In reply to purplemonkeyelephant:
> I'm not sure, but I'd guess older icebergs in cold climates probably get eaten away by seawater until their centre of gravity is almost in line with the water level.
An iceberg is probably about 90% as dense as cold sea water, hence why 90% of it is generally below the surface. (Because sea water adding up to 90% of the volume of the iceberg weighs the same.)
So for a uniform shape, you'd expect the centre of gravity of the thing to remain at the same level relative to the water level as it melts. A big rectangular slab might sink as it melts from below, whereas a sphere or a cylinder would tend to roll over. With an irregular shape I guess it'll be a combination of the two. And I guess there will be times as the shape changes that it becomes very unstable causing it to roll quite suddenly, for the taller and more pointy ones particularly.
Have you ever seen the pub 'game' where you try to balance a coin on a lemon floating in a pint pot of water? (It's sometimes offered as a kind of competition to encourage people to drop a quid in a charity box: if the lemon rolls over and your coin falls into the water you've lost it, if it doesn't you win the pot.) Like an iceberg the lemon is only just less dense than the water so the centre of gravity is well below the surface, but the lemon *always* rolls over.