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spherical harmonic series
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  球谐级数
     1. Isostatic gravity and geoid anomaly of China and its adjacent regionsBase on theory of lithosphere elastic flexure isostatic compensation, the spherical harmonic series expressions of topography-isostasy compensation gravity and geoid are established.
     对于均衡重力大地水准面异常的研究无疑将会使我们对地球内部结构和动力学过程的认识更加深入。 本文的主要研究内容如下:1、中国及邻区均衡重力大地水准面异常依据岩石圈弹性挠曲均衡补偿理论建立地形—均衡补偿重力、大地水准面异常的球谐级数表达式。
短句来源
     The Solution of Altimetry-Gravimetry Problem by Spherical Harmonic Series
     卫星测高问题的球谐级数解法
短句来源
     Analysis of the Precision on Computation of Geomagnetic Field Lines at Low Latitude by Means of Spherical Harmonic Series
     用球谐级数计算低纬地磁场力线的精度分析
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     Then we can research the relationship between topography-isostatsy compensation gravity and geoid and order and degree of spherical harmonic series, and discuss the characters of topography-isostatsy compensation gravity and geoid.
     由此我们可以研究地形—均衡补偿重力、大地水准面异常与球谐级数阶次的关系,以及不同波长地形荷载与岩石圈挠曲补偿的关系,探讨地形—均衡补偿重力、大地水准面的频谱特性。
短句来源
     A solution method for the satellite altimetry problem with the spherical harmonic series
     卫星测高混合边值问题的球谐级数解法
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  “spherical harmonic series”译为未确定词的双语例句
     In the pysical geodesy,spherical harmonic series are frequently used to compute geoidal undulation,deflection of vertical and gravity anomalies. However if the Clen- shaw summation were used,the computation could be made more convenient. Some comparisons have been made between the initially developed models A and B in our country and Rapp model,by 5°×5°mean geoidal undulation and deflection of vertical,covering an area of 80°—120°east longitude and 20°—40°north latitude.
     本文采用克林索求和的方法,应用三个重力模型计算了东经80°~120°和北纬20°~40°之间的大地水准面差距、垂线偏差和重力异常。
短句来源
     This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.
     ALMOST EVERYWHERE CONVERGENCE AND APPROXIMATION OF SPHERICAL HARMONIC EXPANSIONSLiLuoqing(李落清)(DepartmentofMathematics,Hubeiu...
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     Under the boundary values such as disturbing potential, gravity anomaly, gravity disturbance and two or three of them together, the spherical harmonic series representations and cloed solutions on harmonic density anomaly are given.
     建立起在边界条件分别为扰动位、扰动重力、重力异常以及其中两类以上同时作为边界输入的情况下,对应的调和性扰动场源的球谐函数表达式及封闭解式。
短句来源
     This paper mainly focuses on the generalized spherical harmonic series representation of satellite gradiometry and on the generalized spherical harmonic analysis of satellite gradiometry.
     在文献 [1 ]的基础上 ,进一步研究全张量重力梯度数据的全局和局部分量的广义球谐谱表示和轨道根数表示 ,并给出了广义球谐函数与球谐函数之间的关系。
短句来源
     IGRF(International Geomagnetic Reference Field) are the models of geomagnetic main field and secular variation. The IGRF errors are from neglecting external field, truncation level of the spherical harmonic series, observatory distribution, measurement, and neglecting the crust geomagnetic anomalies .
     IGRF(国际地磁参考场 )是有关地球主磁场与长期变化的模型 ,IGRF的误差主要来源于 :忽略外源场、球谐级数的截断、台站分布的不均匀、测量、忽略地壳磁异常场等 .
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  相似匹配句对
     The Improvement on Spherical Harmonic Expansion
     球谐函数级数式的改化形式
短句来源
     The spherical harmonic analysis in geomagnetism and gravitation
     在地磁学与地球重力学中的球谐分析
短句来源
     The Solution of Altimetry-Gravimetry Problem by Spherical Harmonic Series
     卫星测高问题的球谐级数解法
短句来源
     Harmonic and Administration
     谐波及其治理
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     ON HARMONIC OF VVVF
     交流变频调速(VVVF)的谐波问题
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  spherical harmonic series
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.
      
Expansion of geoid heights over a triaxial earth's ellipsoid into a spherical harmonic series
      
An algorithm is derived to compute the coefficients of a spherical harmonic series for the geoid radius vector that are a solution to a system of linear equations, containing Stokes' constants of the geopotential.
      
Expansion of geoid heights into a spherical harmonic series
      
This magnetic scalar potential can be expanded into a spherical harmonic series.
      
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In the pysical geodesy,spherical harmonic series are frequently used to compute geoidal undulation,deflection of vertical and gravity anomalies.However if the Clen- shaw summation were used,the computation could be made more convenient. Some comparisons have been made between the initially developed models A and B in our country and Rapp model,by 5°×5°mean geoidal undulation and deflection of vertical,covering an area of 80°—120°east longitude and 20°—40°north latitude.Each model has been truncated up...

In the pysical geodesy,spherical harmonic series are frequently used to compute geoidal undulation,deflection of vertical and gravity anomalies.However if the Clen- shaw summation were used,the computation could be made more convenient. Some comparisons have been made between the initially developed models A and B in our country and Rapp model,by 5°×5°mean geoidal undulation and deflection of vertical,covering an area of 80°—120°east longitude and 20°—40°north latitude.Each model has been truncated up to 22 degree and order.The comparison of mean gravity anomalies has been made between observational and each one of three models. The results show that:(1)ΔN_A,the difference of geoidal undulations between A model and Rapp model,has a systematic tilt near east-west direction.ΔN_B,the dif- ference between B model and Rapp model,has a strong ascent in North-West China and a descend in North-West China.(2)Δξ_B,the difference of components ξ,between B model and Rapp model,has a descend in Central China,and Δη_A,the differnce of components η,between A model and Rapp model,has a systematic tilt.(3)The mean errors of the differences of mean gravity anomalies obtained by obsevations and each one of three models separately are similar. The conclusion is that A and B models are not more suitable than Rapp model for our country.

本文采用克林索求和的方法,应用三个重力模型计算了东经80°~120°和北纬20°~40°之间的大地水准面差距、垂线偏差和重力异常。各模型截取到22阶次为止,并且将各模型计算的5°×5°大地水准面差距和垂线偏差平均值进行了比较。另外还对模型计算的平均重力异常与实测的平均重力异常进行了比较。

We make spherical harmonig salyses of geomagnetic secular variation using the annual means of three components X, Y, and Z of 157 observatories ,all over the world during 1960.0-1965.0. Twenty five analyses have been made with five different weighting approaches (ranged from the weighting approach S in which the condition number of normal matrix Is mainly considered to the weighting approach D in which only the data errors are considered) and five truncation levels (from n=4 to n = 8, where n is the maximum...

We make spherical harmonig salyses of geomagnetic secular variation using the annual means of three components X, Y, and Z of 157 observatories ,all over the world during 1960.0-1965.0. Twenty five analyses have been made with five different weighting approaches (ranged from the weighting approach S in which the condition number of normal matrix Is mainly considered to the weighting approach D in which only the data errors are considered) and five truncation levels (from n=4 to n = 8, where n is the maximum degree of truncated spherical harmonic series). Both the condition numbers of normal matrices and the degree of fitting of the spherical harmonic models to data in these analyses are investigated. From this investigation we find that spherical harmonic model SVSHM 1960-1965, the model with n = 6 and the weighting approach S(3/4) D(1/4) may be the most effective one based on the data stated above.

本文利用1960.0—1965.0全球157个地磁台站的X、Y、Z三分量年均值资料,进行了地磁场长期变化的球谐分析。我们采用5种加权方案(从主要考虑法矩阵条件数的方案S过渡到仅考虑资料误差的方案D),并选择5种截断水平(球谐函数的截取级次从n=4到n=8),共作了25次分析,从获得的法矩阵条件数和拟合残差两者的分析中发现,对这一组资料球谐级数的截取级次取为n=6,而加权方案采用S 3/4 D 1/4可能是最有效的,其结果即为地磁场长期变化球谐模型SVSHM 1960—1965。

The approximation properties for spherical functions by the Cesaro means of the spherical harmonic series are studied, The uniform approximation esrimate of the Cedaro means at The critical index and the almost everywhere approximation order of the Cedaro means below the critical index are established.

Cesaro平均逼近球面函数杨汝月,李落清(宁夏大学数学系,银川,750021)(北京师范大学数学系,北京,100875)APPROXIMATIONFORSPHERICALFUNCTIONSBYCESAROMEANS¥YANGRUYUE(Depart...

 
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