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Displacementlength scaling relations for faults on the terrestrial planets
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Displacement-length scaling relations for faults on the terrestrial planets ... envelope that accounts for joints, fractures, lithology, and pore-H2O conditions. ... – PowerPoint PPT presentation
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Title: Displacementlength scaling relations for faults on the terrestrial planets
1
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
2
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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