1. 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

2. 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.

3. How do we study deformation in active volcanoes? InSAR

4. 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.

5. Benchmark with Analytical Solution Z=10 km, R=2 km, ΔP = 18 MPa, G=32 GPa, n=0.25

6. Surface unloading: changes in hoop stress Unloading = 2 MPa

7. Surface unloading: changes in hoop stress Ts = 20 MPa

8. Formation of eruptive vents in calderas

9. 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.

10. Contact elements: Newton Raphson

11. Caldera Mesh E = 80 GPa E = 10 GPa, 1km, frictional contact

12. Caldera Boundary Conditions ΔP = 126 Mpa (simulates an eruption)

13. Does the fault slip or open?

14. Are the displacements measurable? Ulos = 0.93Uz -0.37Ur

15. 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.