(A gravitational wave) is a compression wave traveling as a compression wave through a medium.

A compression wave travelling through a medium will move a test particle alternately away and towards the source, in the direction of travel.

However, gravitational waves move test particles in a plane

*perpendicular* to the direction of travel, as illustrated by the animations here:

http://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passingI conclude that gravitational waves are not a compression wave.

This medium in other words is a physical presence with physical characteristics that influence such propagation

I conclude that gravitational waves do not require spacetime to be a physical medium that supports compression waves.

(A gravitational wave) is a compression wave traveling as a compression wave through a medium .... EM waves are as far as I understand not dependent on a medium. Entirely different methods of propagation.

I agree that they have different methods of propagation - after all, gravity seems to be attractive only, while electromagnetism attracts and repels. Their polarization angles seem to be somewhat different (see animations referenced above).

Not being dependent on a medium, both are able to propagate through a vacuum.

Sometimes when we think of waves, we think of ocean waves or sound waves, which require a medium to propagate.

However, the beauty of the quantum interpretation is that we can also imagine a quantum wave as a particle; like a bullet, it can pass through the vacuum of space, without dependence on a medium.

Gravity being the distortion of this spacetime itself is not a compression wave. It is the influence of Mass on the shape of all of spacetime, from the coordinates of the mass to infinity. It is, rather than it propagates.

I agree that if a mass were present from eternity, then the shape of all spacetime will reflect the presence of this mass, from the coordinates of the mass to infinity. It just "is".

...Just as in electromagnetism, if an electric charge were present from eternity, then the electromagnetic field of all spacetime will reflect the presence of this electric charge, from the coordinates of the charge to infinity. It just "is".

If, however, the electric charge is not present from all eternity, but is modified at some point in history (by colliding an electron and a proton, for example), then an electromagnetic influence will spread out throughout spacetime as a ripple on the electric field. This disturbance (an electromagnetic wave) travels at the speed of light.

Similarly, if the mass is not present from all eternity, but is modified at some point in history (by colliding two black holes, for example), then the gravitational influence will spread out throughout space as a ripple on the fabric of spacetime. This disturbance (gravitational wave) travels at the speed of light (according to Einstein).

Although they are ripples on different underlying fields, with different polarization angles, gravitational waves are no more difficult to imagine than radio waves.