I see plenty of Quarries above ground but never under the sea. It stands to reason that if the land above sea level has valuable resources then the land beneath sea level should have the same in equal abundance. There must be underwater rock full of metals such as Iron etc that could be mined/quarried and sold onto the world market. Has nobody ever thought of reclaiming land from the sea and quarrying for resources? It seems to me to be an un-thought of idea. Companies are willing to erect massive oil rigs to drill beneath the sea and obtain oil but why not go out to sea and obtain anything else? Off the coast of Scotland there could be an abundance of natural resources, all it would need is a study to find the locations and then some land reclamation. Following the resources being mined the reclaimed area of land could then be utilised for something else.
What about tunnels from land reaching out under the sea? Think of how the channel tunnel was mined. A few million tonnes of material would have been removed boring that out. If only it were mineral rich...
Undersea mining would be significantly more expensive than mining on land. As long as the costs retrieving the materials from land, even if they have to be transported long distances, is less expensive than mining from the sea any undersea minerals will remain unused.
As for reclaiming land for the purposes of doing things one would normally do on land, isn't that what the Dutch did several years ago?
And Japan is still doing it. People often forget that their country is very hilly except for the coastal areas, so very little natural space is available to locate industry.
It occurs to me that the words "cost benefit" never enter your mind when you think up something like this. However, we already do a lot of undersea resource claiming, just not in the way you're thinking of. http://www.waterencyclopedia.com/Mi-Oc/Mineral-Resources-from-the-Ocean.html
There are several reasons why no/very few mineral deposits are mined from the ocean. The high cost is of course the most important. But it's also important to consider the geological environments in which ore deposits form. Many are associated with igneous intrusions associated with volcanic mountain chains. However, nearly all shallow ocean shelves are underlain by sedimentary rocks that accumulated in the basins formed by rifting of the continents. I suppose there is the possibility of finding Sedex (sedimentary exhalative) lead-zinc ore deposits associated with the rifting or VMS (volcanogenic massive sulfides), but they would likely be buried under several kilometers of overlying sediment. In short, the continental shelves simply don't have particularly favorable environments for forming commercial ore deposits. The one exception is deep-sea manganese nodules, and they have actually attracted a fair amount of attention from companies. They are somewhat poor for manganese (compared to terrestrial ore deposits) but contain other metals like cobalt. Plus, there are huge areas of the deep ocean containing nodules. I've heard ideas of creating giant suction hoses to suck up nodules from the ocean floor 4-5 km deep. Of course, this concept is tremendously expensive and there are legal and environmental issues (no one owns the deep ocean).
It seems to me that whenever I see "mining" being done on TV it involves explosives (something you certainly don't want to detonate in large quantities underwater) and lots of heavy machinery (not practical underwater.)
Mines don't so much use a single big charge but a lot of more moderate charges placed in an array of holes in the rock. The goal is to expend the energy breaking up the rock, not producing an impressive aerial shock wave. Any equipment used to collect the resulting material would have to be powered by engines on the barge or surface ship they would be tethered to. A possible form for the equipment would be a clam shell suspended with and operated by steel cables. Since the operator probably wouldn't be able to see the clam shell bite into the material the cab would probably be equipped with an LCD screen showing the GPS based data on the current clam shell position and the depth and position of prior "bites".
There are salt and mineral mines all over the US Great Lakes that go out and under the lakes. Many companies now have their data and paper documents stored in those salt mines (and, supposedly, a lot of government stuff as well....)
Actually, quite a few coal mines extend out under the sea. I imagine that works for other mineral assetts as well.