Attenuation effect and neutrino oscillation tomography

The attenuation effect is the effect of weakening contributions to the oscillation signal from remote structures of the matter density profile. The effect is a consequence of integration over the neutrino energy within the energy resolution interval. Structures of a density profile situated at distances larger than the attenuation length, λₐₜₜ, are not ``seen'' at the level ε≡2EV/Δm², where V is the matter potential. We show that the origins of attenuation are (i) the averaging of oscillations in certain layer(s) of matter, (ii) the smallness of the matter effect: ε1, and (iii) the specific initial and final states on neutrinos. We elaborate on the graphic description of the attenuation that allows us to compute explicitly the effects in the ε² order for various density profiles and oscillation channels. The attenuation in the case of partial averaging is described. The effect is crucial for the interpretation of oscillation data and for the oscillation tomography of the Earth with low energy (solar, supernova, atmospheric, etc.) neutrinos.