Detectability of the Earth matter effects on the neutrino energy spectrum of a core-collapse galactic supernova requires collecting a large number of events, as well as having a detector with good energy resolution. A JUNO-like detector with an exceptional energy resolution better than 3% at 1 MeV could detect about 5000 inverse beta decay signals from a supernova explosion at a distance of 10 kpc from us. However, this number of events is not sufficient to discriminate between the products associated with Earth matter effects (formation of peaks after taking the Fourier transform of the inverse energy spectrum) and the peaks that appear as a result of statistical fluctuations. Here, the impact of incorporating invisible neutrino decay into the physics of the problem is studied together with a more detailed analysis of the supernova neutrino energy spectrum.