Gravity Anomaly Over a Buried Sphere
It can be shown that the gravitational attraction of a spherical body of finite
size and mass m is identical to that of a point mass with the
same mass m. Therefore, the expression derived on the previous page for
the gravitational acceleration over a point mass
also represents the gravitational acceleration over a buried sphere.
For application with a spherical body, it is convenient to rewrite the mass, m,
in terms of the volume and the
density contrast of the sphere with the surrounding
earth using
where v is the volume of the sphere, Dr is
the density contrast of the
sphere with the surrounding rock, and R is the radius of the sphere. Thus, the
gravitational acceleration over a buried sphere can be written as
Although this expression appears to be more complex than that used to describe the gravitational
acceleration over a buried sphere, the complexity arises only because we've replaced m
with a term that has more elements. In form, this expression is still identical to the
gravitational acceleration over a buried point mass.
