Numerical modeling experiments have shown that mantle diapirs could be important agents in the growth of continental roots during the Archean and Proterozoic [de Smet et al., 1998]. These mantle diapirs are generally on a scale of 50 to 100 km and penetrate an existing root while producing melt, and a complementary depleted low density residue, thus adding depleted material to the continental root. Plumes rising through the mantle are strongly influenced by the type of rheology.
 The two important deformation mechanisms in the upper mantle are diffusion creep and dislocation creep [Karato and Wu, 1993]. Diffusion creep takes place through diffusion of mass between grain boundaries. The strain rate increases linearly with applied stress, and decreases in a power law fashion with the grain size. Dislocation creep, on the other hand, takes place through the transport of dislocations in the crystal structure. It has a power law relation between applied stress and resulting strain rate (nonlinear), and it is insensitive to grain size [Karato and Wu, 1993]. The viscosity corresponding to dislocation creep flow decreases with increasing stress, a phenomenon known as shear-thinning. For the present mantle, dislocation creep is generally the dominant mechanism in the asthenosphere, whereas diffusion creep dominates in the lithospheric mantle and in the deeper upper mantle and lower mantle [Karato et al., 1995; van den Berg and Yuen, 1996]. Since olivine is the weakest major phase in mantle peridotite, the rheology of the upper mantle is probably dominated by olivine [Karato and Wu, 1993]. Next to the microphysical approach to mantle rheology, the inversion of glacial rebound data also gives information on the viscosity of the mantle. Using this approach, Lambeck et al.  have found the upper mantle viscosity to be about 3–4 × 1020 Pas. The hotter Archean upper mantle, however, may have had a viscosity several orders of magnitude lower than this figure due to the strong temperature dependence of both diffusion creep and dislocation creep. Furthermore, the temperature dependence of the dislocation creep mechanism as expressed in the activation energy parameter of the rheological flow is higher than for the diffusion creep component. From this one can predict a greater predominance of the dislocation creep component under higher temperature conditions, representative for the early Earth. This has motivated us to extend our previous work on growth mechanisms of continental roots, based on purely diffusion creep models [de Smet et al., 1998, 1999, 2000a, 2000b; de Smet, 1999], with a detailed investigation of more complete viscous rheology including also the rheological effect of dislocation creep flow and sensitivity for the degree of dehydration induced by partial melting.
 Nonlinear rheology can greatly enhance the velocity of plumes [Weinberg and Podladchikov, 1994; Larsen et al., 1997; Larsen and Yuen, 1997; van Keken, 1997] relative to a Newtonian rheology case, and can therefore more effectively transport heat up to shallow lithospheric levels. Another important effect of nonlinear rheology is the generation of localized high strain rates, which may result in viscous heating, with a lubricating effect through the temperature dependence of the rheology [van den Berg and Yuen, 1997; Larsen et al., 1999]. Combined, these two effects can cause regions of high temperature at shallow depths, which may induce secondary melting and crustal diapirism [Campbell and Hill, 1988]. On the other hand, melting lowers the temperature by means of latent heat consumption, and may also increase the viscosity of the residue directly. This is due to the fact that at low degrees of partial melting, water tends to concentrate in the melt phase, effectively drying the residue. Experiments have shown that water has a weakening effect [e.g., Chopra and Paterson, 1981], and from these observations, Karato  concluded that at low degrees of partial melting, the strength of the residual matrix is increased by melting. This increase of viscosity of the residual depleted peridotite could be as high as a factor of 100 to 180 [Hirth and Kohlstedt, 1996]. The importance of this effect for plumes has been ascertained by Ito et al.  and Ito . Karato and Jung  find that this dehydration effect does not only influence the viscosity, but is also connected to the low seismic velocity and high attenuation in the asthenosphere.
 Samples of cratonic lithosphere are found as xenoliths in kimberlite intrusions [Nixon and Boyd, 1973] and as larger bodies in some orogenic belts [Brueckner and Medaris, 1998; van Roermund and Drury, 1998]. It is proposed that many of these mantle rocks are emplaced into the lithosphere by diapirs from the convecting sublithospheric mantle [Nicolas, 1986] in a variety of geodynamic environments [Green and Gueguen, 1983; Nicolas et al., 1987; Fabriès et al., 1991]. The PT paths derived from some cratonic peridotites from the Norwegian Western Gneiss Region [van Roermund and Drury, 1998; Drury et al., 2001] imply that these rocks were part of diapirs that intruded cratonic lithosphere of Archean to early Proterozoic age (the cooling age of these rocks is 1.7–1.8 Ga, but the Sm-Nd model age indicates a depletion age of 2.5–3.0 Ga). Drury et al.  have shown that the PT path of these peridotites is consistent with PT paths of diapiric upwellings calculated from the thermochemical convection models of de Smet  and de Smet et al. .
 In this paper, we present results of numerical modeling experiments which were devised to model the interaction of diapirs with the continental root, and we investigate in particular the sensitivity of the model for the rheological parameterization. We place the models in an Archean setting by prescribing a potential mantle temperature of 1750°C. We determine the effect of varying the rheological flow law from Newtonian diffusion creep only, into a composite law combining both grain size sensitive Newtonian diffusion creep and power law (grain size independent) dislocation creep. Different grain sizes are used to test for varying strengths of the diffusion creep component (dislocation creep is grain size independent). Furthermore, we investigated the effect of dehydration during partial melting. This extends earlier work by de Smet et al. [1998, 1999, 2000a, 2000b] and de Smet  based on purely Newtonian rheology.
 The potential temperature of 1750°C which we use is relatively high and may be representative of the earlier half of the Archean. Parametric cooling models for the Earth of Richter  show mantle potential temperatures for the Archean of about 1450 to 1700 centigrade. However, the high MgO contents of Archean komatiites point to higher potential temperatures, up to 1800°C for 2.7 Ga old Belingwe komatiites and even 1900°C for 3.45 Ga old Barberton komatiites [Nisbet et al., 1993]. Melting experiments of Walter  show that Archean komatiites can be formed by dry batch melting of pyrolite at pressures of 7 to 10 GPa. Extrapolation along an adiabat of the solidus temperature (using the solidus of Herzberg and Zhang ) at these pressures shows that this corresponds to potential temperatures in the range of 1700 to 1800 centigrade. These temperatures probably represent plume temperatures in a cooler mantle. For the current mantle, estimates for the excess temperature of plumes are up to 200 to 250 centigrade [Herzberg and O'Hara, 1998]. In a hotter Earth, the temperature controlled viscosity would be lower and therefore also the maximum horizontal temperature variations would be reduced [McKenzie and Bickle, 1988; Nisbet et al., 1993] to about 50–150°C [Nisbet et al., 1993], which puts our potential temperature of 1750°C within the range indicated by the komatiites of Nisbet et al. . Some authors have suggested that komatiites may be formed by hydrous melting [Stone et al., 1997] at temperatures only about 100°C higher than present mantle temperatures [Parman et al., 1997]. Arndt et al.  however conclude that most komatiites were the product of dry melting. The potential temperature of 1750°C of our models is also consistent with the results of the numerical models of de Smet et al. [2000b] which form the starting point of our investigations.
 The analysis of structures and microstructures in mantle rocks may provide estimates of the differential stresses and strain rates during high temperature deformation associated with diapir upwelling in a cratonic lithosphere. We use this information to compare our model results to the peridotites from western Norway mentioned above, which are interpreted as a natural example of a Precambrian asthenosphere diapir [Drury et al., 2001].
 In the work of de Smet et al. [2000b], small-scale diapirs are generated in a self-consistent way in hot upwelling limbs of large-scale (∼1000 km) mantle convection cells. Here we take a different approach and zoom in on a smaller region surrounding a single uprising diapir and follow the detailed evolution during its ascent into and within the chemically distinct mantle root.