The mystery may now be solved. I have 6 dogs of my own and take care of my daughter's lab mix because she is TOO LAZY to do it. Two of my dogs are pugs. Herein lies the answer.
The two pugs are the only dogs I have ever seen do this in the yard. They go out and sit down and twirl and twirl and twirl. They get dizzy and so do I. Round and round they go. They are either scratching their behinds or chasing their curly tails or a combo of both. Henceforth they flatten the grass in a circle pattern as they go round and round therefore making a small crop circle. So the giant crop circles must have been made by gigantic pugs from long ago. Of course the giant pugs arrived here from outer space via spaceships or possibly were beamed down here! Mystery solved!
No, I have not had any margaritas or Sangria while arriving at this conclusion! Nor have I been smoking wacky tobaccky. I'm serious! Do any of your pugs perform this strange ritual?