We present a detailed study of the advective contribution to the radial flow of heat in the mantle as deduced using a compressible internal loading theory in which the flow is assumed to be driven by the density heterogeneities implied by recent global seismic tomographic models. We calculate the radial flow velocity response of a viscous mantle and find that for reasonable values of the parameters which enter the theory, the heat flow correlation integral delivers the correct areaintegrated value of the heat flow observed at Earth's surface. This result is unlikely to be significantly affected by the low-degree truncation of the tomographic models we employ as in both the upper mantle and lower part of the lower mantle, heat is primarily transported by the degree 2 components of the flow. We propose that the radial profile of heat advection is a particularly useful diagnostic with which to "prospect" for the existence of thermal boundary layers in the mantle. For split mantle tomographic models, we find a sharp drop in advected heat at a depth of 670 kin. We investigate in detail the theological consequences of a circulation that is layered at this depth by the action of the endothermic phase transformation of spinel to a mixture of perovskite and magnesiowiistite. On physical grounds this is expected to lead to the development of a dipolar viscosity structure centered on the internal thermal boundary layer. We investigate the impact that such a structure has on the predicted aspherical geoid. A sequence of forward modeling calculations of this geophysical observable demonstrates that a viscosity profile which includes a dipolaf structure centered at 670 km depth and a significant increase of viscosity below mantle depths of 1200-1500 km optima!ly reconciles the long-wavelength GEM-T2 observations. The increase in viscosity in the lower part of the lower mantle is also required by the heat flow data whereas the introduction of the dip olaf structure in the viscosity profile allows the upper mantle value of the viscosity which is close to that inferred by Haskell of 10 •'• Pa s to be continued to a depth of 1200-1500 km in accord with the requirements of recent postglacial rebound inferences. In the context of a whole mantle model of the circulation, we axe also able to accommodate the constraints imposed by the data by introducing only a low-viscosity notch at 670 km depth rather than the dipolaf structure. The viscosity models derived herein therefore provide a fully self-consistent reconciliation of these distinctly different geodynamic data and would appear to resolve a previously unresolved conflict between them. Recent numerical simulations of mantleconvection which incorporate the effects of the endothermic phase transformation of ff-spinel to a mixture of perovskite and magnesiowfistite at the depth of the 670-kin seismic discontinuity have revealed a style of circulation that is episodically layered [Macbetel and Weber, 1991; Peltier Paper number 95JB01078. 0148-0227/95 / 95J B-010785 05.00 and Solhelm, ...

Abstract. The depth extent, density, and dynamical role of apparent subcontinental keels are investigated by using constraints provided by the very long-wavelength representations of several geophysical fields. We first consider local cross correlations between the nonhydrostatic free-air gravity field, the map of the ice sheets at Last Glacial Maximum, and the surface expression of continental cratons. We initially confine our analyses to North America and observe that equally good local correlations exist between the gravity field and either of the others. The case of Eurasia is also considered. We observe that correlation analyses of this type cannot be employed to unambiguously infer the cause of long-wavelength continental gravity anomalies; therefore we revert to explicit postglacial rebound and tomography-based viscous flow modeling of the gravity field. For viscosity profiles that optimally reconcile relative sea level constraints from the Laurentide platform, we find that the rebound process accounts for only 10% of the observed free-air gravity low over Hudson Bay. We consider mantle convection as the more likely source of this gravity anomaly and alternatively investigate the implications of assuming that seismically fast, deep structure imaged tomographically beneath the continent represents either negatively, neutrally, or positively buoyant material. In addition to the gravity constraint we introduce the independent constraint of continental dynamic surface topography. We infer this new datum by using the Crust 5.1 global model of crustal structure. Remarkably, continents are found to systematically reside in topographic depressions of the order of 1-2 km. Within the context of our modeling assumptions we find that optimal model descriptions of the joint gravity and dynamic surface topography constraints over the continents require deep and dense subcontinental undercurrents.

Abstract. We investigate the very long-wavelength, global pattern of surface heat flux anomalies within the context of whole-mantle and layered-mantle anelastically compressible internal loading •heories. Since the internal loading framework does not yield a direct estimate of the geotherm, we argue that accurate predictions for the surface heat flux may nevertheless be obtained by assuming that it is linearly related to the radial component of flow velocity at shallow depth in the mantle. The mantle convective circulation is assumed to be driven by density heterogeneity inferred from global seismic tomography models. Best results for the pattern of surface heat flux anomalies are obtained for models that significantly impede the circulation at a depth of 670 km. Total variance reductions of 60-65% (degree 1-5) are obtained when the viscosity profile includes a low-viscosity asthenosphere. Within the context of our modeling assumptions, however, whole-mantle circulation models provide best descriptions of the long-wavelength nonhydrostatic gravity data. In order to resolve the gravity-heat flux impasse that is revealed herein, we consider the possibility of modifying the a priori global seismic models employed in the calculations. We show that the rigidly layered-mantle internal loading theory is equivalent to a theory in which no explicit flow-blocking boundary condition is imposed at 670 km but in which the buoyancy field inferred from the a priori tomographic model is supplemented by flow-blocking heterogeneity in the form of an appropriately constrained sheet mass load. We develop a general mathematical formalism describing how the introduction of appropriately constrained sheet mass loads allows the exact reconciliation of a number of a priori constraints or hypotheses concerning the structure of the circulation. Using this formalism, we explore the extreme nonuniqueness that not only characterizes internal loading theory inferences of the depth profile of mantle viscosity but also inferences of the radial style of the circulation. On this basis, we suggest that great caution is warranted with respect to tomography-based inferences of mantle properties. Based on a viscosity profile whose depth dependence is close to that independently inferred within the context of postglacial rebound studies, we present plausible resolutions of the gravity-heat flux impasse effected either within the framework of whole-mantle or layered-mantle circulation models.

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 coatinents. 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.

SUMMAR YWe employ the recently published Crust 5.1 model of global crustal structure (Mooney et al. 1998) to estimate the topographic contributions of isostatically compensated crustal loads and, in turn, infer a long-wavelength ®eld for Earth's dynamic surface topography. Our inference of dynamic surface topography is characterized by peak-to-peak variations of the order of 4 km. We argue that the square root of age variation of the oceanic bathymetry has a dynamic origin. Remarkably, continental regions are the site of deep (approximately 1.5 km) dynamic surface topography depressions. The power spectrum of the ®eld is dominated by spherical harmonic degrees l=1, 4 and 5, suggesting the importance of continent±ocean differences, rather than deep lower mantle heterogeneity, to its origin. We model the Crust 5.1-based inference of dynamic surface topography within the context of seismic tomography-based internal loading theories. We compute the depth dependences of dynamic surface topography response functions for various viscosity pro®les that we consider in our analyses. Our best descriptions of the Crust 5.1-based inference achieve total variance reductions of the order of 70 per cent in the spherical harmonic degree range l=1±8. These are obtained for wholemantle circulation models that preclude lower mantle heterogeneity from maintaining signi®cant vertical stresses on the outer surface. These models are characterized by a signi®cant increase in viscosity across the depth of the 660 km seismic discontinuity, by a factor of at least 50 relative to the average viscosity of the upper mantle. We also consider results of a layered circulation model but, in this case, we are unable to reconcile constraints provided by large-scale superswell topography. We propose that the antipodal Paci®c and African superswells are dynamically maintained by positively buoyant lower mantle superplumes imparting on the outer surface a large-scale, low-amplitude, predominantly degree 2 pattern of vertical stresses. Finally, we note that the Crust 5.1based inference of dynamic surface topography provides useful geodynamic constraints on the nature of deep subcontinental structure: optimal descriptions of the data require deep subcontinental keels composed of anomalously dense material.