A simple approach to the transformation of spherical harmonic models under coordinate system rotation

Abstract

The transformation of a set of spherical harmonic coefficients characterizing a model of the geomagnetic field, or a general function defined on a sphere, subject to a rotation of the coordinate system, is given by the direct relations between the coefficients and then by using a numerical approach. The parameters for a pair of such rotations (from one set to another, and vice versa) are given, along with a few examples of their application. The method is particularly useful for the comparison of geophysical characteristics derived from models developed under different coordinate systems. It offers a practical solution to the problem, which can be implemented without difficulty.