Page 102 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 4

Table 4-4. Successive lithologic states encountered in a drill hole through
the Coal Measures in the Midland Valley of Scotland (after Doveton,
1971); mutually exclusive states are barren shale (A), shale with fossils
of nonmarine bivalves (B), siltstone (C), sandstone (D), and coal or
root zone (E); read across rows. Data are in file MIDLAND.TXT.
TOP -

BEAEADACDCDCABEADCDCDCAE
DCADCA ECDCB EADCDCDCABA ED
CA ECAD EADACAB EADCA ECDCA B
A EAD EADC EACDCDCDCA B EA BA B
A B EA BACACA BA B EACDCDCDCAC
B EACACB ECADCACDCEACDACDC
BA B EACDCABAB EADAC EADADCA
EACDA EA EACDC ECABC ECADB EA
DCD EADACA B EA BA B EA BA B ECAC
DAEACDCDCACACEACDCDCABEA
DEACDCDECDCEACAEACAEACAB
CDA EACDC EACB EACA EADAB EAC
D EADCAB EADCD EADCDA EACDCA
DAEADADCACEDABDBAEACAECD
CDCDAEAECDABEABEAEACDEAD
ADECDCAEAEACDAECDBEADCDC
ADA BA B EAD BA EA - Bottom

others. The data are taken from one of a large number of wells studied by Doveton
(1971).
The four-state transition frequency matrix for the section in the Scottish well
is given below. One obvious difference between this matrix and the one we have
considered previously is that all the diagonal terms must be zero, since a state
cannot succeed itself. The transition probability matrix, computed by dividing each
element of the transition frequency matrix by the appropriate row total, shares
this same characteristic. Sequences in which transitions from a state to itself are
not permitted are called embedded Mavkov chains, and their analysis presents
special problems that have not always been appreciated by geologists studying
stratigraphic records.
to
A B C D E Z Z s
A- 0 13 36 19 52- 120
B29054O 38
from c 35 2 0 45 12 94
D 29 1 44 0 3 77
E 26 23 9 9 0 67

The lithologic states have been coded as (A) unfossiliferous shale and mudstone,
(B) shales containing nonmarine bivalves, (C) siltstone, (D) sandstone, and (E) coals
and root zones. The corresponding transition probability matrix is

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