An algorithm for reduction to the pole that works at all magnetic latitudes

Abstract

Classical fast Fourier transformation methods for reduction to the pole cease to produce realistic results at low magnetic inclinations because the factor by which the frequency domain field representation must be multiplied becomes infinitely large due to the denominator of this term approaching zero. The problems of the Fourier transformation method however can be avoided by performing the transformation in the space domain by convolving the field with a set of filter coefficients which perform the desired transformation. Such filter coefficients may be calculated using the Wiener design principle which produces filter coefficients for transformations such that a known input is transformed to a desired output in a manner that the mean square error between an actual output and a desired output is minimised.