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1.
2.
A data-driven approach to local gravity field modelling using spherical radial basis functions 总被引:3,自引:0,他引:3
We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology
comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing
potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions
(SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized
cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly
weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences
between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution
of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local
gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric
and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference
surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has
been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector
surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces
shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms
that our solution is in no way inferior to NLGEO2004. 相似文献
3.
Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is
the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen
of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation
to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their
tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal
expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts
directional properties to the polycrystalline material.
A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation
density function on SO(3) from measured pole intensities on
, which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into
mathematical texture analysis. Wavelets on the two-dimensional sphere
and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the
ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon
transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets
on
. A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship
is developed. 相似文献
4.
文章设计了一个以均匀网格差分模式为基础的全球变网格多层原始方程差分模式。还证明了如果前者满足了一定条件,从而具有质量与能量守恒性质以及与连续情况一致的动能、位能和表面位能之间的转换关系,则变网格模式也同样具有。而且,把前者改变为后者增加的运算量很小,也非常方便。 相似文献
5.
Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.Deceased. 相似文献
6.
本文讨论了参考椭球面之外,地球质量产生的扰动位的球谐展开式。分别在地球的平均球面上以及地球表面之外,给出了该扰动位的球谐展开式,为进一步研究外部质量对扰动位的影响建立了理论基础。 相似文献
7.
地磁场模型和冠谐分析 总被引:4,自引:2,他引:4
地磁场是由内源场(地核场和地壳场)和外源场(电离层场和磁层场)组成的,地磁场模型是表示地磁场时空分布的数学表达式.本文简述了地磁场全球模型和区域模型的计算方法和应用;评述了冠谐分析方法及其在地磁学中的应用;介绍了地磁场模型误差的主要来源. 相似文献
8.
A fast algorithm is proposed to integrate the trajectory of a low obiter perturbed by the earth's non-sphericity. The algorithm
uses a separation degree to define the low-degree and the high-degree acceleration components, the former computed rigorously,
and the latter interpolated from gridded accelerations. An FFT method is used to grid the accelerations. An optimal grid type
for the algorithm depends on the trajectory's permissible error, speed, and memory capacity. Using the non-spherical accelerations
computed from EGM96 to harmonic degree 360, orbit integrations were performed for a low orbiter at an altitude of 170 km.
For a separation degree of 50, the new algorithm, together with the predict-pseudo correct method, speeds up the integration
by 145 times compared to the conventional algorithm while keeping the errors in position and velocity below 10−4 m and 10−7 m/s for a 3-day arc.
Received: 28 July 1997 / Accepted: 1 April 1998 相似文献
9.
Solutions for chaotic dynamos driven by thermal convection in a rotating spherical shell are obtained numerically for different Prandtl numbers. The influence of this parameter which is usually suppressed in the magnetostrophic approximation is emphasized in the present analysis. 相似文献
10.
为了获取LAMOST焦面板上光纤的零位位置,提出了一种基于分离式标准靶标的高精度摄影测量方法。首先,根据Tsai摄像机标定参数模型介绍了CCD相机的标定原理。然后介绍了用光重心算法求取靶标发光点像面坐标及通过球面三角公式计算靶标发光点物面坐标。接着,利用最小二乘法导出了含标定参数的方程组。最后,介绍了标准靶标的放置方法以及提高光纤位置测量精度的靶标取法。实验结果表明:CCD相机的标定残差平均值为8.8μm;标定残差的标准差为5.3μm。测量方法简单易行,通过仔细分析,找出了残差偏大的原因,对后续进一步测量实验有重要指导意义。 相似文献