Using an equivalent source with positivity for low-latitude reduction to the pole without striation

We present a reformulation of reduction to the pole (RTP) of magnetic data at low latitudes and the equator using equivalent sources. The proposed method addresses both the theoretical difficulty of low-latitude instability and the practical issue of computational cost. We prove that a positive equivalent source exists when the magnetic data are produced by normal induced magnetization, and we show that the positivity is sufficient to overcome the low-latitude instability in the space domain. We further apply a regularization term directly to the recovered RTP field to improve the solution. The use of equivalent source also naturally enables the processing of data acquired on uneven surface. The result is a practical algorithm that is effective at the equatorial region and can process large-scale data sets with uneven observation heights.