[The Might]

I'm personally against the reasoning shown above by Gordis, when speaking of the Seven as Rings of Earth and the Nine as Rings of Aether.

It was only a coincidence that Dwarves were naturally inclined to love gold and gems that the Rings increased this lust.

As for the Nine, they worked very much like the Seven, only difference is Men wanted rather power then treasures.

So in the end you could rather say the Nine = the Seven, there was not any big difference between them really, only the consequence was due to the different bearers. So attributing them to different elements makes little sense.

As for the Three, that is a different story, as after all they were not touched by Sauron. Here you really can see a certain connection to the elements, especially in the case of Gandalf, of whom it is said that his innate power of controlling flames and fire was enhanced by the ring.

Why is there no ring of earth?
Well, I believe because the Rings were not intended to symbolise the elements in the first place.
Usually, the classical elements are thought of as being equal, but in Tolkien's works this equality is clearly broken by Vilya being stronger than the other two.

My conclusion?
It was never intended to have a Ring of Earth and the other three elements were chosen so as to fit with their bearers.