What part of earths interior layers are in motion due to density differences?

Answer 1

The outer core is liquid and convects. The mantle also convects, although it is almost entirely solid and it is a matter of debate whether the entire mantle convects, or whether there are seperate layers each individually convecting.

Answer 2

we examine the caracteristics of seismic waves.seismic waves move at with different parameters in each of the layers.If these parameters are analysed graphically,the graphs show regions in which these waves propagate and in which they cannot,also they show where they can propagate faster and slower.thus we see that the graph will have the first region in which propagation is slow,the middle region there is speed tending to zero and the last region propagation is highest,thus we begin to question why this behavior occurs.The only explanation is that the waves are at each stage passimg through materials of different properties of matter e.g Density.Therefore that is how each different region of the graph represents a different layer of the earth.