Geomath Geology 351 - Final Review - Part 2 tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University

Integrals Integration Review the problems in the text and homework. 1. Volume of Mt. Fuji; where

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

3. Be able to integrate the discontinuous function used to approximate internal density contrast and mass distribution within the Earth’s interior. 11,000 kg/m3 We can simplify the problem and still obtain a useful result. Approximate the average densities 4,500 kg/m3 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.

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? 3500 3000 2000 4000 =N69W ~625’ highest lowest 3500 3000 2500 2500 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’ What is this angle? =73o

T, the actual thickness? 100’ Apparent thickness =17o

You can get a good sense of the shape of this A look at some select problems from the review sheet handed out in class Tuesday 1. 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

Evaluating sedimentation rate: taking the derivative For =30My and Smax=2.5km

Substitute in for the constant terms 2. Substitute in for the constant terms

Salinity Variations

Salinity Gradients Since

In this particular problem  is given as 0.1My-1 Differentiate the radioactivity relationship to evaluate the rate of radioactivity decay 3. Recall this derivative equals the original function times the derivative of the terms in the exponent; thus, In this particular problem  is given as 0.1My-1 What would a sketch of these two functions look like?

The difficulty with this one is that the t is in the exponent. 7. Solve for t in the following relationship 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 in which the units of 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 10m

The exam is on Wednesday from 3 to 5pm Final Exam 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. Study hard & Good luck!