  We develop a detailed and comprehensive description of neutrino oscillations
driven by the 1-3 mixing in the matter of the Earth. The description is valid
for the realistic (PREM) Earth density profile in the whole range of nadir
angles and for neutrino energies above 1 GeV. It can be applied to oscillations
of atmospheric and accelerator neutrinos. The results are presented in the form
of neutrino oscillograms of the Earth, i.e. the contours of equal oscillation
probabilities in the neutrino energy--nadir angle plane. A detailed physics
interpretation of the oscillograms, which includes the MSW peaks, parametric
ridges, local maxima, zeros and saddle points, is given in terms of the
amplitude and phase conditions. Precise analytic formulas for the probabilities
are obtained. We study the dependence of the oscillation pattern on theta_13
and find, in particular, that the transition probability P > 1/2 appears for
sin^2(2theta_13) as small as 0.009. We consider the dependence of the
oscillation pattern on the matter density profile and comment on the
possibility of the oscillation tomography of the Earth.
