Gravitational anomoly of a burried magnetite sphere 1. [5 marks] Geophysicists d

Question

Gravitational anomoly of a burried magnetite sphere 1. [5 marks] Geophysicists discover a deposit of magnetite (density of 5000 kg/m°) located in the Earth’s crust (density 2670 kg/m°). Using a gravimeter, they measure the gravitational anomalous cross-section of the deposit (shown to the right) and determines that the profile is consistent with a sphere with a radius to depth ratio of F = 0.5. Determine the depth and the Gravity variation (mgal) . : : : * E E radius of the deposit. 400 100 200 300 distance from vertical, x (m)

Explanation / Answer

Geophysicists discover a deposit of magnetite (density of 5000 kg/m3) located in the Earth’s crust (density 2670 kg/m3)

here,

Gmax value is 1.2 mgal at x=0

Then using half widht method, for spherical body,

Half of gmax is 0.6 and distance at this value is about 120 m.

Z=0.652* x1/2.

Z= 78.24 m

Now density variation is (5000-2670) = 2330 kg/m3

Formulae to find radius is

Gmax= ((4/3)r3* density* gravitational constant)/z2

Here, Using this Formula, You can Easily Calculate Radius of the deposit.

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