Smoothing of geomagnetic data using a piecewise cubic polynomial

Abstract

SUMMARY A method is presented for fitting a piecewise cubic polynomial to a sequence of geomagnetic data which contains oscillations such as Pi2 pulsations superposed on rapid background changes such as bay-type disturbances. The first step of smoothing is performed by a one-pass method with a piecewise cubic polynomial where the polynomial pieces are calculated as the data is scanned only once from left to right. The knots of the approximating piecewise cubic polynomial are determined successively using a modified Powell criterion which has a free parameter μ determining the degree of smoothing. As μ grows large, the approximating function becomes smoother and the oscillations with longer periods can be separated (μ= 1 corresponds to the original Powell criterion). If a rapid background change needs to be preserved in the smoothed data, the sum of squares of residuals is locally minimized in the neighbourhood of the rapid change as the second step. The proposed method which involves two steps is capable of separating the oscillations from the rapid background changes. Some examples of good separation are displayed.