Inverse problem in ionospheric science: prediction of solar soft-X-ray spectrum from very low frequency radiosonde results.

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. This leads us to the possibility of uninterrupted observation of X-ray photon spectra of solar flares that are often hindered by the restricted observation window of space satellites to avoid charge particle damages. Such continuous means of observation are essential in deriving information on time evolution of physical processes related to electron acceleration and interaction with plasma in solar atmosphere. 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 Earth's atmosphere. We thus show that to certain extent, the Earth's atmosphere could be used as a gigantic detector of relatively strong astronomical events. [ABSTRACT FROM AUTHOR]