Including the Temporal Dimension in the SECS Technique

The equivalent source method of Spherical Elementary Current Systems (SECS) has contributed valuable results for spatial magnetic interpolation purposes where no observations are available, as well as for modeling equivalent currents both in the ionosphere and in the subsurface, thus providing a separation between external and internal sources. It has been successfully applied to numerous Space Weather (SW) events, whereas some advantages have been reported over other techniques such as Fourier or Spherical (Cap) Harmonic Analysis. Although different modalities of SECS exist (either 1-D, 2-D, or 3-D) depending on the number of space dimensions involved, the method provides a sequence of instantaneous pictures of the source current. We present an extension of SECS consisting in the introduction of a temporal dependence in the formulation based on a cubic B-splines expansion. The technique thus adds one dimension, becoming 4-D in general (e.g., 3-D + t), and its application is envisaged for, though not restricted to, the analysis of past events including heterogeneous geomagnetic data sets, such as those containing gaps, different sampling rates or diverse data sources. A synthetic model based on the SW Modeling Framework is used to show the efficacy of the extended scheme. We apply this method to characterize the current systems of past and significant SW events producing geomagnetically induced currents, which we exemplify with an outstanding geomagnetic sudden commencement occurred on 24 March 1991.