Maybe the New Madrid fault is starting to slip a little and you have your personal earthquake warning system.
http://hsv.com/genlintr/newmadrd/
On the other hand, you may be getting a vacuum on your sewer outlet or a problem with your sewer vents. There could also be a pressure difference in your house due to ventilation systems.
The period of cycling is probably related to the natural frequency of the slug of water moving back and forth in the bowl, possibly until it breaks the trap seal and then moves back by gravity.
Try opening a window in the basement and see if the surging stops. That will equalize the pressure between inside and the sewer vent that goes to the roof.
Then put in some water to fill the trap but not enough to start a siphon and see if that makes it go away.