It seems to me that a major earthquake could potentially release a lot of methane if fissures opened up along coasts where a lot had been sequestered. But short of that, as you point out, things are likely to unfold more slowly than this apparent event suggests. And yes, even Shakhova' estimates look tame compared to this amount and rate. But then, though many assume she was pushing the envelope a bit, it is possible that she was being conservative in that number, too, or just underestimating.
Much as I favour submarine clathates as a driver of abrupt climate change (not necessarily catastrophic by earth system standards in most cases), I don't think you can get to where you need to be to fit the paper without quite a bit of explanation.
When you say a major earthquake could theoretically release a lot of methane - perhaps - but you need to consider the figures. The amounts required in total within those few years are (for example) a very significant portion of the total amount in the ESAS (or virtually all of it) and only a fraction of the methane present exists as pressurised free gas. The probability of an earthquake releasing amounts on the scale required seems to be essentially nil.
I think to get clathrates involved on a short timescale, deep water clathrates can be ruled out unless one can propose an extremely rapid way to get the necessary heat to destabilise them.
Even with shallow water clathrates, I can't see how they could act in such a short timescale. So far in the ESS we've seen that the permafrost is thawing on the seafloor and that the seafloor is warming. Localised emissions of methane appear to have grown and be growing and I personally think Shakhova is on to something with respect to the risks of a large release. The more I think about it though, the more I think it seems impossible to do it as fast as this paper requires.
To start to release the methane from the clathrates and sea floor, one must first destabilise the containment and get heat down to them. That much appears to have happened today (some of it over thousands of years, some of it as a result of current climate change - earlier sea ice retreat, sea ice retreat where it previously didn't, warmer water run off from land, etc). The existence of massive craters in various places on the seabed and a certain amount of thought make it seem plausible to me that abrupt releases are possible. I don't think the argument about it taking a very long time to move heat down into the sediments automatically holds once the process properly starts.
However:
1. True methane catastrophes seem exceptionally rare (and possibly require the involvement of deep water clathrates, which cannot proceed abruptly in human terms), limited now to one promising example (end Permian). Methane does however seem significant - generally moving with temperature and carbon dioxide paleoclimatically (does anyone have good information on what mechanisms are thought to cause this, besides shallow clathrates?).
2. Even the very worst case scenarios one can construct around shallow clathrates cannot act fast enough. If Shakhova were proved right that an abrupt release of 50GT from ESAS on a decadal timescale is possible - the worst case concern would be that the warming implied by that would lead to the onset of a positive feedback causing subsequent larger events (the best case is a more limited pulse of above trend warming - still very serious in human terms). That warming would still take
time. Therefore even if there was a very abrupt period during such a positive feedback - the time it takes to build up should still be clearly present in the record - which doesn't seem to be the case here.
I just can't see any way to move that amount of methane from clathrates in that timescale, at least not using any mechanism that seems logical in the context of Arctic climate change and the ESAS.
You also still need to move the earth system to a point whereby the clathrates can destabilise in a big way. For the end Permian that seems to be tens of thousands of years of eruption from the Siberian traps - in the modern era - it's the injection of carbon dioxide by human activity - what would it be for the PETM?
What does that leave? Earthquakes ruled out, self reinforcing feedback ruled out - what else is there?
My biggest problem with this paper is that as far as I can follow it (a little too technical for me without spending a lot of time looking things up), it seems to suggest the change was global. That would make it - if true - something rather new - quite different from abrupt and major regional changes such as the Younger Dryas.
So for a methane clathrate based theory - is there any way to release such massive volumes in such a short timescale, without an obvious escalation previously?