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   

GOCE Quick-Look Gravity Solution: Application of the Semianalytic Approach in the Case of Data Gaps and Non-Repeat Orbits     

Preimesberger  T.  Pail  R. 《Studia Geophysica et Geodaetica》2003,47(3):435-453

The satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), the first Core Mission of the Earth Explorer Programme funded by ESA (European Space Agency), is dedicated to the precise modelling of the Earth's gravity field, with its launch planned for 2006. The mathematical models for parameterizing the Earth's gravity field are based on a series expansion into spherical harmonics, yielding a huge number of unknown coefficients. Their computation leads to the solution of very large normal equation systems. An efficient way to handle these equation systems is the so-called semianalytic or lumped coefficients approach, which theoretically requires an uninterrupted, continuous time series of observations, recorded along an exact circular repeat orbit. In this paper the consequences of violating these conditions are analyzed. The effects of an interrupted observation stream onto the estimated spherical harmonic coefficients are demonstrated, and an iterative strategy, which reduces the negative influence depending on the characteristics of the data gaps, is proposed. Additionally, the impact of an imperfectly closing orbit (non-repeat orbit) on the gravity field model is analyzed, and a strategy to minimize the corresponding errors is presented. The applicability of the semianalytic approach also to a joint inversion of satellite-to-satellite tracking data in high-low mode (hl-SST) and satellite gravity gradiometry (SGG) observations is demonstrated, where the analysis of the former component is based on the energy conservation law. Several realistic case studies prove that the semianalytic approach is a feasible tool to generate quick-look gravity solutions, i.e. fast coefficient estimates using only partial data sets. This quick-look analysis shall be able to detect potential distortions of statistical significance (e.g. systematic errors) in the input data, and to give a fast feedback to the GOCE mission control.  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   

局部重力场球冠谐分析中的导数计算及应用     

吴招才  刘天佑  高金耀 《海洋与湖沼》2006,37(6):488-492

在建立局部地区的地球重力场模型中,球冠谐分析是一种有效的方法。在球冠坐标系下建立重力场模型时,仅涉及到重力位的垂向分量,不必进行关于极角的微分运算,所以仅用单个正交基来建模,但若要在球冠坐标系下对重力场作进一步分析,如类似于平面处理的导数运算,来突出地质体的边界,要计算极角的微分,利用单个正交基表示则不易收敛,且误差较大。本文中作者采用两个正交基函数在球冠坐标系下对重力场建模,推导计算了径向导数和曲面导数模,并利用棱柱体正演模型进行检验,结果表明双基函数建模更适合曲面上的位场表示。最后计算了冲绳海槽地区卫星测高重力异常数据的曲面导数,径向导数清晰划分了东海陆架上大构造单元,曲面导数梯度带显示了东海陆架外缘隆起带,也指示了陆架盆地内的一些局部构造。这表明双基函数的球冠谐分析是一种有效的曲面位场建模方法。  相似文献   

广义Radon变换的正交展开和反演     

王金平 《CT理论与应用研究》1999,8(4):14-19

本文具体给出了广义Ｒａｄｏｎ变换在函数空间Ｌ＾２（Ｒ＾ｎ,Ｗｎ）上的正交函数展开形式,由此得到了广义Ｒａｄｏｎ变换的反演公式,从而推广了Ｌｏｕｉｓ和Ｄａｖｉｓｏｎ的工作。  相似文献   

应用非线性高阶谐波衰减和尾波干涉监测高温作用后水泥制品的损伤演化     

张尧  马强  肖武军 《震灾防御技术》2018,13(1):52-64

非线性高阶谐波和尾波波速变化均能够反映水泥材料内部微结构的应力变化。利用高阶谐波和尾波干涉实验测量系统,对引入高温作用后的3类不同粒径共6块水泥试样进行单轴加载的损伤演化实验,并与无高温作用的完整试样的实验结果进行对比。结果表明,从初始状态到25%抗压强度的过程中,高温作用后的试样的谐波幅值和尾波波速变化出现明显增强的现象（谐波幅值最大增幅约20%）,而无高温作用的完整试样的谐波幅值和尾波波速变化较为平稳（谐波幅值最大增幅约5%）;在达到65%抗压强度的过程中,高温作用后的试样的谐波幅值和尾波波速变化急剧增大（谐波幅值最大增幅约100%）,且粒径较大的试样的增幅高于粒径较小的试样,而无高温作用的完整试样的谐波幅值和尾波波速变化的增幅较小（谐波幅值最大增幅约10%）;当抗压强度超过75%以后,高温作用后的试样的谐波幅值和尾波波速变化急剧衰减（谐波幅值最大衰减幅度约140%）,而无高温作用的完整试样的谐波幅值和尾波波速的最大衰减幅值在40%以内。基于以上观测结果对高温作用后水泥制品损伤演化的物理机制以及这两类监测方法的适用性进行了讨论。  相似文献