  We study in details the Earth matter effects on the boron neutrinos from the
Sun using recently developed 3D models of the Earth. The models have a number
of new features of the density profiles, in particular, a substantial deviation
from spherical symmetry. In this connection, we further elaborate on relevant
aspects of oscillations ($\epsilon^2$ corrections, adiabaticity violation,
entanglement, {\it etc.}) and the attenuation effect. The night excesses of the
$\nu e-$ and $\nu N-$ events and the Day-Night asymmetries, $A_{ND}$, are
presented in terms of the matter potential and the generalized energy
resolution functions. The energy dependences of the cross-section and the flux
improve the resolution, and consequently, sensitivity to remote structures of
the profiles. The nadir angle ($\eta$) dependences of $A_{ND}$ are computed for
future detectors DUNE, THEIA, Hyper-Kamiokande, and MICA at the South pole.
Perspectives of the oscillation tomography of the Earth with the boron
neutrinos are discussed. Next-generation detectors will establish the
integrated day-night asymmetry with high confidence level. They can give some
indications of the $\eta-$ dependence of the effect, but will discriminate
among different models at most at the $(1 - 2)\sigma$ level. For high-level
discrimination, the MICA-scale experiments are needed. MICA can detect the
ice-soil borders and perform unique tomography of Antarctica.
