Abstract
A new method for performing a spherical harmonic analysis, using only observed components of the earth's magnetic field, is presented. Essential features of the method involve the use of (1) multidimensional vector spaces to exhibit clearly and to make use of the coupling among the X, Y, and Z expansions and to simplify the logic; (2) the Gram-Schmidt orthogonalization process to simplify the solution of the normal equations of least squares and, more important, to provide a system of orthogonal functions with their many useful properties; and (3) the variance ratio test applied to each orthogonal function in such a way that the significant functions are used in the final approximation and the insignificant ones are used to estimate error. The method is verified by applying it to two independent sets of data, both derived by evaluating a given set of Gaussian coefficients. That the method works in the error-free case is proved conclusively by the remarkable agreement between input and output coefficients for both sets of data.
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