geology 351 - geomath tom wilson, department of geology and geography tom.h.wilson...
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Geology 351 - Geomath
Tom Wilson, Department of Geology and Geography
Department of Geology and GeographyWest Virginia University
Morgantown, WV
Estimating the coefficients of linear, exponential, polynomial, logarithmic, and
power law expressions
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
3.10 & 3.11 Hand in at the beginning of class
Tom Wilson, Department of Geology and Geography
Settling velocity, lake depth and velocity settling time relationship – hand in before leaving
Tom Wilson, Department of Geology and Geography
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
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 4th.
Today we take a closer look at several familiar quantitative models using Excel
Tom Wilson, Department of Geology and Geography
/0
x Xt t eThe 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 t0 and X are constants.
Problem 4.7
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 to) .
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.
Pump Test Data0
10
20
30
40
50
S (ft)
-2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0
LOGT (days)
RecoveryPumping
Compute slope in this regionfor the pumping stage analysis
Recovery Phase Water Level Response
0.2 0.4 0.6 0.8 1.0 1.2 1.4
LOGTRAT
15
20
25
30
35
40
45
50
sa (ft)
Fit a straight line to the points in this region
Where else does line fitting come in handy? Basic pump test data
Evaluating lateral well path placement and steering
Tom Wilson, Department of Geology and Geography
Data from laterals enhances accuracy of structure contour maps
Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
MH5 East Lateral
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
0 100 200 300 400 500 600
Distance (meters)
Dep
th S
ub
surf
ace
(fee
t)
Main Track
Exit 2
Exit 3
Exit 1
Residual track relative to the regression line for a horizontal well
Landing the drill string: trial and error
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 25th).
• start reading Chapter 8 – Differential Calculus
4.7 and 4.10 – Quick Look
Tom Wilson, Department of Geology and Geography
xX
ot t e
4.7 Bottom set bed thickness (t) versus distance from the delta toe ..
1) Rearrange into an expression for ln (to)2) Solve for X3) 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 topAre the units on the left (time) matched by those on the right?
Tom Wilson, Department of Geology and Geography
Estimating the coefficients of various Mathematical relationships in Geology