Hyper-Kamiokande could measure the average core density with an uncertainty around -14%/+40% at nominal resolution, improving to about -8%/+10% with better resolution, after 6500 days.
Multi-Messenger Tomography of the Earth
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Neutrino Oscillation Tomography of the Earth with the Hyper-Kamiokande Detector
Hyper-Kamiokande could measure the average core density with an uncertainty around -14%/+40% at nominal resolution, improving to about -8%/+10% with better resolution, after 6500 days.