Elasticity and Anisotropy of Common Crustal Minerals

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Elasticity and Anisotropy of Common Crustal
Minerals
Alex Teel Earth and Space Sciences, Physics
Mentor J. Michael Brown Earth and Space Sciences
What is Elasticity?
Premise
What is Anisotropy?
What are Common Crustal Minerals?
Seismology is the best tool for probing Earths
interior. Using a technique called seismic
tomography, velocity profiles of Earths interior
can be created. Velocity profiles provide
valuable information regarding the structure,
mechanical behavior and composition of Earth. A
current issue is the link between seismic
velocity and composition is poorly determined.
The mineral elasticity data is necessary to
determine composition from velocity however the
elasticity of many minerals has never been
calibrated and in some cases these calibrations
are biased. I performed these calibrations on
several common mineral compositions in Earths
crust.
Anisotropy is directional dependence. The
opposite is isotropy which is the same in every
direction. Water is isotropic because it is the
same no matter how you look at it. Most Earth
materials are anisotropic to some degree and in
the case of plagioclase feldspars and amphiboles
the anisotropy is very large.
For materials which return to their original
shape after deformation, elasticity is a measure
of how much the material will deform given an
applied stress. Examples of elastic behavior are
diving boards, springs and tennis balls.
Elasticity can be quantified with a linear
relationship between deformation (strain) and
stress. These linear constants can be put into a
matrix called the elastic constants tensor.
Experiment
I experimented on plagioclase feldspars and
amphiboles. The table above lists common
literature values for the volumetric percentage
of the crust by mineral group. Plagioclase
feldspars range from the Sodium rich end-member
albite to the Calcium rich end-member anorthite.
Amphiboles come in many different compositions
featuring a wide range of elemental variation.
This plot shows acoustic wave speed with changing
angle for a simulated rock made entirely of
Sodium rich plagioclase. If this rock was
isotropic the lines would all be flat because
they would not change with direction.

• A pulsed laser creates surface waves on polished
  surfaced of oriented single crystals. 
• The acoustic wave velocities are measured as a
  function of direction.
• These velocities are inverted to determine the
  elastic constants.

This is a velocity profile below Seattle from
Preston et al. 2004. Some structural and
compositional features are marked.
Plagioclase Results
Amphibole Results
Conclusions

• New plagioclase feldspar and amphibole elasticity
  data
• Higher seismic velocities
• These minerals are highly anisotropic
• Anisotropy is a large effect and will need to be
  calculated into the next generation of seismic
  models

Shown above are composition ranging from albite
to anorthite on the x-axis and velocity in km/s
on the y-axis. Plotted are velocities from
previous elasticity data and from my data. The
vertical lines are not error bars they are the
maximum and minimum velocity values observed at
each respective composition studied. In the case
of plaioclases, shear wave velocities differ by
about 15 and compressional waves differ by about
7. In both cases my new data is higher than the
old data. Important to notice is the velocity
anisotropy. Velocity variations due to
anisotropy dwarf velocity variations due to
composition in plagioclase feldspars.
These figures plot maximum and minimum observed
velocity for the three amphibole compositions
studied. The purple lines represent the prior
isotropic average velocities. The most remarkable
feature of the amphiboles is their anisotropy.
For example the sodic-calcic amphiboles
compressional velocities range from about 6.25
km/s to 9 km/s. This is a range characteristic
of upper crust to mantle transition zone
velocities.