Frictional Heating During an Earthquake

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Frictional Heating During an Earthquake

• SIO 234 Geodynamics
• Xiaowei Chen
• Richard Wood
• November 16, 2007

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Outline

• Problem Derivation
• Determining the Frictional Heat Generation Rate
• Temperature Profile
• Discussion

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Derivation of Temperature Change

• Governed by 1-D diffusion equation
• Neglected heat conduction in the slip-parallel
  direction
• Fault thickness is much smaller than other
  dimensions

(Fialko, 2004)
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Derivation Definitions

• Definition of terms
• T - rock temperature
• y fault perpendicular coordinate
• ? thermal diffusivity
• ? density
• c heat capacity
• Q rate of frictional heat generation

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Derivation Part 1
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Derivation Part 2
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Slip Velocity Across Fault

• Slip velocity across the fault linearly
• Does not vary along the fault

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Temperature Distribution due to Linearly slip
velocity across fault

• Substitute expression of velocity as into
• temperature distribution.

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Determining Temperature Distribution due to Fault
Slip

• The rate of frictional heat generation is
• D crack displacement
• v - slip velocity, derivative of D with respect
  to time
• t slip duration
• 2w fault zone thickness
• µ coefficient of friction
• sn fault normal stress

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Determining Temperature Distribution due to Fault
Slip
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Results for 2w 1mm (stress 100 MPa)
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Results for 2w 10mm (stress 100 MPa)
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Results for 2w 1mm (stress 10 MPa)
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Results for 2w 10mm (stress 10 MPa)
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Maximum Temperature Changes
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Further Discussion

• Rock tends to melt between 870-1270 K
• easily melts in analysis
• Basaltic compositions 1220 K
• Granitic compositions 970 K
• After melting, change in T reduced
• additional term created in energy balance of
  system
• L latent heat of fusion/crystallization
• F volumetric melt fraction

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Additional Considerations

• Melt fraction - 50, a transition occur
• a dramatic drop in friction
• strain localization due to decreases in melt
  viscosity with increasing temperature
• Maximum temperature corresponds to 50 melting of
  the fault gouge.

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References

• Fialko, Yuri. Fusion by Earthquake Fault
  Friction Stick or Slip. Journal of Geophysical
  Research. V110. Dec 2005.
• Fialko, Yuri. Temperature Fields Generated by
  the Elastodynamic Propagation of Shear Cracks in
  the Earth. Journal of Geophysical Research.
  V109. Jan 2004.