From my father and his colleagues in the merchant navy I have heard stories of being on the open sea during an underwater earthquake (I never remember them being referred to as sea-quakes by these men before). The place to be, by all accounts, is as close to the epicentre as possible. The sensation experienced then is as if one is in a high speed elevator caught in a sequence of rapid ascents and descents, even though the surrounding water looks calm, not unnatural as in fact the entire body of viewable water on which you are sitting is undergoing the same process. A disconcerting experience, right enough, but pretty safe. Further away from the epicentre is far more scary if the event has been large enough and located in a place likely to produce tsunamis. But even then the drill out on the open sea is the same as in any situation where your craft has to negotiate turbulent waters and oncoming waves of larger proportion than the ship is designed to ride abeam. Depending on the vessel's nature and size this varies, but the principle of meeting high waves head-on applies in general.
The above article is still interesting, and though the author has done a good job collating details from incidents he assumes are related to the circumstances surrounding the Mary Celeste's experience, they actually describe other events. Large expanses of turbulent foaming water and doming of the sea's surface are features much more indicative of underwater volcanic activity than seismic shifts of the seabed. Similar incidents have been reported in fisheries around Iceland, Hawaii and elsewhere. A small vessel caught in one of these events is much more vulnerable than a large one today, but the Mary Celeste would be defined on the lower end of tonnage ranges by modern standards so definitely merits examination in the context of such an event being possible cause.
He has done a great job too listing off the specific instants of damage on board the Mary Celeste, though again he ascribes them to a common cause related to an earthquake's effect. Even at the time of the incident however it was recognised by mariners that it was way too presumptious to ascribe a single cause. Once the ship was abandoned - and for at least part of that time subject to gale force winds - then it would repeatedly have assumed a completely unrecommended attitude in the face of high waves. Without being steered a ship will naturally present its broadest surface to moving water. If you've ever been caught broadside by even moderate waves in a small vessel you'll know just what this can mean in relation to torque, pitch, yaw and roll. Basically it causes the natural verical axis of the ship to constantly shift and the oscillation will very rapidly, even in a relatively mild squall, shift to the extremes accommodated by the craft's design. Not a nice place to be at all and the damage to fittings, infrastructure and even the superstructure of the craft can be immense, depending on what's there to be broken and by what.
He is on surer grounds of speculation when he postulates that damage to the casks containing alcohol might have encouraged the crew to temporarily abandon ship. That would have been no laughing matter at the time, though the fact that the cargo and the ship survived and those who salvaged her noticed no immediate danger from such a source suggests that natural ventilation remedied this problem if it occurred. The suggestion that the crew "forgot" to thether their lifeboat to the Mary Celeste is his attempt to answer why what would have been short-term precautionary evasive action turned into tragedy. It would also have been standard practice to have at least some crew remain on board anyway in such a situation to work with diffusing the potential catastrophe. The ship was imperilled, not doomed, by this situation - one that would have been anticipated as a possibility in any turbulence and with a pretty standard drill to tackle it. In the absence of evidence that anyone undertook this drill it was this apparent anomaly which perplexed investigators attempting to pursue this theory of the lifeboat set adrift through error rather than design, and their dilemma remains unanswered today, whether one ascribes the turbulence that led to the cargo's instability to seaquakes, storms, spacemen or sea monsters.