Analyzing the formation mechanism of hotspot swells enhances our understanding of intraplate volcanism and the underlying geodynamical processes. The two main hypotheses for the origin of the archetypal Hawaiian swell are thermal lithospheric thinning, and dynamic support by an ascending plume. Any successful model would have to be able to simultaneously explain the swell topography and the corresponding geoid anomaly. In simple models of isostatic compensation, the geoid-to-topography ratio (GTR) is linearly related to the depth of the compensating mass; therefore it is often considered a fundamental parameter to assess swell support mechanisms. Previous estimates for the geoid-to-topography ratio (GTR) of the Hawaiian swell however are biased towards low values by incomplete removal of the effects of volcanic loading and lithospheric flexure. In order to resolve these issues, we here apply a continuous wavelet transform, which allows resolution of lateral variations of the GTR at various spatial scales. In a series of synthetic tests, the robustness of this approach and its power to identify the origin of hotspot swells are established. With 8 m/km on the youngest part of the chain, the recovered GTR agrees well with the predictions for dynamic support, therefore ruling out thermal rejuvenation as an important mechanism. We also find that the depth of the compensating mass decays by 20 km over a distance of 500 km from Hawaii to Kauai, and identify sublithospheric erosion by small-scale convection in the ponded plume material as a viable mechanism to support this decay.