  A future large-volume liquid scintillator detector would provide a
high-statistics measurement of terrestrial antineutrinos originating from
$\beta$-decays of the uranium and thorium chains. In addition, the forward
displacement of the neutron in the detection reaction $\bar\nu_e+p\to n+e^+$
provides directional information. We investigate the requirements on such
detectors to 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 both
unloaded and gadolinium-loaded scintillators. We find that a 50 kt detector
such as the proposed LENA (Low Energy Neutrino Astronomy) will detect
deviations from isotropy of the geoneutrino flux significantly. However, with
an unloaded scintillator the time needed for a useful discrimination between
different geophysical models is too large if one uses the directional
information alone. A Gd-loaded scintillator improves the situation
considerably, although a 50 kt detector would still need several decades to
distinguish between a geophysical reference model and one with a large neutrino
source in the Earth's core. However, a high-statistics measurement of the total
geoneutrino flux and its spectrum still provides an extremely useful glance at
the Earth's interior.
