Download Quantitative aspects of research

GEOLOGY BY NUMBER:
solving petrology problems with
quantitative skills
Jennifer M. Wenner
Geology Department
University of Wisconsin Oshkosh
GEOLOGY BY NUMBER
µ = µinf
Ea/RT
e
* [1+A(mT
+
-2.5
b)]
The research question:
• How is continental crust
formed? (especially in
continental arcs since they best
approximate “average
continental crust”)
Observations

Continental
arcs are sites
of voluminous
continental
crustal addition
Observations

The major rock
type in continental
arcs is granodiorite (although
there are close
associations of
mafic and felsic
rocks).
Observations

Field and chemical
observations
suggest that two
(or more) distinct
magmas were
interacting to
generate a variety
of different rocks
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Hypothesis

Average
continental crust
is formed by
mixing basaltic
magmas and
granitic magmas
to make
GRANODIORITE!
Problems (perceived?)

Early calculations
suggested that
physical properties
(melting
temperature,
viscosity and
density) limit the
abilities of magmas
to mix.
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VISCOSITY CALCULATIONS
µ =µ0(1+A)-2.5(Marsh, 1981)
§

 = mT + b (empirical data)
§
§
µ = µ0[1+A(mT + b)]-2.5
µ0 = µinf eEa/RT (theoretical -- Arrhenius)
§
µ = µinf eEa/RT * [1+A(mT + b)]-2.5
VISCOSITY CALCULATIONS-students need to be able to:
§
µ =µ0

(1+A)-2.5
• Manipulate others’
(Marsh, 1981)
 = mT + b
•
•
§
µ = µ0[1+A(mT + b)]-2.5
§
§
µ0 = µinf eEa/RT
µ = µinf eEa/RT * [1+A(mT +
b)]-2.5
•
•
equations
Use and evaluate
empirical data
Assess a model’s
assumptions
Discern rate and order
of magnitude
Use tools such as
Excel
GEOCHEMICAL ANALYSIS
GEOCHEMISTRY -students need to be able to:





Read and interpret graphs
Recognize and assess
sources of error
Approximate slope / shape
of data
Articulate meaning of data
with reference to
quantitative chemical
concepts (i.e., KD values, µ, eNd)
Use computer programs
(i.e., Excel, etc.)
Petrology and Petrography
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Petrology and Petrography-students need to be able to:



Express scale
(including features at
a variety of scales)
Assess changes/
contrasts in rates
(i.e.,
cooling/crystallization,
tectonic, diffusion)
Recognize different
orders of magnitude
Field work
Field work -Students need to be able to:

Approximate distances /
height / scale

Estimate slope

Calculate angles and plot
structural data on a map

Determine magnetic
declination

Visualize 3-D from a 2-D map
Important quantitative skills

Approximation
and/or estimation
of:





Rates
Slope / shape of curve
Distances / angular
relationships
Order of magnitude
Appreciation of the
power of graphical
solutions





Assessment of
assumptions
Spatial relations
Statistics, sources
of error, data
analysis
Use of technologic
tools such as Excel
Others?