Dynamics of magma ascent with crystallization during extrusive eruptions.

1
Lecture 4

• Dynamics of magma ascent with crystallization
  during extrusive eruptions.
• Simplified and complete transient models.
• Cycles in eruptive activity, influence of
  controlling parameters.
• Case studies Mount Sent Helens and Santiaguito.
• Conclusion remarks

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Mechanical 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.

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System of equations

• Boundary conditions

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Dimensionless variables
Parameters
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• IC nnchconst
• BC nnchconst
• ? nnchconst

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Momentum equation
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Crystal growth rate
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Crystal growth rate
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System of equations
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Steady-state solution
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Solutions
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Period of pulsations
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Mount St Helens (1980-1987)
3 periods of dome growth I - 9 pulses 12
m3s-1, Qav0.67 m3s-1 II - continues, Qav0.48
m3s-1 III- 5 pulses lt15 m3s-1, Qav0.23 m3s-1
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Santiaguito
Cycles 8 after 1922 high (0.5-2.1m3 s-1)
3-6-years low (?0.2 m3 s-1) 3-11-years Average
discharge0.44 m3 s-1
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COMPARISON
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Model development

• Crystal growth kinetics
• Gas exsolution and escape through the magma
• Realistic magma viscosity model
• Temperature variation due to latent heat of
  crystallization

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Model development
Mass conservation
Momentum
Rheology
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Undercooling
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Crystal nucleation and growth
Undercooling

Mass flux to crystals
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Boundary conditions
Chamber with elastic walls
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Gas escape and overpressure
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Rheology
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Santiaguito
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Latent heat of crystallisation
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Alternative model Whitehead Helfrish (1991)

• Temperature dependent viscosity
• Heat flux to surrounding cold rocks
• Constant temperature of the rocks
• Elastic magma chamber walls
• Cyclic behaviour

• J.A. Whitehead, K.R. Helfrich, Instability of
  flow withtemperature-dependent viscosity a
  model of magma dynamics,J. Geophys. Res. 96
  (1991) 4145-4155.

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Alternative model Maeda 2000

• Constant magma viscosity.
• Conduit is surrounded by visco-elastic rocks
  speeded up to infinity.
• Magma chamber is in purely elastic rocks.
• Constant or variable influx into the chamber from
  below.

• 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.

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Results
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Mt. Unzen case
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Parameters used in calculations

• Low viscosity of the rocks lt1014 Pa s
• If magma chamber is in visoco-elastic rocks - no
  oscillations

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Unsolved problems

• Magma rheology for high crystal and bubble
  content
• Crystal growth kinetics
• Overpressure development in ascending magma
• Elaborate model of lava dome growth
• Coupling of conduit flow model with the model of
  magma chamber and lava dome

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Lots of open questions