tom.h.wilsontom.wilson@mail.wvu.

eduDept. Geology and

GeographyWest Virginia University

2 2400 800400

3 3

z zr km

IntegrationReview the problems in the text and homework.

1. Volume of Mt. Fuji; where

lf

li

f

i

l

l

dl

l

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.

Evaluate

11,000 kg/m3

We can simplify the problem and still obtain a useful result.

Approximate the average densities

4,500 kg/m3

2

04

RM r dr

3. Be able to integrate the discontinuous function used to approximate internal density contrast and mass distribution within the Earth’s interior.

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

Be able to calculate the total heat generated in a given volume by an object with a specified

heat generation rate.

320

z kWQ

km

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

2500

3000

3500

2500

35003000

2000

4000

100 feet

~625’=N69W

Now, how would you calculate the dip?

highest

lowest

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

2000’

625’

~73

If the thickness of a dipping bed intersected by a vertical well is 100’, what is the actual bed-normal

thickness of the layer?

100’

Actual thickness = ?

=73o

What is this angle?

100

’

Apparent thickness

T, the actual thickness?

=17o

100sin(17)

29.24 '

T

T

max 1t

S S e

0

max

1max max max

2 2max max max

(0) 1 0

( ) 1 1 1 0.37

(2 ) 1 1 1 0.14

S S e

S S e S e S

S S e S e S

What is S at t=0, , and 2

You can get a good sense of the shape of this curve just by plotting up these three values

A look at some select problems from the review sheet handed out in class Tuesday

1.

max0.63S S

max0.86S S

0S

maxtSdS

edt

0max max

max max

2max max

( 0)

( )0.37

( 2 )0.14

S SdS te

dtS SdS t

edt

S SdS te

dt

max 2.50.083

30

S

For =30My and Smax=2.5km

Evaluating sedimentation rate: taking the derivative

0s X

sX x

0 1400

40

s X

X

0 1400

40

s Xs

X x x

Substitute in for the constant terms

2.

0 0, at x s s

0 0

0

s X s Xs

X X

1400

(5) 4040 5

s ppt

1400

(10) 46.640 10

s ppt

1400

(15) 5640 15

s ppt

1400

(20) 7040 20

s ppt

Since ds s

dx X x

( 10) 46.6

1.5630

ds x s ppt

dx X x km

( 15) 562.25

30

ds x s ppt

dx X x km

Differentiate the radioactivity relationship to evaluate the rate of radioactivity decay

0Given , evaluate t daa a e

dt

00

tt d tda e

a edt dt

Recall this derivative equals the original function times the derivative of the terms in the exponent; thus,

00

ttda e

a edt

In this particular problem is given as 0.1My-1

What would a sketch of these two functions look like?

3.

Solve for t in the following relationship

0ta a e

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?

7.

Given the following 10.

2

GMg

r

in which the units of

2

2

mg

sM kg

r m

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.