Displacementlength scaling relations for faults on the terrestrial planets

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Displacement-length scaling relations for faults
on the terrestrial planets

• Richard A. Schultz, Chris H. Okubo, Scott J.
  Wilkins
• Journal of Structural Geology vol. 28, no. 12,
  2006
• Presentation by Daniel A. Petrizzo

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Background

• Faulting has been observed on almost every
  geologic surface in the solar system.
• Extension most common
• Thrust faults on Mercury, Venus, Mars and the
  Moon
• Strike-slip on Mars and some icy satellites
• Planetary surfaces provide unique natural
  laboratories for studying faulting processes.

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Purpose

• Demonstrate how and predict how much D/L ratios
  for faults scale with planetary gravity.

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Why should fault displacements scale with gravity?

• Stress difference (sv- sh) is proportional to
  driving stress (sd)
• Substitute Hookes Law relations for 3-D strain
  for (sd) resulting in
• E Youngs Modulus
• v Poissons Ratio

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• Rewrite crustal strain difference (ev eh) by
  noting sv q sh
• q related to max static coefficient on faults by
• Results in
• ? rock density, z depth, g gravitational
  acceleration

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• Using relationship between crustal strains and
  the geometric moments of a fault population
• Where
• ? Davg/Dmax
• V volume of faulted layer
• H down-dip fault height
• d fault dip angle
• ? Dmax/L

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• Results in
• Substituting and solving for D
• For constant
• Fault shape (?, L, H, d)
• Crustal rock properties (E, v, ?)
• Size of deforming domain (z, V)
• Displacement scales with planetary gravity!

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Mechanical Models of Faults

• 1) Symmetric linear stress distribution
• Assumes a linear increase in fault frictional
  strength from center to tip
• Produces a linear displacement distribution
• 2) End-zone
• Assumes a central well-slipped portion bounded by
  frictionally stronger end-zones
• Used in this paper across all planetary bodies

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End-zone Model

• General form
• Shows D/L ratio depends on 3 factors
• Driving stress sd
• Yield strength sy
• Modulus E
• Provides a physical basis for D-L scaling
  relations of the form D ?L

All influenced by planetary g
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Driving Stress (sd)

• The shear stress leading to Columb frictional
  sliding and displacement along fault.
• Reduced on lower gravity planets because normal
  stress, horizontal and vertical far-field
  stresses all depend on sv and therefore g.

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Yield Strength (sy)

• Yield strength peak shear strength of the rock
  mass.
• Normal faulting (sv sh)
• Thrust faulting (sH sv)
• Stronger rock requires greater near-tip stress to
  break, leading to larger displacements along
  fault.

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• Yield strength is calculated using a non-linear
  Mohr envelope that accounts for joints,
  fractures, lithology, and pore-H2O conditions.
• Since sv increases with g, so does the diameter
  of the Mohr circle.
• Rock strength increases with planetary gravity
  for the same depth below surface.

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Modulus

• As modulus increases, displacement decreases.
• Youngs Modulus decreases with g for equivalent
  conditions and depth ranges.

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• Curves of Youngs modulus vs. depth for earth and
  Mars.

Note slower rate of increase at depth on Mars.
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Applications to Terrestrial Planets

• Effects of gravity are not simple for sd, sy, E.
• Total reduction of D/L exceeds the gravity ratio.

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Mars

• For normal faults in basaltic rock masses
• gMars/gEarth 0.38
• Yield strength sy 0.5
• Modulus E 0.84
• 0.380.50.84 0.16
• D/L reduced by a factor of 5-6 consistent with
  observations!

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Mercury

• Scaling relations overpredict fault displacements
  for thrust faults.
• Explanation the aspect ratios (L / H) of the
  terrestrial and planetary thrust faults in
  dataset are not equal. Aspect ratios of 1-3 do
  fit model. These faults may be long faults
  which are not linked down-dip to decollements as
  on earth.

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Moon

• Fault displacement values are not sufficiently
  accurate for D-L values to be well defined.
• Methods used in this paper predict D/L ratio
  0.04 of similar size faults on earth.

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Other Bodies

• Assessment of D-L scaling relations of faults on
  Venus and icy satellites of the outer solar
  system is hindered by large uncertainties of both
  displacement and length.
• D/L ratio would also depend on ice stiffness and
  near-tip strength (currently unknown).

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Predicted D/L Values
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Conclusion

• D/L ratios scale with gravity.
• Other structures should also scale with gravity
• joints
• dikes
• deformation bands

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Critique

• Valuable early effort in using unique natural
  laboratories to learn more about geologic
  processes.
• Lack of data for use in study made conclusions
  seem a little thin.
• Future studies should be interesting.

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