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 $bar u_e+pto n+e^+$ 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 Earths core. However, a high-statistics measurement of the total geoneutrino flux and its spectrum still provides an extremely useful glance at the Earths interior.
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