Is a creature's Z-axis tracked while it burrows?

Question

When a creature uses the burrow movement mode, should its Z-axis position be tracked, much like it would be if it were using the fly movement mode?

Consider the Warden power Shake the Earth from the Earth Shaker Paragon Path described in Primal Power:

Close Burst 4
If the target is burrowing, you slide it 4 squares to the square nearest to it that is within your line of effect.

This seems to suggest that Z-axis is tracked and that a creature up to 4 squares deep underground would be slid directly upwards to the surface of the ground. If Z-axis is not tracked, what does the 4 squares of sliding imply?

See this closed question for prior discussion on the topic of burrowing.

Answer 1

Yes

All movement is tracked, even if it is activated by the burrow ability. Same goes for levitation and spring traps.

Answer 2

The Z-axis is tracked

So the Forced Movement would be handled the same as with horizontal Slides