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Decays of radionuclides throughout the Earth's interior produce geothermalheat, but also are a source of antineutrinos. The (angle-integrated)geoneutrino flux places an integral constraint on the terrestrial radionuclidedistribution. In this paper, we calculate the angular distribution ofgeoneutrinos, which opens a window on the differential radionuclidedistribution. We develop the general formalism for the neutrino angulardistribution, and we present the inverse transformation which recovers theterrestrial radioisotope distribution given a measurement of the neutrinoangular distribution. Thus, geoneutrinos not only allow a means to image theEarth's interior, but offering a direct measure of the radioactive Earth, both(1) revealing the Earth's inner structure as probed by radionuclides, and (2)allowing for a complete determination of the radioactive heat generation as afunction of radius. We present the geoneutrino angular distribution for thefavored Earth model which has been used to calculate geoneutrino flux. In thismodel the neutrino generation is dominated by decays in the Earth's mantle andcrust; this leads to a very ``peripheral'' angular distribution, in which 2/3of the neutrinos come from angles > 60 degrees away from the downward vertical.We note the possibility of that the Earth's core contains potassium; differentgeophysical predictions lead to strongly varying, and hence distinguishable,central intensities (< 30 degrees from the downward vertical). Otheruncertainties in the models, and prospects for observation of the geoneutrinoangular distribution, are briefly discussed. We conclude by urging thedevelopment and construction of antineutrino experiments with angularsensitivity. (Abstract abridged.)Comment: 25 pages, RevTeX, 7 figures. Comments welcom

Imaging the Earth’s Interior: the Angular Distribution of Terrestrial Neutrinos