We implement three mathematical techniques to reconstructed the magnetic field around a multispacecraft configuration taking sparse measurements: Linear, Radial Basis Function (RBF), and Timesync.
The Linear method does not assume Taylor's hypothesis holds. It therefore scans through the timeseries of magnetic field measurements and uses tetrahedra drawn from measurements made at the same time to perform a reconstruction of the magnetic field near the barycenter of the configuration. See the GitHub repo Curlometer_Extension for details on how the Linear method is applied to configurations of
The RBF method assumes Taylor holds, and therefore uses all
Timesync reconstruction is our own method of reconstructing magnetic fields. It computes the time/space offset of the measurements made by all of the spacecraft assuming Taylor's hypothesis holds. It then selects one measurement per spacecraft to be used in the interpolation scheme at any reconstructed point. This results in a reconstructed field that is interpolated separetly along the spacecraft's direction of travel and the plane perpendicular to this direction. This distinct treatment of the parallel and perpendicular directions was divised because spacecraft data is often well sampled in time, but poorly sampled in space. This inhomogeneous sampling is known to be non-optimal for the RBF method.
We compute the point-wise error in the reconstructed vs simulated magnetic field. We also demonstrate how to compute the relative Wasserstein distance
This work is based on a paper in Earth and Space Sciences