92 miles south of Vermillion bay puts it in relatively shallow water so this was a standing platform. Now I want to clarify something that many people use the improper terminology on. This was not a rig, it was a platform, a production platform. A rig is what is used for drilling the well and setting the casings and wellhead. That is the extent of what a rig does in normal shallow water operations. When it is done, the well is still full of drilling mud which keeps the well string balanced so really, the well head is not required. At the end of it all, the BOP gets removed from the wellhead and it gets capped off so there are three to four safeties, there is concrete plugging in the well string, there is a subsea safety valve which gets opened and closed with a tool at the end of a wire line that gets sent down hole, there is the drilling mud, and then there is the well head. The rig then pulls off site. The rigs for shallow water are generally "Jack Up Rigs" which have legs to the bottom which they raise the rig above the surface typically to the planned wellhead height which will be above the storm wave height, so depending on the depth of the water we're talking like 10' on the near shores like the Rabbit field just outside of Fourchon to 40 or 50' when you get out to say East Cameron 254 where the water may be 120' (which is still considered shallow water). From the looks of the picture, they were around the Vermillion Block 30 area in about 15' of water.
This is a typical jackup rig that works shallow water (usually around 200+' is where you start using floating rigs)
After the rig leaves, they put a permanent steel structure in known as a platform. There are two basic types of platforms, you main production platform and satellite platforms. Most lease blocks (oil/gas companies bid on "blocks" charted square segments of offshore areas where they are allowed to exploit the resource) have multiple wells spread out across them, some are very crowded as is the "Rabbit Field" I mentioned earlier. The satellite platforms are small structures that surround the well casing and have a platform on the top which surrounds the wellhead for the workers to be able to go out, inspect and service the wellhead.
They get tied by pipe, Over head if they are very nearby satellites, and subsurface if they are further away (depending on the bock, they can be several miles or more across) to Production Platforms.
The production platforms collect all the product from all the wells in the field and typically will contain several wells themselves. The production platforms house the equipment for whatever initial processing the company wants to do with the product from that field before putting it in the pipeline that takes it into shore. It also contains the living quarters for everybody working in that field. Typical hitches are 28 days on and 14 or 28 days off.
On the deep water projects, thousands of feet of water, it becomes more typical to combine the drilling rig into the production platform.
Just remember, Rigs drill, Platforms produce.
Here's a pretty good describer of the difference in platforms for various depths and areas: