Modeling the process of magma rising in the bowels of the Earth and its eruption to the surface

Abstract

This paper presents a numerical model for simulating magma ascent in the Earth’s interior and its eruption to the surface, aimed at improving earthquake prediction. Magmatic flows are modeled as highly viscous fluids with a low Reynolds number (Re) using simplified Navier–Stokes equations. The approach incorporates hydrodynamic instability arising from density differences between magmatic and asthenospheric layers. Initial and boundary conditions were formulated for magma outflow from a narrow crack, and a dimensionless Euler–Reynolds (ER) parameter was introduced to characterize flow behavior. Numerical experiments for different ER values revealed that at low ER, magma spreads slowly, forming stable layers, while higher ER values accelerate vertical rise, increase pressure gradients, and enhance instability. The model identifies zones of stress accumulation that may precede seismic events. An additional method—monitoring fluid levels in deep wells—showed correlation with seismic fluctuations, supporting its potential for early warning. The results confirm the reliability of the proposed approach, demonstrating good agreement with seismological data. The developed methodology can be applied to enhance early warning systems and reduce risks in seismically active regions.