SHAVEL: A program for the spherical harmonic analysis of a horizontal vector field sampled in an equiangular grid on a sphere

A method for performing a spherical harmonic analysis, using observed horizontal components of a tangent vector on a sphere, is presented. The vector data samples are assumed to be provided in an equiangular grid, which essentially simplifies the least-squares analysis by making use of (1) the block diagonal structure of the normal equations of least squares; (2) the even–odd symmetry of the associated Legendre functions, and (3) the fast Fourier transform of mix-radix. The correct function of the program and its numerical precision is verified by applying it to a data set, derived by evaluating a given set of vector spherical harmonic coefficients. That the program works correctly is demonstrated by the excellent agreement between the input and output spherical harmonic coefficients.

本文提出了一种基于球谐分析的方法，该方法利用球面上切向量的观测水平分量进行计算。假设向量数据样本以等角网格提供，这本质上简化了最小二乘分析，通过利用（1）最小二乘法正则方程的块对角结构；（2）相关勒让德函数的偶奇对称性；（3）混合基数的快速傅里叶变换。通过将程序应用于由评估一组给定的向量球谐系数得到的数据集，验证了程序的正确功能和数值精度。程序的正确性通过输入与输出球谐系数之间卓越的一致性得到证实。