Cyclic behaviour in lava dome building eruptions.

1. Cyclic behaviour in lava dome building eruptions. Oleg Melnik, Alexei Barmin, Antonio Costa, Stephen Sparks

2. Cyclic activity (Montserrat) • Short-term (hours to days) • Tilt data • Seismological data • Long term (2-3 years) • Episodes of dome extrusion • Pauses in eruption • Ground deformation (deflation during growth, inflation during repose periods) • Intermediate (5-7 weeks) • Rapid, irreversible change in tilt • Seismic swarms and pyroclastic flows in the beginning • Rapid increase in dome growth rate

3. Mount St. Helens (1980-1987) 3 periods of dome growth; I- 9 pulses ~12 m3s-1, Qav=0.67 m3s-1 II - continues, Qav=0.48 m3s-1 III- 5 pulses <15 m3s-1, Qav=0.23 m3s-1

4. Santiaguito (1922-2006-?) Cycles: 8 after 1922 high (0.5-2.1m3 s-1): 3-6-years low (0.2 m3 s-1): 3-11-years Average discharge:~0.44 m3s-1

5. Shiveluch (1981-2006-?) 3 episodes of done growth with long repose periods High intensity in the beginning of each episode Non-periodic oscillations

6. Main features of extrusive eruptions • Slow ascent rates: 0.1-20 m3/s. • Gas can easily escape from ascending magma. • Crystals can nucleate and grow during the ascent. • Magma chamber can be significantly recharged during eruption.

7. Short term pulsations

8. Conduit was split to upper and lower part • Upper part • Volatile exsolution with time delay • Friction is controlled by volatile dependent viscosity • Lower part • Elastic conduit deformations due to pressure variation • No friction • Conduit inlet • Constant influx rate

9. Cyclic eruptive behavior of silicic volcanoes R. Denlinger, R. Hoblitt • magma is fed at a constant rate; • the magma is compressible; • m= const; • slip occurs when Q > Qcr;

10. Lensky N.G., Sparks R.S.J., Navon O. Lyakhovsky V.Cyclic Activity in Lava Domes: Degassing-induced pressurization. Stick-slip response of the conduit. • Compression phase - exsolution of volatiles into bubbles under limited volume as long as Pgas<Pslip • Diffusion growth of bubbles, crystallization – P increase • Gas filtration, inflation of the conduit – P decrease • Decompression - friction controlled extrusion as long as Pgas>Parrest • Rate and state dependent friction

11. 3 4 2 Gas diffusion no seismicity 1 seismicity Pressure increasing no seismicity τ τ Gas loss τ τ τ τ Magma slowing Pressure decreasing Gas diffusion Diffusion lags behind Neuberg et al, 2006 FEMLAB, 2D

12. Long-term pulsations • J.A. Whitehead, K.R. Helfrich, Instability of flow with temperature-dependent viscosity: a model of magma dynamics, J. Geophys. Res. 96 (1991) 4145-4155. • A. Costa, G. Macedonio Nonlinear phenomena in fluids with temperature-dependent viscosity: An hysteresis model for magma flow in conduits. GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 10, 1402 • I. Maeda, Nonlinear visco-elastic volcanic model and its application to the recent eruption of Mt. Unzen. Journal of Volcanology and Geothermal Research, 2000, v. 95, p. 35-47. • Melnik O., Sparks R.S.J., Barmin A., Costa A. Degassing induced crystallization, rheological stiffening.

13. Whitehead & Helfrish and Costa & Macedonio • Temperature dependent viscosity • Heat flux to surrounding cold rocks • Constant temperature of the rocks • Multiple steady-state solutions • Cyclic behaviour Problem: assumption of constant rock temperature. Heating of wallrocks decrease heat flux => oscillations stop.

14. Maeda 2000 • Constant magma viscosity. • Conduit is surrounded by visco-elastic rocks. • Magma chamber is in purely elastic rocks. • Constant or variable influx into the chamber from below. • Low viscosity of the rocks <1014 Pa s • If magma chamber is in visoco-elastic rocks - no oscillations

15. Main assumptions. • Magma is viscous Newtonian liquid. • Viscosity is a step function of crystal content. • Crystal growth rate is constant and no nucleation occurs in the conduit. • Conduit is a cylindrical pipe. • Magma chamber is located in elastic rocks and is feed from below with constant discharge. Simplified model

16. System of equations Boundary conditions

17. Steady-state solution discharge rate chamber pressure

18. Transient Solutions Q/Qin

19. Mount St Helens (1980-1987) 3 periods of dome growth; I- 9 pulses ~12 m3s-1, Qav=0.67 m3s-1 II - continues, Qav=0.48 m3s-1 III- 5 pulses <15 m3s-1, Qav=0.23 m3s-1

20. Santiaguito (1922-2005-?) Cycles: 8 after 1922 high (0.5-2.1m3 s-1): 3-6-years low (0.2 m3 s-1): 3-11-years Average discharge:~0.44 m3s-1

21. Model development • Crystal growth kinetics • Gas exsolution and escape through the magma • Realistic magma viscosity model • Temperature variation due to latent heat of crystallization • Dyke shape of the conduit

22. Governing Equation System d Mass Conservation Momentum equations Energy equation

23. Newtonian vs. Bingham rheology

24. Non-periodic eruption regimesRandom chamber temperature variation ± 15 K

25. Shiveluch (2001-2002) Crystal size distributions

26. Intermediate cycles

27. Intermediate cycles • Conduit is a combination of a dyke and cylinder • Dyke has elliptical cross-section • Elastic deformation of wall-rocks • Crystallization and rheological stiffening

28. Elastic deformation of wallrocks a0 and b0are unperturbed semi-axis lengths

29. Variation in discharge rate and cross-section area

30. Experimental simulations of pulsating eruption 1D theory

31. 2D theory (FEMLAB) discharge rate (cm3/s) Pressure (bar)

32. Pressure and temperature evolution

33. What do we need for cyclic behaviour? • Friction decreases with increase in ascent velocity • Variable viscosity • Stick-slip • Non-Newtonian properties • Delay process in the system • Crystallization • Heat transfer • Diffusion