  A future large-volume liquid scintillator detector such as the proposed 50
kton LENA (Low Energy Neutrino Astronomy) detector would provide a
high-statistics measurement of terrestrial antineutrinos originating from
$\beta$-decays of the uranium and thorium chains. Additionally, the neutron is
scattered in the forward direction in the detection reaction $\bar\nu_e+p\to
n+e^+$. Henceforth, we investigate to what extent LENA can distinguish between
certain geophysical models on the basis of the angular dependence of the
geoneutrino flux. Our analysis is based on a Monte-Carlo simulation with
different levels of light yield, considering an unloaded PXE scintillator. We
find that LENA is able to detect deviations from isotropy of the geoneutrino
flux with high significance. However, if only the directional information is
used, the time required to distinguish between different geophysical models is
of the order of severals decades. Nonetheless, a high-statistics measurement of
the total geoneutrino flux and its spectrum still provides an extremely useful
glance at the Earth's interior.
