Nonlinear convective motion of the asthenosphere and the lithosphere melting: a model for the birth of a volcano

The processes of heat transfer occurring between the Earth's asthenosphere and lithosphere are responsible for partial melting of rocks, leading to the magma generation and its migration and segregation in the crust and, possibly, to volcanoes generation at the surface. Convection is the dominant mechanism regulating the heat transfer from the asthenosphere to the lithosphere, although many aspects of the whole process are not yet clear. Therefore, the knowledge of the physical processes leading to the melting of the lithospheric rocks has important consequences in understanding the interior Earth dynamics, the surface volcanic dynamics, and its related hazards. Rock melting occurs when the temperature gradient meets the rock solidus. Here, we propose a nonlinear convective 1D analytical model (representing an approximation of more 3D complex models). The steady-state solution of our equation is in good agreement with the estimated geotherms of the asthenosphere. A perturbative approach leads to a heat swelling at the boundary between asthenosphere and lithosphere able to determine its melting and the birth of a volcano.