The toilet venting air can create a toilet geyser when large amounts of air are being pushed into a lower toilet when an upper toilet is flushed. This is usually trapped air in the pipes caused by a clogged vent pipe. The vent is the pipe that runs from your kitchen and bathroom drains and extends through the roof. This lets air flow behind draining water so it does not become air trapped.
Start your bathroom trouble-shooting from the roof. Take a flashlight and check if you can see all the way down the vent. Look for debris or any obstructions. Something as thin as a layer of rust off the wall of the vent pipe can restrict air flow and cause problems.
Then have someone flush the toilet and listen to the vent. The sound should be rushing water all the way down. If you hear any gurgling it is an indication that the vent or drain is clogged.
From the roof, run a snake of 1/2-inch diameter in the vent. Rent a snake long enough to go from the roof to the basement plus 20 feet, a 50-footer should do the job. If possible, get a snake with interchangeable cutters that connect to the end of the cable. Start with the smallest cutter-head first, probably an arrowhead at one-inch wide. After running the cable with the arrowhead cutter, change it to a two-inch cutter. Be careful not to run it in too fast and chance getting it jammed in the drain. This should insure that the drain and vent are clear. Test-flush the toilet and listen for the gurgling again.
If there is no gurgling, then there could be a restriction in the drain close to the vent. There should be a clean-out plug at the base of the vent. If not, pull the toilet and run the snake down that hole. Now is the time to run the snake from here out to the city sewer. Repeat the same procedure as with snaking the vent. Use the snake with the small cutter first and then with a larger one. Be careful, the overzealous guy uses a large cutter first and gets it jammed in the main drain. Don’t let this happen to you.
If after cleaning the vent and the main line you are still getting air in the basement toilet the problem could be in the plumbing design.
There is a chance the basement toilet was connected too close to the base of the vent. By code the toilet should be connected 30 to 40-inches away from the base of the vent. If it is connected too close to the vent, flushing the upstairs toilet can cause the burping.
You may have to break some floor to move the connection farther down the drain line.