Apart from numerous straight (or nearly straight) grooves seen on the Atlantic Ocean floor, there are interesting "foot" marks south of Tenerife: 27 deg. 10' N, 16 deg. 30' W
In a north-south direction.

Can anybody suggest the cause or speculate on this?

Can you provide a reference? I read an article in the NY Times today about how some people are misinterpreting what look like grid marks in some data that Google now has available on the web - these "marks" are actually vestiges of incomplete data - could that be what you're referring to?

See:
Google Explains Watery Mystery of 'Atlantis' - Bits Blog - NYTimes.com

It also could just be shapes looking oddly familiar to footprints but being something else entirely.. how big are these.. they could be remnants of fish nests where they push away all the big rocks, debries away from where they are laying their eggs... Also I did see a thing on Google earth showing an underwater shape resembling a scarab (egyptian beetle) and people were trying to reference it to atlantis and they are inaccurate. So it could really be just anything (plus if anyone believes in atlantis.. there is also writings from before plato (whom everyone says knew where atlantis was) that pointedly state that atlantis could be in the atlantic ocean due to the misspelling of atlantis, atlantiens, etc... )