Abstract The medium-wavelength geoid to depth anomalies ratio (GDR) at oceanic hotspot swells has been found to increase from ∼ −0.5 m/km to ∼ 5 m/km according to the age of the lithosphere they occur on. In order to interpret this trend, the geoid and topography anomalies associated with mantle convective plumes crossing a sublithospheric low viscosity zone (LVZ) have been derived from numerical models and a systematic investigation of the GDR dependence on the viscosity and depth extent of the LVZ, on the thickness and thermal structure of the lithosphere and on the Rayleigh number has been conducted. It is shown that, for viscosity drops across the base of the LVZ, greater than one order of magnitude, the GDR is strongly dependent on the depth of shallow interfaces such as the lithosphere/ athenosphere boundary and on the LVZ's thickness. Consequently, the empirical trend can be accounted for by the thickening of the lithosphere with age provided it occurs at the expense of a LVZ whose base is at a fixed depth (around 200 km). In such a frame, no significant variation with age of the LVZ's viscosity is required by the GDR data. Best fit with the empirical trend is found for a LVZ about 50 times less viscous than the underlying mantle. The mantle flow starts to fluctuate when the local Rayleigh number of the low-viscosity layer exceeds the Rayleigh number of the underlying mantle. The fluctuations are initiated in the upper boundary layer, in the diverging part of the plume, at a distance of a few hundreds of kilometers from the main ascending current. For viscosity contrasts in the range of 40–60, deduced from the present study, the conditions for the development of these small-scale instabilities are realized only where the lithosphere has not yet grown significantly downwards (ages < 50 Ma). These fluctuations are tentatively related to the small wavelength (∼ 200 km) geoid anomalies pattern observed in a young and hot area of the southwestern Pacific Ocean. This pattern could be the surface expression of a mantle plume rising just beneath the East Pacific Rise axis.