Stable reduction to the pole at the magnetic equator

The solution of reduction to the pole (RTP) of magnetic data in the wavenum ber domain faces a long standing difficulty of instability when the observe d data are acquired at low magnetic latitudes or at the equator. We develop a solution to this problem that allows stable reconstruction of the RTP fi eld with a high fidelity even at the magnetic equator. The solution is obta ined by inverting the Fourier transform of the observed magnetic data in th e wavenumber domain with explicit regularization. The degree of regularizat ion is chosen according to the estimated error level in the data. The Fouri er transform of the RTP field is constructed as a model that is maximally s mooth and, at the same time, has a power-spectral decay common to all field s produced by the same source. The applied regularization alleviates the si ngularity associated with the wavenumber-domain RTP operator, and the impos ed power spectral decay ensures that the constructed RTP field has the corr ect spectral content. As a result, the algorithm can perform the reduction to the pole stably at any magnetic latitude, and the constructed RTP field yields a good representation of the true held at the pole even when the red uction is carried out at the equator.