Fig. 3: Buoyancy modelled as traction on boundary of a magma body.
From: Unexpected large eruptions from buoyant magma bodies within viscoelastic crust
Overpressure is calculated with reference to the deepest point of the magma body. This pressure is transferred to a surface force at the boundary, in a direction normal to it. The vertically directed upward force on the column shown in red is ΔAΔρg (h2–h1). Here ΔA is a horizontal cross-sectional area element, equal to (cosφ)δA, where φ is the local angle that the boundary of the magma body makes with respect to horizontal. The integrated upward force due to all columns in the magma body gives an overall upward force following Archimedes law. For this geometry, the integrated horizontal force on the entire boundary will be zero (cancels out for this geometry because of symmetry).
