“…To gain solvability of this problem, we assume that these tangential currents are located on a sphere R , with fixed radius R > 0, which is situated somewhere in the ionospheric E-region, generally at an altitude of about 115 km above the Earth-centered sphere of mean Earth radius R E = 6,371.2 km. In this setting, we can now relate the magnetic field measured at some altitude R sat with a tangential current system at altitude R tan = R sat via the spherical Biot-Savart operator, as has been done, e.g., in Mayer 2004. Observing the result of Fukushima 1976, i.e., tangential surface-curl-free currents produce no magnetic effect inside the sphere on which they are present, one can only hope to recover an equivalent current system j equiv via the inversion of the spherical Biot-Savart operator (in this context, 'equivalent' current system means that j equiv produces the measured magnetic field but does not necessarily represent the true current system in the ionosphere).…”