Numerical model for the generation of the ensemble of lithospheric plates and their penetration through the 660-km boundary

Abstract

In the kinematic theory of lithospheric plate tectonics, the position and parameters of the plates are predetermined in the initial and boundary conditions. However, in the self consistent dynamical theory, the properties of the oceanic plates (just as the structure of the mantle convection) should automatically result from the solution of differential equations for energy, mass, and momentum transfer in viscous fluid. Here, the viscosity of the mantle material as a function of temperature, pressure, shear stress, and chemical com position should be taken from the data of laboratory experiments. The aim of this study is to reproduce the generation of the ensemble of the lithospheric plates and to trace their behavior inside the mantle by numer ically solving the convection equations with minimum a priori data. The models demonstrate how the rigid lithosphere can break up into the separate plates that dive into the mantle, how the sizes and the number of the plates change during the evolution of the convection, and how the ridges and subduction zones may migrate in this case. The models also demonstrate how the plates may bend and break up when passing the depth boundary of 660 km and how the plates and plumes may affect the structure of the convection. In con trast to the models of convection without lithospheric plates or regional models, the structure of the mantle flows is for the first time calculated in the entire mantle with quite a few plates. This model shows that the mantle material is transported to the mid oceanic ridges by asthenospheric flows induced by the subducting plates rather than by the main vertical ascending flows rising from the lower mantle.

Late Paleozoic and Early Mesozoic rare-metal magmatism of Central Asia: Stages, provinces, and formation settings

“…small-scale convection, occur under the lithosphere. The estimated scheme of convection in the entire mantle in [Trubitsyn V.P., Trubitsyn A.P., 2014] is consistent with our ideas of the primary genetically emerging block divisibility of the protolithosphere. In the initial state, the protolithosphere remains uniform at the surface, has a roughly constant thickness and increased quasi-strength at the primary inter-cell boundaries whereat the viscosity of the medium is increasing due to cooling of the protolithosphere.…”

“…Publications on convection in the Earth's mantle and its role in global geodynamic processes are quite numerous. In the majority of papers, recent geodynamic processes are considered with an assumption that the evolution of convection in the mantle and asthenosphere took place in two-or three-layer or more complicated patterns [Lobkovsky, 1988;Lobkovsky, Kotelkin, 2000;Lobkovsky et al, 2004;Rykov, Trubitsyn, 1994a, 1994bTrompert, Hansen, 1988;Trubitsyn, Rykov, 2002;Trubitsyn V.P., Trubitsyn A.P., 2014]. Mantle convection was discussed in a number of publications many years ago, the most famous of which are [Pekeris, 1935;Molnar et al, 1979].…”

“…In [Trubitsyn V.P., Trubitsyn A.P., 2014], a digital model is described in detail to show that the present set of the lithospheric plates is a result of the evolution of convection. It provides an insight into the possible mode of flows in the entire mantle, movements of the masses between the upper and lower mantle, as well as between the central and lateral limits of the convection cells.…”

“…In standard experimental conditions, Rayleigh-Bénard convection cells occupy the entire thickness of the cooling layer, and their typical horizontal size is comparable to the vertical size or slightly exceeds it. In the majority of problems solved by geodynamics, it is assumed that convection cells occupy the entire mantle or partially occupy the layer or occur between the layers [Kirdyashkin, Dobretsov, 1991;Dobretsov et al, 2001;Trubitsyn V.P., Trubitsyn A.P., 2014]. In such conditions, the main factor predetermining convection is viscosity of the medium, which is included in equations of interrelated Rayleigh, Grashof and Prandtl numbers.…”

“…Numerical solutions of equations of energy, mass and momentum transfer suggest that mantle convection takes place while a set of plates is self-generated. According to [Trubitsyn V.P., Trubitsyn A.P., 2014], "the set of plates is inevitably generated, without requiring any additional boundary and initial conditions" (p. 146). The foregoing explains why the Earth has been subject to numerous transformations, including the catastrophic ones, in the natural course of its geodynamic evolution.…”