The City of New Orleans Is in the Delta of a Great

The city of New Orleans is in the delta of a great river. During hurricane Katrina most of the city flooded but the area along the river, like the French Quarter, did not. Why didn't these areas flood?

A) These areas were natural levees of the river, and were higher in elevation than adjacent areas.
B) The water couldn't flow fast enough to cover these areas and was halted before it could flood these areas.
C) The army corps of engineers must have dredged the river and built these areas up before the city was built.
D) The river flowed away from these areas into other parts of the city when it broke the levees, and these areas just happened to be spared.