The inverse problem: reconstruction of sources from the SR

The inverse problem means deriving the location and intensity of the sources — that is, global lightning activity — backward from the measured field components of the Schumann resonance (the electric and magnetic components, their spectra and ratios). It is the opposite direction to the forward model (cluster E), which, from an assumed distribution of sources and the properties of the Earth-ionosphere cavity, computes the expected field.

The principle of inversion lies in "reversing" the forward model: one seeks the source distribution for which the forward-computed field best matches the measured one Pracser 2019. In practice this is done by optimization — the assumed position and intensity of the storm centers are gradually adjusted until the modeled spectrum agrees with the observed one.

The inverse problem is, however, typically ill-posed: different source distributions can give very similar fields at a single station. Therefore a single measurement has only limited resolving power, and for a reliable reconstruction one needs either additional assumptions (e.g., the three main tropical storm centers — the Americas, Africa, Southeast Asia), or data from several stations at once (#79).