This is just speculation, but I'm also guessing that we don't have a whole lot of data about what happens to the geology of a deepwater oil reservoir when a nuclear bomb is detonated in the general vicinity. I'd hate to be the president who authorized a nuclear strike against an oil well and discover that the blast created numerous fractures in the seafloor that allowed even more oil and gas to escape. It seems to me that one might want to hold such a tactic in reserve as a last resort.
I am a petroleum geologist and worked in the industry, I am no explosives expert but the reference you mention are real. The reservoir is quite deep compared to where the bomb would be placed. The rock strata, largely semi consolidated shale and sand, at least at shallower depths is quite plastic and would quickly heal itself any fractures. The idea is to hydraulically shock the existing borehole pinching it off. The upper hundreds of feet of strata are mostly mud. The blast would be a hydraulic pile driver to the casing flattening it out like a soda straw pinched between your fingers.
I know I am not explaining the concept well and that I am missing much information as that is not an area I am familiar with and BP and the government have created a "cloud of confusion" on purpose so that the public I am sure do not know all of the facts.
There is no likelihood that the there would be a global "hydrate" explosion any more than the particle accelerator in Switzerland will create a black hole and suck the earth into it. There is fantasy and reality and the unknown but the Twilight Zone, well, that was a television show.
Whenever nuclear anything comes up people get all weird acting reacting on emotion and TV junk science rather than fact.
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