Local relationships between the disturbing density, the disturbing potential and the disturbing gravity of the Earth's gravity field

A function having some properties of a wavelet and being harmonic around a given point in R ³ is defined, and three models showing the local relationships between the disturbing density, the disturbing potential and the disturbing gravity are established by using the function as the kernel function of the integrals in the models. The local relationship has two meanings. One is that we can evaluate with a high accuracy the integrals in the models by using mainly high-accuracy and high-resolution data in a local area. The other is that we can obtain a stable solution with high resolution when we invert the integrals in the models because of the rapid decrease of the kernel function of the integrals. As a result, with these models we evaluate one quantity with high resolution, in a band limited by the maximum degree of a set of geopotential coefficients or by the resolution (spacing) of the local data, from another quantity (or quantities) in a local area, and the resulting solution is stable. Received: 6 April 1998 / Accepted: 16 June 1999     

基于超高阶重力场模型阶方差的截断误差分析

针对利用重力场模型方法计算地球外空间扰动引力的精度时,模型截断误差是主要的影响因素这一问题,该文利用重力场模型阶方差分析地球外部空间扰动引力截断误差,并与用重力异常阶方差Rapp模型进行比较。实验结果表明:在低阶低空部分,Rapp模型与实际重力异常阶方差相差最大,达到17.125 3mGal;重力场模型计算扰动引力与计算点高度有着密切联系,截断误差的大小随着高度的增加迅速衰减;当计算高度为0.2km时,使用36阶的模型计算扰动引力,截断误差达到25.957 8mGal;当计算高度超过400km时,即使用36阶模型,截断误差也可以控制在1.5mGal内。     

A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential

 A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation. Received: 27 December 2000 / Accepted: 3 September 2001     

Integral formulas for computing the disturbing potential, gravity anomaly and the deflection of the vertical from the second-order radial gradient of the disturbing potential

Integral formulas are derived which can be used to convert the second-order radial gradient of the disturbing potential, as boundary values, into the disturbing potential, gravity anomaly and the deflection of the vertical. The derivations are based on the fundamental differential equation as the boundary condition in Stokes’s boundary-value problem and the modified Poisson integral formula in which the zero and first-degree spherical harmonics are excluded. The rigorous kernel functions, corresponding to the integral operators, are developed by the methods of integration.     

重力异常阶方差模型精度及其截断误差分析

在评估重力场模型计算空间扰动引力精度时,对模型截断误差常采用阶方差方法。文中将6种经典的重力异常阶方差模型与现有超高阶重力场模型的阶方差进行比较,TSD模型与重力场模型的差值最小。根据重力异常阶方差模型TSD,文中分析不同高度、不同阶次利用重力场模型计算空中扰动引力时截断误差的影响。实验结果表明:36阶模型截断误差最大径向和水平方向分别为26.455 1mGal、25.946 3mGal;360阶模型截断误差最大径向和水平方向分别为9.969 0mGal、9.960 9 mGal;2160阶模型截断误差最大径向和水平方向分别为2.538 5 mGal、2.538 1mGal;2160阶模型计算空中扰动引力时,即使在低空附近,截断误差在2.5mGal以内,计算高度超过5km,截断误差可以忽略;超过400km的高度,都可以用36阶模型计算,截断误差在1mGal以内。     

密度误差对城市断层参数重力反演的影响

针对断层参数重力反演中密度误差对反演结果影响不确定的问题,该文采用控制变量方法,通过理论模型系统分析了密度误差对断层几何参数反演造成的影响,实现了定量确定密度误差与反演结果之间关系。研究结果表明:随着密度变化增大,反演误差逐渐增加;反演误差整体上处于10-5 m/s2量级,比采用的重力数据低两个量级,说明反演结果是可靠的。密度变化对断层埋深的影响相对较小,对断层倾角影响较大;当密度变化为-2%~2%时,断层上盘上底面、断层上盘下底面、断层下盘上底面、断层下盘下底面和倾角分别变化-0.5%~0.3%、0.2%~-0.4%、-0.38%~0.4%、0.25%~-0.3%和4%~-5%。当密度变化较小(-2%~2%)时,密度变化与断层参数变化之间存在近似线性关系。     

A-10绝对重力仪残差谱分析

自由落体式绝对重力仪A-10的测量数据拟合残差呈现出明显的周期信号,对4个测站的残差进行FFT处理,并进行频谱分析,结果表明残差组平均的频谱更加稳定,主峰频率与测站无关,主峰幅值与测站明显相关,加周期项改正的绝对重力值偏小。     

Truncated geoid and gravity inversion for one point-mass anomaly

The truncated geoid, defined by the truncated Stokes' integral transform, an integral convolution of gravity anomalies with the Stokes' function on a spherical cap, is often used as a mathematical tool in geoid computations via Stokes' integral to overcome computational difficulties, particularly the need to integrate over the entire boundary spheroid. The objective of this paper is to demonstrate that the truncated geoid does, besides having mathematical applications, have physical interpretation, and thus may be used in gravity inversion. A very simple model of one point-mass anomaly is chosen and a method for inverting its synthetic gravity field with the use of the truncated geoid is presented. The method of inverting the synthetic field generated by one point-mass anomaly has become fundamental for the authors' inversion studies for sets of point-mass anomalies, which are published in a separate paper. More general applications are currently under investigation. Since an inversion technique for physically meaningful mass distributions based on the truncated geoid has not yet been developed, this work is not related to any of the existing gravity inversion techniques. The inversion for one point mass is based on the onset of the so-called dimple event, which occurs in the sequence of surfaces (or profiles) of the first derivative of the truncated geoid with respect to the truncation parameter (radius of the integration cap), its only free parameter. Computing the truncated geoid at various values of the truncation parameter may be understood as spatial filtering of surface gravity data, a type of weighted spherical windowing method. Studying the change of the truncated geoid represented by its first derivative may be understood as a data enhancement method. The instant of the dimple onset is practically independent of the mass of the point anomaly and linearly dependent on its depth. Received: 26 September 1996 /Accepted: 28 September 1998     

Improved convergence rates for the truncation error in gravimetric geoid determination

 When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained. Received: 21 April 1998 / Accepted: 4 October 1999     

最小二乘支持向量机回归的卫星钟差非线性组合预报

针对应用单一方法预报卫星钟差的局限性,文章提出了基于最小二乘支持向量机回归的卫星钟差非线性组合预报方法:首先根据历史钟差数据建立二次多项式模型和灰色模型,然后利用这些模型进行钟差预报,最后采用最小二乘支持向量机回归算法对两种模型的预报结果进行非线性组合,以获得最终预报值;对比了RBF核函数、线性核函数和多项式核函数对组合预报性能的影响,并将本文组合预报方法与经典权组合方法进行比较。结果表明,本文方法优于经典权法,且线性核函数更适合组合预报。     

利用重力资料研究华北地区构造应力场

本文结合相关数据、模型和软件分别利用重力场、重力垂线偏差与构造应力场的内在关系式对华北地区陆地构造应力值进行了计算,通过对相关数据结果进行对比分析,总结并得出了华北地区重力总水平梯度、构造应力场和研究方法本身的一些规律和特征。     

我国陆地均匀重力测量补点问题的研究

推导了重力布点公式,应用全国重力点检验了原有代表误差系数的可靠性,估计了我国目前和将来5'×5'平均高的精度,阐述了陆地重力测量布点系统的建立方法和应用方法,给出了我国陆地重力点补测方案,应用它即可确定我国陆地每个5'×5'内应补测的重力点数及其分布     

基于ObjectARX校正AutoCAD矢量图之方法应用研究

针对现有的AutoCAD不能对矢量地图实施误差校正这一问题,本文阐述了矢量地图误差校正的原理和方法,以及如何用ObjectARX在V isual C++环境下开发运行在AutoCAD平台下实现误差校正的应用程序,并对该校正程序进行了试验分析,证明了运行的可靠性。该程序为AutoCAD软件增加了一项实用功能,为地图编绘提供了方便。     

A method of error adjustment for marine gravity with application to Mean Dynamic Topography in the northern North Atlantic

International compilations of marine gravity, such as the International Gravity Bureau (BGI) contain tens of millions of point data. Lemoine et al. (The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861) chose not to include any marine gravity in the construction of the global gravity model EGM96. Instead they used synthetic anomalies derived from altimetry, so that no independent information about Mean Dynamic Topography (MDT) can be deduced. Software has been developed not only to identify and correct those aspects of marine gravity data that are unreliable, but to do so in a way that can be applied to very large, ocean-wide data sets. First, we select only straight-line parts of ship-tracks and fit each one with a high-degree series of Chebyshev polynomials, whose misfit standard deviation is σ _line and measures the random error associated with point gravity data. Then, network adjustment determines how the gravity datum is offset for each survey. A free least squares adjustment minimises the gravity anomaly mismatch at line-crossing points, using σ _line to weight the estimate for each line. For a long, well crossed survey, the instrumental drift rate is also adjusted. For some 42,000 cross-over points in the northern Atlantic Ocean, network adjustment reduces the unweighted standard deviation of the cross-over errors from 4.03 to 1.58 mGal; when quality weighted, the statistic reduces from 1.32 to 0.39 mGal. The geodetic MDT is calculated combining the adjusted gravity anomalies and satellite altimetry, and a priori global ocean model through a new algorithm called the Iterative Combination Method. This paper reports a first demonstration that geodetic oceanography can characterise the details of basin wide ocean circulation with a resolution better than global ocean circulation models. The result matches regional models of ocean circulation from hydrography measurements (Geophys Res Lett 29:1896, 2002; J Geophys Res 108:3251, 2003).     

GPS phase accelerations for moving-base vector gravimetry

For airborne gravimetry using INS and GPS, the accelerations from both systems are differenced to yield the gravity acceleration. Usually, the GPS acceleration is determined by first solving for the position of the vehicle relative to a base station and subsequently taking two time derivatives of the vertical component. An alternative method is to time-differentiate the observed phases directly, thus avoiding the cycle ambiguity problem that must be solved for positioning and that is fraught with (certainly not insurmountable) difficulties in the event of a cycle slip. Due to the largely unpredictable receiver-clock errors and the imposition of the Selective Availability degradation, doubly differenced (in space) phase accelerations are used to obtain the relative vehicle accelerations. Test results for stationary receivers show that the acceleration vector can be determined from phase accelerations to an accuracy of 1 mgal for 40-s averages. The mathematical formulation of the acceleration determination also highlights certain other advantages over traditional methods, such as the avoidance of the E?tv?s correction, although a similar kind of velocity effect must be determined. Received: 9 September 1996 / Accepted: 14 April 1997     

A harmonic spline model for local estimation of planetary gravity fields from line-of-sight acceleration data

The spline interpolation technique is applied to estimate locally the radial component of a planetary gravity field from residual acceleration data along a special direction, the direction of observation from the Earth. After the presentation of the theoretical framework, the method is tested on synthetic and real data in the case of Venus. It is shown that this spline technique can be used succesfully to build local models of radial gravity fields at the planet surface. Received: 13 March 1997 / Accepted: 17 November 1998     

On calculating the Earth's C21 and S21 gravity coefficients in the IERS terrestrial reference frame

Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference frame. In this frame the mean values for gravity coefficients of the second degree and first order, C ₂₁(IERS) and S ₂₁(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure their values as given by the same source. The relevant error of the normalized mean values for C ₂₁(IERS) and S ₂₁(IERS) is 3×10⁻¹², far above the adopted cutoff (10⁻¹³) for variations of these coefficients. Such an error in C ₂₁ and S ₂₁ can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable to the accuracy of current tracking measurements. Received: 14 September 1998 / Accepted: 20 May 1999     

矢量GIS平面一般曲线误差模型定位精度

基于等概率密度误差模型建模原理和数值算法,研究矢量GIS平面一般曲线误差模型定位精度,给出定位精度捕述指标,并通过实例计算与分析,得出使川误差模型平均带宽比使用误差模型面积更能反应一般曲线的真实精度的结论,便于指导生产与应用。     

A new method for indentifying the model error of adjustment system

Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given.     

A new method for indentifying the model error of adjustment system

Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given. Project supported by the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University (No. 905276031-04-10).