Inverse problem in Ionospheric Science: Prediction of solar soft-X-ray spectrum from Very Low Frequency Radiosonde results

Abstract

X-rays and gamma-rays from astronomical sources such as solar flares are mostly absorbed by the Earth's atmosphere. Resulting electron-ion production rate as a function of height depends on the intensity and wavelength of the injected spectrum and therefore the effects vary from one source to another. In other words, the ion density vs. altitude profile has the imprint of the incident photon spectrum. In this paper, we investigate whether we can invert the problem uniquely by deconvolution of the VLF amplitude signal to obtain the details of the injected spectrum. We find that it is possible to do this up to a certain accuracy. Our method is useful to carry out a similar exercise to infer the spectra of more energetic events such as the Gamma Ray Bursts (GRBs), Soft Gamma Ray Repeaters (SGRs) etc. by probing even the lower part of the atmosphere. We thus show that to certain extent, the Earth's atmosphere could be used as a gigantic detector of relatively strong events.