  Attenuation effect is the effect of weakening of contributions to the
oscillation signal from remote structures of 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, $\lambda_{att}$, are not "seen". We show
that the origins of attenuation are (i) averaging of oscillations in certain
layer(s) of matter, (ii) smallness of matter effect: $\epsilon \equiv
2EV/\Delta m^2 \ll 1$, where $V$ is the matter potential, and (iii) specific
initial and final states on neutrinos. We elaborate on the graphic description
of the attenuation which allows us to compute explicitly the effects in the
$\epsilon^2$ order for various density profiles and oscillation channels. The
attenuation in the case of partial averaging is described. The effect is
crucial for interpretation of oscillation data and for the oscillation
tomography of the Earth with low energy (solar, supernova, atmospheric, {\it
etc.}) neutrinos.
