1. Geology 351 - Geomath Tom Wilson, Department of Geology and Geography tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Estimating the coefficients of linear, exponential, polynomial, logarithmic, and power law expressions

2. Items due today Tom Wilson, Department of Geology and Geography If you haven’t already, hand in any outstanding isostacy problems we’ve been working through in class. Problems 3.10 and 3.11 are due today along with The settling velocity problem

3. 3.10 & 3.11 Hand in at the beginning of class Tom Wilson, Department of Geology and Geography

4. Settling velocity, lake depth and velocity settling time relationship – hand in before leaving Tom Wilson, Department of Geology and Geography

5. For today Tom Wilson, Department of Geology and Geography Show how to use the computer to estimate the coefficients of various quantitative relationships in geology. We’ll run through some examples to get you started. These include: the linear age-depth relationship discussed by Waltham the exponential porosity-depth relationship polynomial relationship between temperature and depth and general power law relationships such as the Gutenberg-Richter relation

6. Get started on Problems 4.7 and 4.10 Tom Wilson, Department of Geology and Geography Problem 4.7 considers the relationship between bottomset bed thickness and distance from the foot of the delta (an option in the fitting lab assignment), and 4.10 involves some basic practice with units. Although we may not get these returned prior to the test they include efforts on topics already discussed and serve as good pre-test review. We should be able to discuss these in class next Tuesday. The due date will however, be delayed till Tuesday, March 4 th.

7. Today we take a closer look at several familiar quantitative models using Excel Tom Wilson, Department of Geology and Geography The thickness of a bottomset bed at the foot of a delta can often be well approximated by Where t is the thickness, x is the distance from the bottomset bed start and t 0 and X are constants. Problem 4.7

8. Curve fitting: testing the viability of your mathematical model Tom Wilson, Department of Geology and Geography Is this processes accurately represented using an exponential decay model? What are the constants in the relationship (i.e. X and t o ).

9. Tom Wilson, Department of Geology and Geography Original data showing drawdown during pumping and recovery after pumping ceased. Recovery phase data after transformation, which includes a log transformation of the observation times. Where else does line fitting come in handy? Basic pump test data

10. Evaluating lateral well path placement and steering Tom Wilson, Department of Geology and Geography

11. Data from laterals enhances accuracy of structure contour maps Tom Wilson, Department of Geology and Geography

12. Residual track relative to the regression line for a horizontal well Landing the drill string: trial and error

13. Some due dates to put on the calendar Tom Wilson, Department of Geology and Geography Due date for problems 4.7 and 4.10 will be delayed till March 4, however, basic ideas associated with these problems will be included in the mid term, so make sure you understand both these problems. Computer lab – Estimating coefficients of various mathematical relationships in geology will be due next Thursday, March 6. I’ll hand out a practice test this Thursday that you can review for a test review session next Tuesday (February 25 th ). start reading Chapter 8 – Differential Calculus

14. 4.7 and 4.10 – Quick Look Tom Wilson, Department of Geology and Geography 4.7 Bottom set bed thickness (t) versus distance from the delta toe.. 1)Rearrange into an expression for ln (t o ) 2)Solve for X 3)Estimate t at specified x. Units always require our attention and in problem 4.10 you have several equations such as i)Age=(Depth x Rate)+Age at top Are the units on the left (time) matched by those on the right?

15. Tom Wilson, Department of Geology and Geography Estimating the coefficients of various Mathematical relationships in Geology