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Accuracy needed in a mine-shaft gravimeter for deep-Earth determinations?
Assume that a 1-kilometre-deep mine shaft is available in which to mount a device to measure gravity. Assume the device can record the gravity measurement dynamically, by travelling up and down the shaft, or that the device can make measurements statically, with sensors extending down the depth of the shaft. Assume that the density of layers of the Earth increases downwards according to PREM, the preliminary reference earth model. In this model, the Core/Mantle boundary has a sharp discontinuity at a depth of 2885 km. In theory, the variation in gravimeter results for the 1-km stretch should be analyzable to yield the variation in density of the different layers. What accuracy would be needed to detect a change in the Core/Mantle boundary to 2895 km? (ZBL#155). More detail at attached file ZBL155X.pdf.
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This expert response shows that the mine-shaft gravimeter concept would be ineffective, because in a spherically symmetrical Earth, calculations of gravitational forces always behave as if all the Earth's mass was concentrated at its centre. This is independent of density profiles within the Earth.
An explanation is given of more advanced considerations using spherical harmonics, when instruments orbiting the Earth (as in the GRACE mission) are able to give information from the oblateness (departure from spherical symmetry) of the real Earth (or other bodies in space).
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