The long-term growth and stability of compositionally layered continental upper mantle has been investigated by numerical modelling. We present the first numerical model of a convecting mantle including differentiation through partial melting resulting in a stable compositionally layered continental upper mantle structure. This structure includes a continental root extending to a depth of about 200 km. The model covers the upper mantle including the crust and incorporates physical features important for the study of the continental upper mantle during secular cooling of the Earth since the Archaean. Among these features are: a partial melt generation mechanism allowing consistent recurrent melting, time-dependent non-uniform radiogenic heat production, and a temperature-and pressure-dependent rheology. The numerical results reveal a long-term growth mechanism of the continental compositional root. This mechanism operates through episodical injection of small diapiric upwellings from the deep layer of undepleted mantle into the continental root which consists of compositionally distinct depleted mantle material. Our modelling results show the layered continental structure to remain stable during at least 1.5 Ga. After this period mantle differentiation through partial melting ceases due to the prolonged secular cooling and small-scale instabilities set in through continental delamination. This stable period of 1.5 Ga is related to a number of limitations in our model. By improving on these limitations in the future this stable period will be extended to more realistic values.

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[1] A possible mechanism for adding material to a continental root is by means of upwellings from the convecting mantle subject to pressure release partial melting. We present results of numerical modeling of the interaction of melting diapirs with continental roots in an Archean setting characterized by a mantle potential temperature of 1750°C in a two-dimensional (2-D) Cartesian geometry. In an extension of earlier work [de Smet et al., 2000b] we have investigated the influence of mantle rheology on the behavior of diapirs. We have in particular looked at the difference in behavior of diapirs using a composite rheology combining both grain size sensitive diffusion creep and dislocation creep mechanisms. We have used the grain size, here taken to be uniform, as a control parameter to obtain model cases with varying contribution from the two creep mechanisms. The diapirs in the composite rheology model rise much faster than they do in a purely Newtonian model. Observed diapiric ascent times from 230 km depth to the top of the ascent path at about 80 km depth are approximately 1 Myr for a Newtonian model (averaged 14 cm/yr) compared to about 50 thousand years for a composite rheology model (averaged 3 m/yr) with the same parameters for the Newtonian component. This clearly indicates the large impact of the dislocation creep component of the viscous deformation process. We have also investigated the effect of an increase in the viscosity due to dehydration during partial melting. This increase has a strong influence on the development of rising diapirs. The ascent velocity and lateral spreading of the diapirs at the end of their ascent are effectively reduced when a viscosity increase by a factor of 10 is applied, and the effect becomes stronger for larger factors. Average vertical velocities range from 1.4 cm/yr for a factor 10 to 2 mm/yr for a factor 200. The most striking result of the viscosity increase due to dehydration is the reduction of the ascent velocity, thereby stretching the characteristic timescale of the diapiric intrusion process to a value between 5 and 50 Myr for dehydration viscosity prefactor values of 10 and 200, respectively. In contrast with the strong difference between the Newtonian and the composite rheology models, small differences are found in the overall dynamics between the composite rheological models, characterized by different values of the uniform grain size. The composite rheological models exhibit self-regulating behavior where substantial differences between the relative contributions of the two creep components result in very similar effective viscosities, due to a local dominance of dislocation creep at high stresses and corresponding similar flow dynamics. Stress levels and P,T paths in the modeling results are consistent with estimates obtained from Precambrian peridotite bodies which are interpreted to have originated from asthenospheric diapirism.

Summary Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics‐based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter εth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high‐resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure‐released partial melting. In this model, a characteristic phenomenon of small‐scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High‐resolution experiments with grid cells down to 700 m horizontally and 515 m vertically result in highly detailed observations of the diapiric melting phenomenon.