S U M M A R YWide-angle shear wave arrivals, converted from compressional to shear waves at crustal interfaces, enable crustal Vp/Vs ratios to be determined which provide valuable constraint on geological interpretations. Analysis of the converted shear wave phases represents the next logical step in characterizing the crustal structure and composition following multichannel seismic structural imaging and tomographic inversion of the wide-angle compressional wave phases. In this offshore study across two passive margins extending from stretched continental to fully oceanic crust, the high-data density (2-10 km ocean bottom seismometer, OBS, spacing) and a consistent, efficient conversion interface produced shear wave data sets suitable for traveltime inversion. The shear waves were recorded by three orthogonal geophones in each OBS. Arrival phases, visible to 180 km offset, were identified using their arrival times, moveout velocities and particle motions. Across the North Atlantic volcanic rifted continental margins studied, breakup was accompanied by the eruption of large volumes of basalts of the North Atlantic Igneous Province. The interface between post-volcanic sediments and the top of the basalts provides the dominant conversion boundary across the oceanic crust and the continent-ocean transition. However, the shear wave data quality was significantly diminished at the continental ends of the profiles where the thick basalt flows and hence this conversion interface feathers out and crustal attenuation increases. Initial modelling of the converted shear wave phases was carried out using a layer-based approach with arrivals converted on the way up used to constrain the Vp/Vs ratio of the post-volcanic sedimentary sequence beneath each OBS. To produce a model with continuous crustal S-wave velocities, the compressional wave velocities beneath the sediment-top basalt interface were transformed into starting shear wave velocities using a constant value of Vp/Vs and the inversion carried out by specifying the appropriate ray path. Once the data set had been fully interpreted, correction of the traveltimes to effective symmetric ray paths enabled us to apply a regularized grid inversion. Such inversions are less subjective than the layer-based approach and yield more robust minimum structure results with quantifiable errors, except in the vicinity of a known subbasalt low-velocity zone encountered on the Faroes margin. Monte Carlo analyses were performed for this approach; the average model from multiple inversions using randomized starting models and traveltimes shows the structure required by the traveltimes and the model standard deviation gives an estimate of uncertainty. Model and inversion parametrizations were fully tested and optimum parameters chosen for compressional and shear wave inversions. This allows, after appropriate model smoothing, an estimate to be made of the spatial variation of the Vp/Vs ratio within the crust. There are marked gradients in Vp, Vs and Vp/Vs ratio across the continent-ocean ...