Processes lasting for milliseconds to some ten thousand years are described by a viscoelastic model of the Earth that has been basically developed in the first half of the 20th century. To describe longer processes, lasting for a few hundreds of thousands to a few hundreds of millions of years, a mantle convection model including a highly viscous oceanic lithosphere broken into plates has been developed in the second half of the 20th century. Each continent in this model is a part of and moves as a whole with its own rigid oceanic plate. However, lithospheric oceanic plates are renewed over one hundred million years, whereas continents drift on the mantle during a few billions of years. Since strains of continents are much smaller than their displacements, continents can be considered, in the first approximation, as solid bodies floating on a convective mantle. Changes in the shape of continents produced by their deformation, as well as changes in their number associated with breakups and collisions, can be taken into account at each time step of their movement. Therefore, global geological processes on time scales of tens of millions of years to a few billions of years should be described in terms of mantle convection models with continents floating among oceanic plates. The plates are temporarily frozen with continents at their passive margins but, on average, in a hundred million years, the plates become too heavy, break off from the continents and sink into the mantle. The new model generalizes the theory of mantle convection and plate tectonics by incorporating the effects of moving continents and extends the applicability range of the model description to the time scale of the Earth's geological history. The model is based on the classical equations of mantle convection complemented with equations of motion of a system of continents including their thermal and mechanical interaction with the mantle and between each other. If the modern Earth is taken as an initial state in the evolution of mantle flows with floating continents, the initial temperature distribution can be found from tomography data with the use of the temperature dependence of seismic velocities. The initial position and shape of continents can be taken from geographic maps. These data are sufficient in order to calculate from the equations the evolution of mantle flows and global heat flux distribution and motions of continents. Because an average description is only available as yet and several parameters of the mantle and continents are known inaccurately, results of such modeling should be regarded as preliminary, showing a basic possibility of calculating the history and the future evolution of continents and islands.
floating continents, evolutionary models, oceanic plates, numerical modeling.
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