It’s not the city or groundwater themselves causing New Orleans to sink. It’s all of the man-made flood controls and levees. Before all of those were built, every time the river would flood these areas, sediment would be deposited and the ground would not sink.
But with all these flood controls, the river just shoots the sediment out into the gulf without leaving it to rebuild the delta. The Mississippi delta should really begin basically at Baton Rouge. In the past the Mississippi flowed over this entire area building the land in southern Louisiana. It should really be allowed to flow and flood the Atchafalaya today, but the US army corps of engineers won’t allow it.
That’s essentially it. You can have flood control or you can have ground level stability, but you cannot have both. The soils that were replenishing the delta are being dumped somewhere off the continental shelf into the depths of the gulf. The velocity of the water, due to the channelization and levee systems, exiting the mouth of the Mississippi means that the soils which formerly were deposited in the delta in flooding cycles, are now lost. And that’s a lot of soil. So you get subsidence.