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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.
球面距离(角间距)计算是天文或地理学中极常用的计算之一,也是目标查找、锥形检索、交叉证认等方法的基础。数学上,通过球面几何可以直接计算出两点的距离,前人已经推导出了多个复杂程度不一的计算方法。但是由于计算机的精度有限,在进行数值计算时有舍入误差,导致公式计算结果出现偏差。对几个常用的球面距离计算公式进行了考察,测试并对比它们在不同计算环境下的精度与优缺点。此外还展示并比较了几种常用天文软件包、数据库的球面距离计算方法,以期有助于天文工作者选择适合自己当前需要的计算方法。 相似文献
6.
We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based
on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations.
The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity
field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal
energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite.
Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential
at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy
spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation
by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges
to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite
altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical
experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n
max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting
spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical
evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting
the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute
the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics
of satellite coverage, which could not be done using a global spherical harmonic representation.
The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577. 相似文献
7.
Christopher Kotsakis 《Journal of Geodesy》2009,83(1):31-50
All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference
frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework
for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs,
especially when their use is intended for high precision studies. Following the methodology described in an earlier paper
by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including
the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the
differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity
spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model,
the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding
translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted
in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral
band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated
differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae
for the assessment of TRF inconsistencies among global geopotential models. 相似文献
8.
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
9.
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
10.
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