An outstanding geophysical issue concerns the nature, and dynamical role in the mantle general circulation, of the seismically fast body wave anomalies that have been tomographically imaged beneath continents. In this paper, we investigate the possibilities that these seismologically imaged ''roots'' represent either neutrally buoyant, chemically distinct material or cold, negatively buoyant, upper mantle and transition zone downwelling flow. In assessing these alternatives, we first construct disaggregated models of the seismic heterogeneity in which a component associated with subcontinental fast anomalies is isolated from the global tomographic models either by employing the ''continent function'' or a new ''craton function''. We find that the use of the new craton function leads to geophysically more realistic chemical models of subcontinental heterogeneity. The thermal and chemical density fields reconstructed from the disaggregated tomographic models are employed to compute the long-wavelength nonhydrostatic geoid, the free-air gravity field and the upper mantle radial flow pattern within the framework of an anelastically compressible internal loading theory. We find that the radial component of flow velocity provides useful insight into the dynamical implications of the alternative density models. However, since this field is not directly observable, we consider the geoid and free-air gravity anomaly as possible diagnostic discriminants and show that the free-air gravity anomaly provides a sensitive discriminant of the gravitational differences that characterize the chemical and thermal models, whereas the geoid does not. By focusing on the free-air gravity low over the Hudson Bay region of Canada, we are able to rule out the hypothesis that positively or neutrally buoyant subcontinental material that is chemically distinct from the surrounding mantle exists below the Laurentian craton. However, when the fast body wave anomaly is mapped into a high-density downwelling flow beneath this region, we are able to fully explain the fraction of the anomalous free-air gravity low which is inexplicable as a contribution associated with the existing degree of glacial isostatic disequilibrium due to the disintegration of the Laurentide ice sheet. This conclusion concerning the North American craton may be equally valid for other continental nuclei. We explore the general tectonophysical implications of this dynamical model. ¿ American Geophysical Union 1996