While the superficial expression of oceanic ridges is generally symmetric, their deeper roots may be asymmetric. Based on a surface wave tomographic three-dimensional model of the Earth's upper 300 km, we construct a global cross section parallel to the equator of the net rotation of the lithosphere, the so-called tectonic equator. Shear wave velocities indicate a difference between the western and eastern flanks of the three major oceanic rift basins (Pacific, Atlantic, and Indian ridges). In general, the western limbs have a faster velocity and thicker lithosphere relative to the eastern or northeastern one, whereas the upper asthenosphere is faster in the eastern limb than in the western limb. We interpret the difference between the two flanks as the combination of mantle depletion along the oceanic rifts and of the westward migration of the ridges and the lithosphere relative to the mantle. The low-velocity layer in the upper asthenosphere at the depth of 120–200 km is assumed to represent the decoupling between the lithosphere and the underlying mantle. It is also well defined by the distribution of radial anisotropy that reaches minimum values close to the rifts, but with an eastward offset. These results could be explained in the frame of the westward drift of the lithosphere relative to the underlying mantle.