I don't know of any measurements being taken udnerground, but I would haev to say "yes," because we do know that the field strength decreases as one moves away from the Earth (by the universe cube law).
Interesting.. how could you calculate the field strength near the Earth's core?
The nivese cube law wul cotninue to be aplicable at the equator, but close to Earth and far from the equator the inverse square is the rule.
Maybe I should explain that a bit further;
When you're close to the Earth and far from the equator, only one ole is imortant, and the influence from the other pole is negligable (not zero, but small enough). When you're far from the Earth, the difference in distance between one pole and the other is less significant. When dealing with only one pole, the power drops off by the inverse square of the distance, and when dealing with both, it's the inverse cube. Of course, in reality, the accurate prediction would be one that incorperates both formuli to find a value somewhere in between, depending on how close to the core you are and how far from the equator.