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Least squares and integral methods for the spherical harmonic analysis of theSqfield


Spherical harmonic analysis is made of the grid point values of geopotential heights at 700 mb and 300 mb levels for the months April to August for the years 1967 and 1972.


Meridional transport of sensible heat in contrasting monsoon activity: Spherical harmonic analysis


The global distributions of the annual and seasonal means of the diurnal (S1) and semidiurnal (S2) surface pressure oscillations are investigated by spherical harmonic analysis.


The global distribution of the lunar barometric tideL2 is investigated by spherical harmonic analysis, based on 104 stations for the annual mean, and on 85 stations for the three seasons.

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 The improvement of the singlestation Z/H method can be achieved by adding the second dominant term P. The improved Z/H method: simplicity in calculation, only singlestation data are needed and no spherical harmonic analysis is performed. In this paper, we use the spherical harmonic coefficients published in Parkinson's book (1983) to calculate the correction coefficients η1 and η2, which are needed in the application of the modified Z/H method. The inductive scale length C1 estimated by this... The improvement of the singlestation Z/H method can be achieved by adding the second dominant term P. The improved Z/H method: simplicity in calculation, only singlestation data are needed and no spherical harmonic analysis is performed. In this paper, we use the spherical harmonic coefficients published in Parkinson's book (1983) to calculate the correction coefficients η1 and η2, which are needed in the application of the modified Z/H method. The inductive scale length C1 estimated by this improved method appears to be much better than that obtained by the original Z/H method. However, the estimated value of C2 does not change much. The inversion results based on 4layer model are obtained by means of the MonteCarlo method for the Lanzhou, Wuhan and Guangzhou observatories.These inversion results indicate that the buried depth values of the deeper highly conductive layer (i. e. the fourth layer) for the stated three observatories are significantly different.  改良的单台Ｚ／Ｈ法的原理是增加了次强项Ｐ，但仍保留了原Ｚ／Ｈ法的优点：方法简单，只需单台资料，不需作球谐分析。本文用Ｐａｒｋｉｎｓｏｎ（１９８３）书中提供的球谐系数计算了改良的Ｚ／Ｈ法所需的改正项系数η１和η２。由此估算的感应尺度Ｃ１得到了很大的改善，但Ｃ２值却变化不大。本文用Ｍｏｎｔｅ－Ｃａｒｌｏ法得出兰州、武汉、广州三台的四层模型反演的结果，显示出上述三个地区下面的高导层（第四层）埋深有相当大的差别。  In this paper the fast Fourier transform of spherical harmonics for the gravitational POtential is carried out by means of the Walsh transform. The WalshFourier transform of spherical harmonics and the fast WalshHadamard transform algorithm of transition matrix and itS data compaction method are derived, the characteristics of WalshFourier transform and its applications in spherical harmonic analysis are discussed as well. The researches show that the results of WalshFourier transform coincide fully... In this paper the fast Fourier transform of spherical harmonics for the gravitational POtential is carried out by means of the Walsh transform. The WalshFourier transform of spherical harmonics and the fast WalshHadamard transform algorithm of transition matrix and itS data compaction method are derived, the characteristics of WalshFourier transform and its applications in spherical harmonic analysis are discussed as well. The researches show that the results of WalshFourier transform coincide fully with Foaurer transform when the sequency is equated to the frequency, the figures of curve for the tWo transformations are the same; According to the operation of double precision type, the computational accuracy of two different methods can come to±(10  1510 14);The WalshFourier transform can replace the complex transformation of Fourier transform by the real transformation; The range of speeding up the fast WalshHadamaxd transform will be increased with the increase of order;The WalshFourier transform can be used for the case where the sequency and the frequency are equalled or unequalled. The WalshFourier transform is better than the Fourier transform in the computational accuracy, data compaction and representation of potential field spectrum.  借助Walsh变换实现引力位球谐函数的快速Fourier变换导出了球谐函数的Walsh—Fourier变换、转换矩阵的快速Walsh—Hadamard变换算法及其数据压缩方法还讨论了Walsh—Fouriede换的特性及其在球谐分析中的应用研究表明：当序率和频率等同时．Walsh．Fourier变换和Fourier变换的结果完全一致，两者曲线形态相同;按双精度运算，两种方法的计算准确度均可达到±（10－1510－14）；Walsh－Fourler变换可以用实数变换取代Fourier变换的复数变换；快速Walsh－Hadamard变换速度提高的幅度将随着阶数的增加而递增：Walsh—Fourier变换可以用于序率和频率等同或不等同的情形Walsh—Fourler变换可在计算精度、数据压缩和位场谱表示方面好于Fourier变换  The mathematical methods to calculate the theoretical models of satellite magnetic anomalies, spherical harmonic analysis, spherical cap harmonic analysis, rectangular harmonic analysis and equivalent source method, were introduced in this paper The spherical cap harmonic, rectangular harmonic and equivalent source models of satellite magnetic anomalies which derived from the same Magsat data can best express the distribution of the satellite magnetic anomalies... The mathematical methods to calculate the theoretical models of satellite magnetic anomalies, spherical harmonic analysis, spherical cap harmonic analysis, rectangular harmonic analysis and equivalent source method, were introduced in this paper The spherical cap harmonic, rectangular harmonic and equivalent source models of satellite magnetic anomalies which derived from the same Magsat data can best express the distribution of the satellite magnetic anomalies Because there were satellite data in the whole studied region, so these theoretical models have no called "boundary effect" , this conclusion is very significant for calculating the regional models of the geomagnetic field  本文介绍了计算卫星磁异常理论模型的数学方法 ,即球谐分析方法、冠谐分析方法、矩谐分析方法和等效源方法 .根据相同的 MAGSAT资料 ,计算的卫星磁异常冠谐模型、矩谐模型和等效源模型都能很好地表示卫星磁异常的分布 .由于在整个研究区域 ( 1 0°N～60°N,70°E～ 1 40°E)都有卫星资料 ,所以这些理论模型没有所谓的“边界效应”.这一结论对计算地磁场的区域模型是很有意义的 .  
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