Transcript Slide 1

tom.h.wilson
[email protected]
Dept. Geology and Geography
West Virginia University
Integration
Review the problems in the text and homework.
1. Volume of Mt. Fuji; where
r2 
400 z 800 z

 400km2
3
3
2. Determination of the true or total natural strain
evaluated from some initial pre-deformed state to
some final deformed state in a series of infinitesimal
contractions or extensions occurring over a long time period.
li
lf
Evaluate
 
lf
li
dl
l
3. Be able to integrate the discontinuous function used to
approximate internal density contrast and mass distribution
within the Earth’s interior.
We can simplify the problem and still obtain a useful result.
Approximate the average densities
11,000
kg/m3
4,500
kg/m3
R
M   4 r 2  dr
0
Be able to describe what the above integral represents
and how the mass is being calculated; i.e. be able to
discuss the geometry of the problem.
4. Heat flow problems surrounding the basic definition
z kW
Q
20 km3
Be able to calculate the total heat generated in
a given volume by an object with a specified
heat generation rate.
5. Understand problems 9.9 and 9.10.
Refer to your notes from Tuesday’s class
Discussions of problems 1 through 4 are found in the text with
additional material presented in class slides.
See http://www.geo.wvu.edu/~wilson/geomath/FinalReview-P1.pdf
Now, how would you
calculate the dip?
highest
=N69W
~625’
3500
3000
2500
lowest
100 feet
In the preceding slide we showed that the
horizontal distance in the dip direction between
control points subsurface formation depths relative
to sea level of 2000 and 4000 feet is ~625 feet
~73
2000’
625’
If the thickness of a dipping bed intersected by a
vertical well is 100’, what is the actual bed-normal
thickness of the layer?

Actual thickness = ?
100’
=73o
What is this angle?
T, the actual
thickness?
Apparent
thickness
100’
T  100sin(17)
T  29.24 '
=17o
A look at some select problems from the
review sheet handed out in class Tuesday

S  S max 1  e
1.
t


What is S at t=0, , and 2
S ( )  S max
S 0
 0
S  0.63S
1  e   S 1  e   S 1  0.37 
S  0.86S
1  e   S 1  e   S 1  0.14
S (0)  S max 1  e
S (2 )  S max
0


max
1

max
2
max
2

max
max
You can get a good sense of the shape of this
curve just by plotting up these three values
max
Evaluating sedimentation rate: taking the derivative
dS S max  t 

e
dt

For =30My and Smax=2.5km
dS (t  0) Smax 0 Smax

e 
dt


Smax
dS (t   ) Smax  

e  0.37
dt


Smax
dS (t  2 ) Smax 2 

e
 0.14
dt


Smax

2.5

 0.083
30
2.
s0 X
s
 X  x 
Substitute in for the constant terms
s0 X  1400
 X  40
s0 X
1400
s

 X  x   40  x 
s0 X
s0 X
s

 X  0  X
at x  0, s  s0
1400
s(5) 
 40 ppt
 40  5
1400
 46.6 ppt
 40  10
1400
s(15) 
 56 ppt
 40 15
s(10) 
1400
s(20) 
 70 ppt
 40  20
Since
ds
s

dx  X  x
ds ( x  10)
s
46.6
ppt


 1.56
dx
 X  x 30
km
ds ( x  15)
s
56
ppt


 2.25
dx
 X  x 30
km
3.
Differentiate the radioactivity relationship
to evaluate the rate of radioactivity decay
Given a  a0 e  t , evaluate
da
dt
Recall this derivative equals the original function times the
derivative of the terms in the exponent; thus,
d   t 
da0e t
 a0e t
dt
dt
da0e t
  a0e t
dt
In this particular problem  is given as 0.1My-1
What would a sketch of these two functions look like?
7.
Solve for t in the following relationship
t
a  a0e
The difficulty with this one is that the t is in the
exponent.
So what math operation brings out the
exponent (or power a base is raised to) and will
allow us to solve for t in this case?
10.
Given the following
GM
g 2
r
in which the units of
m
g  2
s
 M   kg
 r   m2
determine the units of G
13. You are mapping the geology of an area and you
run across limited exposure of a sandstone interval
near the crest of a steep hill as shown below. The
topographic surface dips at 40 degrees left relative to
the horizontal, and the formation dips 80 degrees to
the right. What is the thickness of this formation?
10m
The exam is on Wednesday from 3 to 5pm
If you have any questions don’t hesitate
to drop by my office or send e-mail. Office
visits are preferred since we can draw
things on the boards. Let me know ahead
of time if you plan on visiting.