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

Published: 03-08-2018| Version 1 | DOI: 10.17632/nppz4y7wg7.1
Zdeněk Martinec,
David Einšpigel


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.