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? What is Anisotropy? What are Common
Crustal Minerals?
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.
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.
Experiment
•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 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.
Plagioclase Results
Mineral
Plagioclase
K-Feldspar
Quartz
Amphibole
Biotite
Chlorite
Other
% Volume
~40%
15-20%
~20%
10-20%
5-10%
0-5%
0-5%
Premise
Seismology is the best tool for probing
Earth’s interior. Using a technique
called seismic tomography, velocity
profiles of Earth’s 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 Earth’s
crust.
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 endmember albite to the Calcium rich end-member anorthite.
Amphiboles come in many different compositions
featuring a wide range of elemental variation.
Amphibole Results
This is a velocity profile below Seattle
from Preston et al. 2004. Some
structural and compositional features
are marked.
Conclusions
•New plagioclase feldspar
and amphibole elasticity
data
•Higher seismic velocities
•These minerals are highly
anisotropic
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 amphibole’s 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.
•Anisotropy is a large effect
and will need to be
calculated into the next
generation of seismic
models