We present GlobSed, a new global 5‐arc‐minute total sediment thickness grid for the world's oceans and marginal seas. GlobSed covers a larger area than previously published global grids and incorporates updates for the NE Atlantic, Arctic, Southern Ocean, and Mediterranean regions, which results in a 29.7% increase in estimated total oceanic sediment volume. We use this new global grid and a revised global oceanic lithospheric age grid to assess the relationship between the total sediment thickness and age of the underlying oceanic lithosphere and its latitude. An analytical approximation model is used to mathematically describe sedimentation trends in major oceanic basins and to allow paleobathymetric reconstructions at any given geological time. This study provides a much‐needed update of the sediment thickness distribution of the world oceans and delivers a model for sedimentation rates on oceanic crust through time that agrees well with selected drill data used for comparison.

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Significance The results show that dynamic variations in the Earth’s interior could have played a key role in the Eocene–Oligocene climatic transition (∼33.9 Ma) and the inception of glaciations. Pulsations in the Iceland mantle plume modified the bathymetry of the Greenland–Scotland Ridge, which affected deep water formation in the North Atlantic. Our model simulations show that the changes in the Atlantic–Arctic oceanic gateways cooled the Southern Hemisphere, and later the Northern Hemisphere, paving the way for the growth of major land-based ice sheets. This supplements the current view that decreasing atmospheric CO 2 concentrations and/or changes to the Southern Ocean gateways or the Tethys Seaway dominated climate changes and the inception of glaciations at the time.

The dominant pacing of glacial‐interglacial cycles in deep‐ocean δ18O records changed substantially during the Mid‐Pleistocene Transition. The precessional cycle (∼23 ky) is absent during the Early Pleistocene, which we show can be explained by cancellation of the hemispherically antiphased precessional cycle in the Early Pleistocene interior ocean. Such cancellation develops due to mixing of North Atlantic and Southern Ocean δ18O signals at depth, and shows characteristic spatial patterns. We explore the cancellation potential for different North Atlantic and Southern Ocean deep‐water source δ18O values using a tracer transport ocean model. Cancellation of precession occurs for all signal strengths and is widespread for a signal strength typical for the Early Pleistocene. Early Pleistocene precessional power is therefore likely incompletely archived in deep‐sea δ18O records, concealing the true periodicity of the glacial cycles in the two hemispheres.