Cyclic behaviour in lava dome building eruptions Oleg

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

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

Cyclic activity (Montserrat) v Short-term (hours to days) Tilt data v Seismological data v

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

Mount St. Helens (1980 -1987) 3 periods of dome growth; I - 9 pulses

Mount St. Helens (1980 -1987) 3 periods of dome growth; I - 9 pulses ~12 m 3 s-1, Qav=0. 67 m 3 s-1 II - continues, Qav=0. 48 m 3 s-1 III- 5 pulses <15 m 3 s-1, Qav=0. 23 m 3 s-1

Santiaguito (19222006 -? ) Cycles: 8 after 1922 high (0. 5 -2. 1 m

Santiaguito (19222006 -? ) Cycles: 8 after 1922 high (0. 5 -2. 1 m 3 s-1): 3 -6 -years low ( 0. 2 m 3 s-1): 3 -11 -years Average discharge: ~0. 44 m 3 s-1

Shiveluch (19812006 -? ) 3 episodes of done growth with long repose periods High

Shiveluch (19812006 -? ) 3 episodes of done growth with long repose periods High intensity in the beginning of each episode Non-periodic oscillations

Main features of extrusive eruptions v Slow ascent rates: 0. 1 -20 m 3/s.

Main features of extrusive eruptions v Slow ascent rates: 0. 1 -20 m 3/s. v Gas can easily escape from ascending magma. v Crystals can nucleate and grow during the ascent. v Magma chamber can be significantly recharged during eruption.

Short term pulsations

Short term pulsations

Conduit was split to upper and lower part v Upper part v Volatile exsolution

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

ü magma is fed at a constant rate; ü the magma is compressible; ü

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

Lensky N. G. , Sparks R. S. J. , Navon O. Lyakhovsky V. Cyclic

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. v Compression phase - exsolution of volatiles into bubbles under limited volume as long as Pgas<Pslip Diffusion growth of bubbles, crystallization – P increase v Gas filtration, inflation of the conduit – P decrease v v Decompression - friction controlled extrusion as long as Pgas>Parrest v Rate and state dependent friction

3 Neuberg et al, 2006 FEMLAB, 2 D 4 2 no seismicity 1 Gas

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

Long-term pulsations J. A. Whitehead, K. R. Helfrich, Instability of flow with temperature-dependent viscosity:

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. v 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 v 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. 3547. v Melnik O. , Sparks R. S. J. , Barmin A. , Costa A. Degassing induced crystallization, rheological stiffening. v

Whitehead & Helfrish and Costa & Macedonio • Temperature dependent viscosity • Heat flux

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.

Maeda 2000 • Constant magma viscosity. • Conduit is surrounded by visco-elastic rocks. •

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

Simplified model ь ь ь Main assumptions. Magma is viscous Newtonian liquid. Viscosity is

Simplified model ь ь ь 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.

System of equations Boundary conditions

System of equations Boundary conditions

discharge rate Steady-state solution chamber pressure

discharge rate Steady-state solution chamber pressure

Q/Qin Transient Solutions

Q/Qin Transient Solutions

Mount St Helens (1980 -1987) 3 periods of dome growth; I - 9 pulses

Mount St Helens (1980 -1987) 3 periods of dome growth; I - 9 pulses ~12 m 3 s-1, Qav=0. 67 m 3 s-1 II - continues, Qav=0. 48 m 3 s-1 III- 5 pulses <15 m 3 s-1, Qav=0. 23 m 3 s-1

Santiaguito (1922 -2005 -? ) Cycles: 8 after 1922 high (0. 5 -2. 1

Santiaguito (1922 -2005 -? ) Cycles: 8 after 1922 high (0. 5 -2. 1 m 3 s-1): 3 -6 -years low ( 0. 2 m 3 s-1): 3 -11 -years Average discharge: ~0. 44 m 3 s-1

Model development • Crystal growth kinetics • Gas exsolution and escape through the magma

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

Governing Equation System d Mass Conservation Momentum equations Energy equation

Governing Equation System d Mass Conservation Momentum equations Energy equation

Newtonian vs. Bingham rheology

Newtonian vs. Bingham rheology

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

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

Shiveluch (2001 -2002) Crystal size distributions

Shiveluch (2001 -2002) Crystal size distributions

Intermediate cycles

Intermediate cycles

Intermediate cycles v Conduit is a combination of a dyke and cylinder v Dyke

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

Elastic deformation of wallrocks a 0 and b 0 are unperturbed semi-axis lengths

Elastic deformation of wallrocks a 0 and b 0 are unperturbed semi-axis lengths

Variation in discharge rate and crosssection area

Variation in discharge rate and crosssection area

1 D theory Experimental simulations of pulsating eruption

1 D theory Experimental simulations of pulsating eruption

discharge rate (cm 3/s) 2 D theory (FEMLAB) Pressure (bar)

discharge rate (cm 3/s) 2 D theory (FEMLAB) Pressure (bar)

Pressure and temperature evolution

Pressure and temperature evolution

What do we need for cyclic behaviour? v Friction decreases with increase in ascent

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