I had a quick read of the paper. Granted, the notation that the author uses is not clear and rather cumbersome.
I am not sure whether this helps, but if I were you, I would derive the gravity effect formula for a simple case (i.e. rectangular prism, semi-infinite slab, etc) and see how the results work out.
I do not have it at hand right now, but Telford et al., 1990 (Applied Geophysics) has a decent section on gravity methods. I would also take a look at Telford as I recall the notation is clearer.