Many times when geologists are talking about the arrangement of the various rock strata, they will say that the A Sand overlays the B Sand, when they really should say “overlies.”
A person can overlay a transparency with another transparency to add a layer of information to the picture. This was done very well in the ancient World Book Encyclopedia my husband had as a kid. You could start with the human skeleton, then add the overlay with the internal organs, then add the overlay with the muscles, then the overlay with the circulatory system, then finally the overlay of the skin. When we threw out that old, dusty encyclopedia, we kept that one volume. That’s something Wikipedia has not been able to duplicate – yet.
Ah, but I digress.
To overlay means to spread over or across, to lay something on top of something else. It denotes the action of placement.
To overlie means to rest upon or lie on top of something. It denotes passive location.
So if you are talking about a sand that is placidly resting on top of a shale, it is overlying the shale, not overlaying the shale.
The river that carried all that sand did the overlaying.
Another meaning for overlie is to kill by lying on top of, which is why you should never have your baby sleep in bed with you. That happened in King Solomon’s day, after which he wisely offered to cut the surviving baby in half so the two women who claimed it could share the remaining infant. Better safe than sorry, eh?