Could One Find Petroleum Using Neutrino Oscillations in Matter?

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.