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 m 3 s -1, Q av =0.67 m 3 s -1 I - 9 pulses ~12 m 3 s -1, Q av =0.67 m 3 s -1 II - continues, Q av =0.48 m 3 s -1 III- 5 pulses <15 m 3 s -1, Q av =0.23 m 3 s -1

4. Santiaguito (1922- 2006-?) Cycles: 8 after 1922 high (0.5-2.1m 3 s -1 ): 3-6-years low (  0.2 m 3 s -1 ): 3-11-years Average discharge:~0.44 m 3 s -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 m 3 /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. magma is fed at a constant rate; the magma is compressible;  const; slip occurs when Q > Q cr ; Cyclic eruptive behavior of silicic volcanoes R. Denlinger, R. Hoblitt

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 P gas <P slip  Diffusion growth of bubbles, crystallization – P increase  Gas filtration, inflation of the conduit – P decrease  Decompression - friction controlled extrusion as long as P gas >P arrest  Rate and state dependent friction

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

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 viscosityTemperature dependent viscosity Heat flux to surrounding cold rocksHeat flux to surrounding cold rocks Constant temperature of the rocksConstant temperature of the rocks Multiple steady-state solutionsMultiple steady-state solutions Cyclic behaviourCyclic behaviour Problem: assumption of constant rock temperature. Heating of wallrocks decrease heat flux => oscillations stop.

14. Maeda 2000 Constant magma viscosity.Constant magma viscosity. Conduit is surrounded by visco-elastic rocks.Conduit is surrounded by visco-elastic rocks. Magma chamber is in purely elastic rocks.Magma chamber is in purely elastic rocks. Constant or variable influx into the chamber from below.Constant or variable influx into the chamber from below. Low viscosity of the rocks <10 14 Pa sLow viscosity of the rocks <10 14 Pa s If magma chamber is in visoco-elastic rocks - no oscillationsIf magma chamber is in visoco-elastic rocks - no oscillations

15. Simplified model 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.

16. System of equations Boundary conditions

17. Steady-state solution chamber pressure discharge rate

18. Transient Solutions Q/Q in

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

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

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

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

23. Newtonian vs. Bingham rheology

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

25. Crystal size distributions Shiveluch (2001-2002 )

26. Intermediate cycles

27.  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 a 0 and b 0 are 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