GG413 Geological Data Analysis
Homework #10: Markov Chains
Reading: Sections 5.1, Due Tue Nov. 11.
As usual please be as complete and concise in explaining your thought process in
solving each problem below.
The stratigraphic column to the right represents a lithologic sequence as a
function of depth (in feet) taken from a delta plain. We identify four lithologies:
A-sandstone (dotted), B-siltstone (gray), C-clay (dashed), and D-coal (black).
1) For transitions occurring every foot, what is the transition frequency matrix
T for this sequence?
2) Determine the fixed probability vector f and the transition probability matrix
P.
3) At the 95% confidence level, are the lithologies at each depth completely
independent of the lithologies 1 foot apart? Be sure to state your null
hypothesis and perform the appropriate test.
4) At the 95% confidence level, are the lithologies at each depth completely
independent of the lithologies 2 feet apart?
5) What about lithologies 3 and 4 feet separated?
6) What are the probabilities for each of A, B, C, D being present at depth of
102 ft (i.e., 2 feet below the bottom-most part of the section, which is known
to be clay?
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