Scanning through Google images; I spotted a suspicious pair of photos. Possibly they were designed with different aspect ratios deliberately - a widescreen one, and something more like 4:3:--
A
B
Look at the 'mushroom cloud' and/or spray and distance detail of ships. Both pictures are identical apart from a few details.
Now look at the trees and local detail.
A has much the same size 'mushroom cloud' image as B, but the trees are much larger. It must have been photographed from a much closer position, with a wider angle lens. What is the chance of the two photos being exposed at the exact same time? And how come the remote cloud detail is the same in both? It would need close examination to be sure, but certainly the prima facie case is that the far background was superimposed. This would explain why it's so flat, and why there's no trace of interruption to the water surface or reflection of the huge cloud.
Note also that a typical US 1940s battleship was about 600 feet long. (Google 1940s battleships if you don't believe me!) About 5 of them would fit end-to-end into the upward bit of water. Making it about 3000 feet across - about half a mile - and the 'mushroom' something like 4 or 5 miles across. One question here is: how could a point source explosion make a column of water of that size all go vertically upwards? It should move out near the edge. It must have been a relatively small explosion designed to go up, I'd guess in shallow water, so the force of the explosives would be directed up. Then the ships added, and the faked horizon effect got by adding photos of an atoll.
And note that an underwater location is ideal for hiding what's going on! (Just as darkness is another good cover)!