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Computer lab: problems 2.11 and 2.12
tom.h.wilsontom.wilson@mail.wvu.edu
Department of Geology and GeographyWest Virginia University
Morgantown, WV
Objectives for the day
• Background on the North Sea Data
• Determining sedimentations rates from age-depth data
• Estimating the time when sedimentation ceased or the age of the surface at “0” depth.
• Working with liquid fraction/concentration data
• Using absolute references and Excel constants to build formulas
• go over problem presentation formats
We didn’t talk much about derivatives, but we will spend time on differential and integral calculus later in the semester.
The problem asked on the warm up sheet requires that you use the power rule, so hopefully you didn’t find that one too difficult.
When the ocean temperature cools O16 preferentially evaporates
Thus ice formed during colder periods will have less O18, while the creatures with carbonate skeletal material will contain increased
amounts of O18
O18 drops in the ice
But rises in organisms living in the colder oceans
Depth (cm)
0 500 1000 1500 2000 2500
AG
E(y
ears
BP
)
0
5000
10000
15000
North Sea Data (Lehman &Keigwan, 1992)
O18
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Lehman and Keigwin undertook one of the first deep sea studies to document changes in sea surface temperature associated with deglaciation
O18 from plankton
Waltham presents us with a small portion of the total data set, just to illustrate some basic ideas.
How do you bring in your data?
How do you plot your data?
How can you change the plot line style (color, thickness, continuous or dashed…)?
How can you change the data point display style (marker line style, line color, …)?
How do you get back to the Chart Tools?
How do you change the chart layout?
How do you format gridlines, chart axes?
How can you add a chart title?
How do you move the graph around in the chart window?
What are the three tabs available under Chart Tools?
You’ll have an opportunity before you leave to print of a plot
See handout
Ctrl C to cut graphs & Ctrl V to paste
Print Screen to capture entire monitor view
Fn+Alt+Print Screen to capture the active dialog window
Ctrl V to paste
0adA A e
)1(0
DFCC
Evaluate the logs of these two functions
What base do you need to use?
Does the age depth relationship in the North Sea suggest that an
exponential age/depth relationship exists in the area?
Put it to the test in Excel- If the relationship follows an exponential
growth function, then the ln or log of Age should transform the
relationship into a linear one.
)1(0
DFCC
C0 is the initial concentration of the element in the liquid before crystallization began,
F is the fraction of liquid remaining and
D is a constant (known as the distribution coefficient).
Calculate the concentration of an element after 50% crystallization (i.e. F = 0.5) if its initial concentration was 200ppm and D=6.5.
We’re going to take a slightly different approach to the solution of Problem 2.12 that will take advantage of the computer resources and provide a more comprehensive evaluation of the concentration liquid fraction relationship.
Rather than solving C for just one value of F let's solve C for a range of Fs extending from 0 to 1 at intervals of 0.05.
F is our independent variable, so for starters, we need to create a column of numbers
corresponding to remaining liquid fraction that run from 0 to 1 at intervals of 0.05
Select, Click and Drag Down to Fill
Assign a variable name
In cell B2 enter the formula =CO*A2^(D-1)
1. Present your graph.
2. Present hand calculations of the concentration after 50% crystallization.
3. Using your calculated data tables compare the change in concentration from 85% to 75% liquid fraction with that occurring between 55% and 45%
As the result of today’s lab you should know how to do the following:
Enter data
Graph data
Format and style graphical output for presentation
Transform exponential functions into linear functions
Assign variable names to specific cells in Excel
How do you bring in your data?
How do you plot your data?
How can you change the plot line style (color, thickness, continuous or dashed…)?
How can you change the data point display style (marker line style, line color, …)?
How do you get back to the Chart Tools?
How do you change the chart layout?
How do you format gridlines, chart axes?
How can you add a chart title?
How do you move the graph around in the chart window?
What are the three tabs available under Chart Tools?
Depth (cm)
0 50 100 150 200 250 300 350 400
Ag
e (
Ye
ars
BP
)
0
5000
10000
15000
DataDepth Age20 1500400 10000
log (F)
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0
log
(C)
-4
-3
-2
-1
0
1
2
3
On the class web page see http://www.geo.wvu.edu/~wilson/geomath/lab1/PresentationOutlineCPS1.pdf
• Hand in Warm-Up 2 problems Today
• Hand in problems 2.11 and 2.12 on Thursday
• Look over problem 2.13 for Thursday
• Bring Questions and Continue your reading
For today and Thursday ….
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