The Canada Basin and the southern Alpha-Mendeleev ridge complex underlie a significant proportion of the Arctic Ocean, but the geology of this undrilled and mostly ice-covered frontier is poorly known. New information is encoded in seismic wide-angle reflections and refractions recorded with expendable sonobuoys between 2007 and 2011. Velocity–depth samples within the sedimentary succession are extracted from published analyses for 142 of these records obtained at irregularly spaced stations across an area of 1.9E + 06 km2. The samples are modelled at regional, subregional and station-specific scales using an exponential function of inverse velocity versus depth with regionally representative parameters determined through numerical regression. With this approach, smooth, non-oscillatory velocity–depth profiles can be generated for any desired location in the study area, even where the measurement density is low. Practical application is demonstrated with a map of sedimentary thickness, derived from seismic reflection horizons interpreted in the time domain and depth converted using the velocity–depth profiles for each seismic trace. A thickness of 12–13 km is present beneath both the upper Mackenzie fan and the middle slope off of Alaska, but the sedimentary prism thins more gradually outboard of the latter region. Mapping of the observed-to-predicted velocities reveals coherent geospatial trends associated with five subregions: the Mackenzie fan; the continental slopes beyond the Mackenzie fan; the abyssal plain; the southwestern Canada Basin; and, the Alpha-Mendeleev magnetic domain. Comparison of the subregional velocity–depth models with published borehole data, and interpretation of the station-specific best-fitting model parameters, suggests that sandstone is not a predominant lithology in any of the five subregions. However, the bulk sand-to-shale ratio likely increases towards the Mackenzie fan, and the model for this subregion compares favourably with borehole data for Miocene turbidites in the eastern Gulf of Mexico. The station-specific results also indicate that Quaternary sediments coarsen towards the Beaufort-Mackenzie and Banks Island margins in a manner that is consistent with the variable history of Laurentide Ice Sheet advance documented for these margins. Lithological factors do not fully account for the elevated velocity–depth trends that are associated with the southwestern Canada Basin and the Alpha-Mendeleev magnetic domain. Accelerated porosity reduction due to elevated palaeo-heat flow is inferred for these regions, which may be related to the underlying crustal types or possibly volcanic intrusion of the sedimentary succession. Beyond exploring the variation of an important physical property in the Arctic Ocean basin, this study provides comparative reference for global studies of seismic velocity, burial history, sedimentary compaction, seismic inversion and overpressure prediction, particularly in mudrock-dominated successions.