为背景场进行了实际计算,结果说明中央区对反演重力异常有不容忽视的贡献。本文导出的公式可为高精度重力异常的反演提供理论依据。     

自主海洋测高卫星串飞模式的设计与重力场反演精度分析

根据自主海洋测高卫星发展需求,设计了双星串飞运行模式,该运行模式下2.3 a时间可满足全球海洋区域1'×1'分辨率的地面轨迹覆盖要求。首先,将测高卫星重力场反演分为不考虑轨道运行特点（思路1）和考虑串飞轨道运行特点（思路2）两种思路,利用逆Vening-Meinesz方法开展了正态分布下随机误差传播的仿真计算,获得了两种思路下对应的误差指标。以该误差指标为基础,分别计算了双星串飞模式下两种重力场反演思路对应的精度指标。其中,反演思路2充分利用了串飞模式双星东西方向地面观测值可以进行相对定轨的特点,并考虑到近距离条件下传播误差、地球物理改正误差的系统误差特性,因此反演思路2的垂线偏差精度较反演思路1有了一定的提高,其重力场反演也具有一定的优势。理论计算结果表明,利用思路1的反演方法,2.3 a时间可获得1'×1'重力异常精度为6~10 mGal,4.6 a时间可达到4.2~7.1 mGal;利用思路2的反演方法,2.3 a时间可获得1'×1'重力异常精度为3.9 mGal,4.6 a时间可达到2.8 mGal。     

垂线偏差时间变化的精度估计

对于利用Vening-Meinesz微分公式计算垂线偏差随时间变化的测定精度进行了初步估计.通过对地形改正项的影响、代表误差的影响、远区域重力异常的影响等3种主要误差的分析和实际估计,论证了它们对计算结果的综合影响不超过0.01″,比铅垂线的时间变化0.1″要高一个量级.因此认为重力方法在实践中是可行的.     

联合多种测高数据确定中国海及其邻域1．5′×1．5′重力异常

联合多种测高资料和Geosat/GM波形重构数据,基于EIGEN_CG01C重力场模型,采用沿轨迹加权最小二乘方法和逆Vening-Meinesz公式,确定了中国海及其邻域1.5′×1.5′重力异常。将计算结果与最新船测资料进行了比较,标准差为3.37×10-5m.s-2。     

High precision vertical deflection over China marginal sea and global sea derived from multi-satellite altimeter

On the basis of gravity field model (EIGEN_CG01C), together with multi-altimeter data, the improved deflection of the vertical gridded in 2′×2′ in China marginal sea and gridded in 5′×5′ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2″ in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy. It shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m·s?2.     

联合多代测高数据建立中国海域重力异常模型

本文联合T/P数据、T/P新轨道数据、ERS数据、GFO数据、GeosatGM数据和ERS-1/168数据,用测高卫星记录点的位置信息直接计算沿轨大地水准面的方向导数,结合测线轨迹方向的方位角在交叉点处推求垂线偏差,然后利用逆Vening-Meinesz公式计算了中国近海(0o～41oN,105o～132oN)2′×2′格网分辨率的海域重力异常模型。将其与CLS_SHOW99重力异常模型比较,统计结果表示与该模型差异的RMS为8.15mgal,在剔除差值大于20mgal的点(剔除3.3%)以后,RMS为4.72mgal;与某海区船测重力异常比较的RMS为8.91mgal。     

联合多种测高数据确定中国边缘海及全球海域的垂线偏差(英文)

On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.     

海洋重力似大地水准面与区域测高似大地水准面的拟合问题

研究了将陆地重力似大地水准面与GPS水；住似大地水准面拟合的处理方法推广到海洋的问题．首先从理论上证明了当存在海面地形．则海洋大地水准面与似大地水准面不重合．导出了在海洋上大地水；住面差距与高程异常之间差值的公式．由此给出了求定平均海面相对于区域高程基准的正常高以及测高似大地水准面的计算公式。由于测高平均海面与GPS大地高有相近的精度．提出了将海洋重力似大地水准面与区域测高似大地水准面拟合的处理方法．并利用当前最新的海面地形模型和测高平均海面模型做了数值估计。     

On the accurate numerical evaluation of geodetic convolution integrals

In the numerical evaluation of geodetic convolution integrals, whether by quadrature or discrete/fast Fourier transform (D/FFT) techniques, the integration kernel is sometimes computed at the centre of the discretised grid cells. For singular kernels—a common case in physical geodesy—this approximation produces significant errors near the computation point, where the kernel changes rapidly across the cell. Rigorously, mean kernels across each whole cell are required. We present one numerical and one analytical method capable of providing estimates of mean kernels for convolution integrals. The numerical method is based on Gauss-Legendre quadrature (GLQ) as efficient integration technique. The analytical approach is based on kernel weighting factors, computed in planar approximation close to the computation point, and used to convert non-planar kernels from point to mean representation. A numerical study exemplifies the benefits of using mean kernels in Stokes’s integral. The method is validated using closed-loop tests based on the EGM2008 global gravity model, revealing that using mean kernels instead of point kernels reduces numerical integration errors by a factor of ~5 (at a grid-resolution of 10 arc min). Analytical mean kernel solutions are then derived for 14 other commonly used geodetic convolution integrals: Hotine, Eötvös, Green-Molodensky, tidal displacement, ocean tide loading, deflection-geoid, Vening-Meinesz, inverse Vening-Meinesz, inverse Stokes, inverse Hotine, terrain correction, primary indirect effect, Molodensky’s G1 term and the Poisson integral. We recommend that mean kernels be used to accurately evaluate geodetic convolution integrals, and the two methods presented here are effective and easy to implement.     

给定内插重力异常精度时对重力数据的要求

基于最小二乘配置误差估计公式,建立了重力异常格网数据的分辨率和精度与重力异常内插值精度的关系,提出了在给定插值精度时反推已知格网数据的分辨率和精度的方法。以EGM2008重力场模型为例,在不同分辨率和精度条件下进行重力异常插值实验。实验结果与本文方法的计算结果基本一致,表明该方法具有一定的可行性。     

A general formula and its inverse formula for gravimetric transformations by use of convolution and deconvolution techniques

A general formula is developed and presented for transformations among geoidal undulation, gravity anomaly, gravity disturbance and other gravimetric quantities. Using a spectral form of the general formula, a criterion has been built in order to classify these transformations into forward and inverse transformations in this paper. Then, the two-dimensional convolution techniques are applied to the general formula to deal with the forward transformation while the two-dimensional deconvolution techniques are employed to treat the inverse transformation and evaluate the inverse general formula. Concepts of convolution and deconvolution are also reviewed in this paper. The stability and edge effect problems related to the deconvolution techniques are investigated using simulated data and numerical tests are done to quantify the stability of the deconvolution techniques for estimated gravity information. Finally, the marine gravity information for the Norwegian-Greenland Sea area has been derived from ERS-1 altimetry data using the deconvolution techniques.     

Ellipsoidal corrections to order e 2 of geopotential coefficients and Stokes’ formula

Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e ² (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e ²/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question.