Thermal convection is the motor of Earth dynamics and therefore is the link between plate motions, hotspots, seismic velocity variations in the mantle, and anomalies of the gravity field. Small scale mantle anomalies, such as plumes, do, however, generally escape detection by tomographic methods. It is attempted to approach the problem of detection in a somewhat statistical manner. Correlations are sought between spherical harmonic expansions of the 'fields' under study: the hotspot distribution, mantle velocity variations, gravity, heat flow. Using spherical harmonic representations of global fields implies integration and averaging over the whole globe. Thus, although relationships may remain masked in the space domain by a multitude of effects, tendencies may become visible in the spectra or in appropriate averages.