共查询到19条相似文献，搜索用时 497 毫秒
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基于Kaula准则,推导卫星重力梯度径向分量Tzz一阶、二阶径向偏导数T.zz、Tzz标准差的近似解析表达式,给出GOCE卫星.Tzz、Tzz标准差的近似估计值,由此分析Tzz延拓处理中可忽略的延拓误差最大高度。解析公式表明：T.zz、Tzz标准差的计算公式可近似表示成若干伽玛函数线性组合的开方,GOCE卫星.Tzz、Tzz标准差近似解析估值分别为1.269×10^-15s^-2m^-1和1.109×10^-20s^-2m^-2,由此若得到满足1 mE的精度要求,可忽略的延拓误差最大高度对于T.zz应小于0.8km,而对于Tzz应小于13.4km,延拓中重力场模型阶次应不低于200。最后基于模拟的GOCE卫星轨道,利用严格公式计算出的T.zz、Tzz标准差,验证近似解析表达式估算结果的正确性,解析结果与严格公式计算结果的相对误差小于2%。 相似文献
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利用空中平均重力异常确定区域大地水准面 总被引：3，自引：0，他引：3
提出了直接利用空中平均重力异常计算区域大地水准面的方法。模拟计算的结果表明, 该方法与传统的利用地面平均空间重力异常确定的大地水准面精度相当, 但其显著优点是勿需空中重力异常的向下解析延拓, 从而可以避免延拓误差对大地水准面精化的影响。 相似文献
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重力异常向上延拓全球积分模型在航空重力测量数据质量评估和向下延拓迭代计算等领域具有广泛的应用。为了消除积分核函数奇异性影响,需要对该模型进行基于积分恒等式的移去-恢复转换及全球积分域的分区改化处理。在此过程中,传统改化处理方法往往忽略了全球积分过渡到局域积分引起的积分恒等式偏差影响,从而导致不必要的计算模型误差,最终影响向上延拓计算结果的可靠性,甚至影响向下延拓迭代解算结果的稳定性。针对此问题,本文开展了重力异常向上延拓积分模型改化及向下延拓应用分析研究,依据实测数据保障条件和积分恒等式适用条件要求,导出了重力异常向上延拓积分模型的分步改化公式,提出了补偿传统改化模型缺陷的修正公式,并将最终的严密改化模型应用于重力异常向下延拓迭代解算。使用超高阶地球位模型EGM2008作为标准位场开展数值计算检验,分别对重力异常向上延拓分步改化模型的计算精度及在向下延拓迭代解算中的应用效果进行了检核评估,验证了采用严密改化模型的必要性和有效性。 相似文献
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《武汉大学学报(信息科学版)》2016,(4)
目前的航空标量重力测量系统主要是在当地坐标系下求解重力垂向分量,该方法涉及厄特弗斯改正,却没有考虑垂线偏差的影响。改进方法在准惯性坐标系下求解重力观测量,给出了一个计算重力值的改进公式,避免了经典方法中的近似处理,从理论上完善了航空重力测量数据处理方法。实例验证了改进方法的正确性,并显示经典方法中的近似处理在实验区域内产生了亚mGal级的误差,这个误差在利用1/60s以下的截断频率进行低通滤波后基本可以忽略。除了理论上对经典方法的改进,改进方法还提供了确定扰动重力水平分量的公式,经过细致的数据处理后其精度可达mGal级。 相似文献
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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. 相似文献
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在空域,利用严密的向上延拓公式将地面重力数据上延至空中不同高度,而后与相应的地面重力数据比较从而得到不同高度的代表误差.在频域,构建了新的代表误差模型,计算了不同高度、不同分辨率下的代表误差.实际算例表明,在空域,对于地形平坦区域,在1 km高度以下,5'空中重力数据直接代表地面重力数据的误差小于1×10-5 m/s2... 相似文献
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全球卫星导航系统反射(GNSS-R)技术对海洋表面地形精确信息的提取和研究具有重要意义,针对镜点搜索的精度需求,本文提出2种镜面反射点搜索算法. 首先,在分析基本反射关系的基础上,提出一种基于斐波那契法的搜索算法,并从数论的角度证明其相对黄金分割法的优越性. 其次,提出一种基于极值求导的做法,[JP2]建立变量K的距离和函数,这种做法省略了传统做法中的不断迭代过程. 最后,通过导航模拟器生成全球卫星导航系统（GNSS）卫星和接收机坐标,并利用MATLAB进行仿真. 仿真结果表明,斐波那契法相较黄金分割有一定的提升,极值求导做法能够计算出镜面反射点的位置信息,并且摒弃了传统的不断迭代步骤. 相似文献
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针对航空重力测量向下延拓过程固有的不确定性,根据海域重力场的变化特点和现有技术条件,分别提出了利用卫星测高重力向上延拓和超高阶位模型(EGM2008)直接计算延拓改正数,从而实现航空重力测量向下延拓归算的两种实用方法,联合使用卫星测高、海面船测和航空重力测量数据进行了实际数值计算和精度评估,验证了新方法的有效性。 相似文献
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海洋磁力测量中，由于受到海流等因素的影响导致磁力仪传感器（拖鱼）的入水深度起伏变化，测得的海洋磁场数据并不在固定的平面上。为了满足不同用户对海洋磁场数据的应用需求，必须采取合理的“曲化平”，实现整个测区磁场数据垂直空间上的统一。针对位场曲面延拓积分方程的迭代解中高阶垂向导数对高频噪声的放大问题，尝试引入Tikhonov正则化方法对其进行改进，以抑制高频噪声的影响。仿真分析表明，在选择合适的正则化参数后，改进的延拓方法可将延拓精度提高1.6 nT。实测数据分析表明，采用改进曲面延拓迭代方法，将磁测成果数据归算到曲面最低平面时，归算后交叉点磁异常不符值精度可提高2 nT，进一步验证了海洋磁力测量数据垂直空间归算的必要性。 相似文献
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Lars E. Sjöberg 《Journal of Geodesy》1996,70(11):724-730
Analytical continuation of gravity anomalies and height anomalies is compared with Helmert's second condensation method. Assuming that the density of the terrain is constant and known the latter method can be regarded as correct. All solutions are limited to the second power of H/R, where H is the orthometric height of the terrain and R is mean sea-level radius. We conclude that the prediction of free-air anomalies and height anomalies by analytical continuation with Poisson's formula and Stokes's formula goes without error. Applying the same technique for geoid determination yields an error of the order of H2, stemming from the failure of analytical continuation inside the masses of the Earth. 相似文献
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本文针对位场向下延拓的不适定问题,在分析最优化算法中高斯-牛顿法基本原理及滤波函数滤波特性的基础之上,提出基于正则参数指数递增计算方法和残差最小步长准则的改进高斯-牛顿法。基于理论重力模型和航磁实测数据的对比实验表明,改进后得到的自适应迭代法具有相对较高的位场向下延拓精度和很好的收敛性。 相似文献
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联合使用位模型和地形信息的陆区航空重力向下延拓方法 总被引：1，自引：0，他引：1
为了规避传统逆Poisson积分向下延拓解算过程的不适定性问题,借鉴导航定位中的"差分"概念,利用超高阶位模型直接计算海域航空重力测量向下延拓改正数的方法。本文在此基础上提出联合使用重力位模型和地形高数据,计算陆部航空重力向下延拓总改正数的改进方案,以飞行高度面与地面对应点的位模型差分信息表征总改正数的中长波分量,以相对应的局部地形改正差分修正量表征总改正数的中高频成分,从而实现航空重力数据点对点向地面的全频段延拓。在地形变化不同区域,联合使用EGM2008位模型、地面实测重力和高分辨率高程数据进行了实际数值计算和精度评估,验证了该方法的有效性。 相似文献
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The fixed gravimetric boundary-value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. Terrestrial gravimetric measurements located by precise satellite positioning yield oblique derivative boundary conditions in the form of surface gravity disturbances. In this paper, we discuss the boundary element method (BEM) applied to the linearized FGBVP. In spite of previous BEM approaches in geodesy, we use the so-called direct BEM formulation, where a weak formulation is derived through the method of weighted residuals. The collocation technique with linear basis functions is applied for deriving the linear system of equations from the arising boundary integral equations. The nonstationary iterative biconjugate gradient stabilized method is used to solve the large-scale linear system of equations. The standard MPI (message passing interface) subroutines are implemented in order to perform parallel computations. The proposed approach gives a numerical solution at collocation points directly on the Earth’s surface (on a fixed boundary). Numerical experiments deal with (i) global gravity field modelling using synthetic data (surface gravity disturbances generated from a global geopotential model (GGM)) (ii) local gravity field modelling in Slovakia using observed gravity data. In order to extend computations, the memory requirements are reduced using elimination of the far-zone effects by incorporating GGM or a coarse global numerical solution obtained by BEM. Statistical characteristics of residuals between numerical solutions and GGM confirm the reliability of the approach and indicate accuracy of numerical solutions for the global models. A local refinement in Slovakia results in a local (national) quasigeoid model, which when compared with GPS-levelling data, does not make a large improvement on existing remove-restore-based models. 相似文献
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A solution to the downward continuation effect on the geoid determined by Stokes' formula 总被引：2，自引：1，他引：2
L.E. Sjöberg 《Journal of Geodesy》2003,77(1-2):94-100
The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes'
formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere.
Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable,
unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation
of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The
practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical
harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the
truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition,
it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral.
Received: 6 February 2002 / Accepted: 18 November 2002
Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of
the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much
appreciated. 相似文献
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Tilt-Depth以及其相关改进方法最初是基于磁异常基本公式推导,一直应用于磁法勘探领域。自2012年以来,不断有学者探讨重力场Tilt-Depth方法,但对重力场与磁场Tilt-Depth方法之间的关系研究较少,存在一些不同认识。梳理了重磁场之间Tilt-Depth方法的联系与区别,得出了Tilt-Depth方法在重力场中相比磁场高一阶导数的结论。验证了方法的有效性,通过对海南石碌矿区重力异常处理,提取了矿体的边界信息,突出了深部隐伏矿体产生的弱异常的边界范围,获取了矿体的位置及埋深参数,通过与已知地质剖面、反演剖面的对比,证实了重力场Tilt-Depth结论的正确性与有效性。 相似文献
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The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model. 相似文献