Hmmm... Randall says "The explosion at the bottom of the Mariana Trench will create a quickly-expanding spherical cavity of hot steam."
If the explosion is at the bottom of the trench (presumably the ocean floor), in order for it to create a spherical cavity, one of two things would have to happen:
1) The explosion would leave the ocean floor undisturbed and produce a spherical cavity in the water above with a center 580 meters above the ocean floor.
2) The explosion would vaporize a portion of the ocean floor, leaving a crater equal to or less than half of the sphere.
If #1 would happen, well then the answer doesn't change, but it seems to me that would be a really weird way for a sphere to form from an explosion -- like blowing a balloon underwater, no? I imagine that the sphere would grow from the center. But I readily admit that I have very little knowledge of physics, so I am also ready to admit the limits of my imagination. But at the least I would appreciate seeing some text addressing that in the answer, and also a bit of drawing like the near-surface explosion.
If #2 would happen, that really changes the answer to the question, and then he would need to estimate how big of a crater in the ocean floor the explosion would produce, the strength of the resulting seismic shock (if any), and the effects of one or both.
What seems the most likely to me is that some of the ocean floor beneath the explosion would be vaporized, and some of the water above would be vaporized, and it might look kind of like the picture in this article: http://en.wikipedia.org/wiki/Trinity_site
. The visible explosion there is somewhat spherical, but not totally, because part of it is below the surface of the ground. It seems most likely to me that the underwater explosion would also create a crater in the ocean floor because the explosion in that article was a surface (actually 30 meters above the surface, but close enough to be called a surface detonation, right?) detonation equal to only 20 kilotons of TNT (far less than Tsar Bomba's 50 megaton yield), and it "left a crater of radioactive glass in the desert 10 feet (3 m) deep and 1,100 feet (330 m) wide." I am guessing that could only result from the heat from the blast that melted the sand below it. Would an explosion from Tsar Bomba not do the same to the ocean floor?
So, if #1 would actually happen, at the least, he should explain why none of the ocean floor would be vaporized or even shocked, even though it is next to the explosion. It doesn't seem likely that such a blast, located on the ocean floor, would not at least make the ocean floor shake, causing a seismic shock which could possibly cause a tsunami. Wikipedia says that the actual Tsar Bomba produced a seismic body wave with a magnitude of about 5 to 5.25 on the Richter scale, and that the energy yield was around 8.1 on the Richter scale but, since the bomb was detonated in air rather than underground, most of the energy was not converted to seismic waves (http://en.wikipedia.org/wiki/Tsar_Bomba