Could one find petroleum using neutrino oscillations in matter?

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Abstract
In neutrino physics, it is now widely believed that neutrino oscillations are influenced by the presence of matter, modifying the energy spectrum produced by a neutrino beam traversing the Earth. Here, we will discuss the reverse problem, i.e. what could be learned about the Earth's interior from a single neutrino baseline energy spectrum, especially about the Earth's mantle. We will use a statistical analysis with a low-energy neutrino beam under very optimistic assumptions. At the end, we will note that it is hard to find petroleum with such a method, though it is not too far away from technical feasibility.