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

Solution method: The vector spherical harmonic coefficients of a horizontal vector field are estimated by the method of least-squares adjustment of data samples distributed in an equiangular grid on a sphere. For such a regular grid the normal matrix is sparse and allows the system of the normal equations to be decomposed into a series of subsystems according to azimuthal order m. The solution of each subsystem is sought by the Gauss elimination. The fast Fourier transform of mix-radix is implemented in (i) setting up the right-hand sides of the normal equations, and (ii) performing the spherical harmonic synthesis where the series of spherical harmonics are summed.