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During the GWADASEIS cruise (Lesser Antilles volcanic arc, February--March 2009) a very high resolution (VHR) seismic-reflection survey was performed in order to constrain Late Quaternary to Present faulting. The profiles we obtained evidence frequent "ponding" of reworked sediments in the deepest areas, similar to the deposition of Mediterranean "homogenites". These bodies are acoustically transparent (few ms t.w.t. thick) and are often deposited on the hanging walls of dominantly normal faults, at the base of scarps. Their thickness appears sufficient to compensate (i.e. bury) co-seismic scarps between successive earthquakes, resulting in a flat and horizontal sea floor through time. In a selected area (offshore Montserrat and Nevis islands), piston coring (4 to 7m long) was dedicated to a sedimentological analysis of the most recent of these particular layers. It corresponds to non-stratified homogenous calcareous silty sand (reworked calcareous plankton and minor volcanoclastics). This layer can be up to 2m thick, and overlies finegrained hemipelagites. The upper centimeters of the latter represent the normal RedOx water/sediment interface. 210Pb and 137Cs activities lack in the massive sands, while a normal profile of unsupported 210Pb decrease is observed in the hemipelagite below, together with a 137Cs peak corresponding to the Atmospheric Nuclear Experiments (1962). The RedOx level was thus capped by a recent instantaneous major sedimentary event considered as post-1970 AD; candidate seismic events to explain this sedimentary deposits are either the 16 March 1985 earthquake or the 8 October 1974 one (Mw =6.3 and Mw =7.4, respectively). This leads to consider that the syntectonic sedimentation in this area is not continuous but results from accumulation of thick homogenites deposited after the earthquakes (as observed in the following weeks after Haiti January 2010 event, McHugh et al., 2011). The existence of such deposits suggests that, in the area of study, vertical throw likely results from cumulated effects of separated earthquakes rather than from aseismic creep. Examination of VHR profiles shows that all major co-seismic offsets are recorded in the fault growth sequence and that co-seismic offsets can be precisely estimated. By using a sedimentation rate deduced from 210Pb decrease curve (0.5 mm yr -1) and taking into account minor reworking events detected in cores, we show that the Redonda system may have been responsible for five >M6 events during the last 34 000 yr. The approach presented in this work differs from fault activity analyses using displaced sets of isochronous surfaces and postulating co-seismic offsets. Combining VHR seismic imagery and coring we can decipher co-seismic vs. slow continuous displacement, and thus actually estimate the amplitude and the time distribution of major co-seismic offsets. [ABSTRACT FROM AUTHOR]