Fermi Gravity (FPOTW)

Here is a Fermi problem with a (perhaps) surprising answer, and several methods of attack.
The question is simply stated thus:

Where is gravitational acceleration greater, on the Earths surface, or 100 km underground?

There is a very easy way to solve this, a Fermi way that will answer the question. There is also a back of the envelope method, which will give a numerical answer.

For a hint I give you the following picture:

Enjoy!