Eruptive vents formation and surface unloading in active volcanoes: insights from axis-symmetric 2D

finite element models

Francisco Delgado

Department of Earth and Atmospheric Sciences

Volcanoes

Deformation < 0.5 m over scales of ˜10-20 km: infinitesimal strain is valid. If deformation is not time dependent and source is above brittle ductile transition (˜10-15 km), linear elasticity is used → stress.

How do we study deformation in active volcanoes? InSAR

Topics to be Addressed

• Benchmark FEM with linear elasticity analytical solution (Mogi model).

• Changes in hoop stress in deep chambers related to unloading.

• Generation of eruptive vents in pre existing discontinuities.

Benchmark with Analytical Solution

Z=10 km, R=2 km, ΔP = 18 MPa, G=32 GPa, n=0.25

Surface unloading: changes in hoop stress

Unloading = 2 MPa

Surface unloading: changes in hoop stress

Ts = 20 MPa

Formation of eruptive vents in calderas

Contact elements: Augmented Lagrangian formulation

In the Augmented Lagrangian method the Lagrange multiplier is a fixed current estimate of the correct multiplier and is updated with each iteration of the method until g(x)<= tolerance, εN is as large as possible.

Simo and Laursen, 1992.

Contact elements: Newton Raphson

Caldera Mesh

E = 80 GPa

E = 10 GPa, 1km, frictional contact

Caldera Boundary Conditions

ΔP = 126 Mpa (simulates an eruption)

Does the fault slip or open?

Are the displacements measurable?

Ulos = 0.93Uz -0.37Ur

Conclusions

• ANSYS can properly model linear elastic analytic solutions widely used in volcanology.

• Hoop stress changes produced by unloading are very small in deep chambers: require other mechanisms to trigger eruptions.

• Co eruptive inflation can open caldera ring faults by several centimeters. However, near field measurements are required to detect them.