Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition     

Z. Martinec 《Journal of Geodesy》1998,72(7-8):460-472

Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e <sup>2</sup> <sub>0</sub>)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant. Received: 5 June 1997 / Accepted: 20 February 1998  相似文献   

Using piecewise linear interpolations in spherical harmonic analysis     

S. Bian  J. Menz 《Journal of Geodesy》1998,72(7-8):473-481

In this paper an alternative approach to spherical harmonic analysis is investigated which uses piecewise linear interpolations (PLIs) to replace conventional block mean values (BMVs). Detailed formulations for using PLIs in spherical harmonic analysis are systematically developed. Research shows that BMVs give rise to larger errors than PLIs. Error estimations for the two approaches are given, convincingly showing that PLIs yield much better results than BMVs. Many numerical examples are illustrated and numerically show that PLIs are more reliable and applicable than BMVs. Received: 8 October 1996 / Accepted: 6 March 1998  相似文献   

再论球面上正压准地转运动的半圆定理     

林乃实 《高原气象》1997,16(3):300-305

进一步了球面上正压准地转运动中不稳定波的Ｈｏｗａｒｄ半圆定理，发现在某些特定的基本流分布下，该定理可以发展成圆弧定理，由此得到不稳定扰动增长率的更为精确的估计式。  相似文献   

Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform   总被引：5，自引：2，他引：5  

R. Pail  G. Plank 《Journal of Geodesy》2002,76(8):462-474

 The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications. Received: 17 December 2001 / Accepted: 17 July 2002 Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency (ESA) under contract No. 14287/00/NL/DC. Correspondence to: R. Pail  相似文献   

A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions   总被引：11，自引：7，他引：11  

S. A. Holmes  W. E. Featherstone 《Journal of Geodesy》2002,76(5):279-299

 Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions (ALFs). However, when evaluated increasingly close to the poles, the ultra-high degree and order (e.g. 2700) ALFs range over thousands of orders of magnitude. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. A common solution in geodesy is to evaluate these expansions using Clenshaw's method, which does not compute individual ALFs or their derivatives. Straightforward numerical principles govern the stability of this technique. Elementary algebra is employed to illustrate how these principles are implemented in Clenshaw's method. It is also demonstrated how existing recursion algorithms for computing ALFs and their first derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and first derivatives, which can then be combined using Horner's scheme to compute partial sums, complete to degree and order 2700, for all latitudes (except at the poles for first derivatives). This exceeds any previously published result. Numerical tests suggest that this new approach is at least as precise and efficient as Clenshaw's method. However, the principal strength of the new techniques lies in their simplicity of formulation and implementation, since this quality should simplify the task of extending the approach to other uses, such as spherical harmonic analysis. Received: 30 June 2000 / Accepted: 12 June 2001  相似文献   

Gravity/magnetic potential of uneven shell topography     

G. Ramillien 《Journal of Geodesy》2002,76(3):139-149

 A fast spherical harmonic approach enables the computation of gravitational or magnetic potential created by a non-uniform shell of material bounded by uneven topographies. The resulting field can be evaluated outside or inside the sphere, assuming that density of the shell varies with latitude, longitude, and radial distance. To simplify, the density (or magnetization) source inside the sphere is assumed to be the product of a surface function and a power series expansion of the radial distance. This formalism is applied to compute the gravity signal of a steady, dry atmosphere. It provides geoid/gravity maps at sea level as well as satellite altitude. Results of this application agree closely with those of earlier studies, where the atmosphere contribution to the Earth's gravity field was determined using more time-consuming methods. Received: 14 August 2000 / Accepted: 19 March 2001  相似文献   

SHORT NOTE: Extending simplified high-degree synthesis methods to second latitudinal derivatives of geopotential     

S. A. Holmes  W. E. Featherstone 《Journal of Geodesy》2002,76(8):447-450

 Simplified techniques for high-degree spherical harmonic synthesis are extended to include gravitational potential second derivatives with respect to latitude. Received: 23 July 2001 / Accepted: 12 April 2002 Acknowledgement. The authors would like to thank Christian Tscherning for recommending Laplace's equation as an accuracy test. Our use of Legendre's differential equation, as the most direct means for extending our simplified synthesis methods to second-order derivatives, was a direct result of this suggestion. Correspondence to: S. A. Holmes  相似文献   

东亚地磁场模型的计算与分析   总被引：4，自引：0，他引：4       下载免费PDF全文

安振昌  N.M.Rotanova 《地球物理学报》2002,45(1):34-41

根据中国、前苏联和蒙古等地区的地磁复测点和地磁台站资料,使用泰勒多项式方法和冠谐分析方法,计算东亚地磁场(X,Y,Z)的泰勒多项式模型和冠谐模型,以及东亚剩余磁场(ΔX,ΔY,ΔZ)的冠谐模型和泰勒多项式模型,并绘制了相应的理论地磁图. 泰勒多项式模型的展开原点位于45°N和100°E,截断阶数为7.地磁场泰勒多项式模型的均方偏差为:X分量是133.0nT,Y分量是107.4nT,Z分量是14.0nT. 球冠极点位于45°N和100°E,球冠半角为42°,冠谐模型的截断阶数为10. 剩余磁场冠谐模型的均方偏差分别为131.2nT(ΔX),112.6nT(ΔY)和13.7nT(ΔZ). 对比分析了上述两种模型. 提出了确定区域模型截断阶数的判据.  相似文献   

汇聚造山带变质矿物冠状反应边及生长环带     

包佳凤  徐桂香  张伟明  李峰 《云南地质》2008,27(4)

哀牢山、澜沧江、高黎贡山、念青唐古拉山等汇聚造山带变质岩中,发现一些标型或特征变质矿物间形成冠状反应边或生长环带。它们是变质过程的真实记录,反映了变形变质环境条件的不断变化,完整或直观地表现了不同地体或构造带PTt轨迹特征。可帮助恢复汇聚造山带中不同地体构造属性,为研究造山带PTtD轨迹和PTDX轨迹,提供准确资料。可从另一侧面了解汇聚造山带的演化史。  相似文献   

三轴磁通门探头球型反馈线圈的设计方法研究          下载免费PDF全文

高嵩  汪莹莹  李志鹏  王绪本  曹彬  薛凯  窦悉丝 《地球物理学报》2019,62(10):3785-3793

长周期大地电磁测量要求三轴磁通门传感器具有低的噪声水平及高稳定性,根据实际需求设计一个尺寸合适的球型反馈线圈可以有效提高反馈磁场的均匀性,进而降低磁通门传感器的噪声水平.本文首先分析了非均匀反馈磁场引入磁通门噪声的机理,然后根据毕奥-萨伐尔定律和矢量叠加原理,以等间距多个单匝线圈构成单轴绕组的形式,建立了球型反馈线圈轴线上的轴向磁场分布及磁场均匀度数学模型,在给定磁场均匀度和球型反馈线圈直径的条件下,运用控制变量法确定了球型反馈线圈的单匝线圈数量和间距等关键结构参数.我们把设计的结构参数代入球型空间磁场分布数学模型,验证了本设计方法的正确性.最后,按照设计的结构参数制作了基于球型反馈线圈磁通门探头的三轴磁通门传感器,通过与体积相近的基于亥姆霍兹型反馈线圈磁通门探头的三轴磁通门传感器对比测试噪声水平,结果表明球型反馈线圈磁通门探头能够使得三轴磁通门传感器具有更稳定和较低的噪声水平.  相似文献