Geoscience Reference
In-Depth Information
Table 3.1 Run 1 in computer
simulation experiment
˄
t
(x
¼
t-4.6)
z
P
log
e
P
4.587 A
4.380
-0.220
0.220
0.5871
-0.5325
7.800 B
8.048
3.448
3.448
2.124 A
2.193
-2.407
2.407
0.9920
-0.0081
0.668 A
2.239
-2.361
2.361
0.9909
-0.0092
6.225 B
5.802
1.202
1.202
0.8853
-0.1218
9.990 B
9.945
5.345
5.345
4.896 A
4.574
-0.026
0.026
0.5102
-0.6730
4.606 A*
6.487
1.887
-1.887
0.0296
-3.5211
0.796 A
0.553
-4.047
4.047
1.855 A
2.526
-2.074
2.074
0.9810
-0.0192
6.292 B
6.923
2.323
2.323
0.9899
-0.0101
3.280 A
1.998
-2.602
2.602
0.9954
-0.0046
2.422 A
1.435
-3.165
3.165
1.397 A
0.912
-3.688
3.688
4.538 A
4.365
-0.235
0.235
0.5928
-0.5230
0.830 A
0.803
-3.797
3.797
6.194 B*
4.033
-0.567
-0.567
0.2854
-1.2540
4.545 A
3.930
-0.670
0.670
0.7490
-0.2890
4.774 A*
4.814
0.214
-0.214
0.4154
-0.8786
0.905 A
0.713
-3.887
3.887
9.763 B
11.197
8.285 B
8.902
4.302
4.302
3.131 A
3.676
-0.924
0.924
0.8224
-0.1955
9.987 B
9.435
4.835
4.835
9.442 B
9.620
5.020
5.020
Total ¼ -8.0397
True dates
t
were classied as A (younger) or B (older) than
5 representing true age of stage boundary. Dates
t
with measure-
ment error are compared to trial age (
t
e
¼ 4.6). Inconsistent ages
are indicated by asterisks.
Z
¼
x
for younger rocks (A) and
z
¼
x
for older rocks (B). Standard
z
-value is fractile of probability
P
. Total of logs of
P
gives value of log-likelihood function for
t
e
¼4.6 (Source: Agterberg
1990
, Table 3.2)
These numbers with uniform frequency distribution can be regarded as true dates
(
mid-point
of interval). Results of two runs (1 and 7) are taken for example here. Values of
˄
) without measurement errors. The stage boundary was set equal to 5 (
¼
˄
less than 5 belong to the younger stage A, and those greater than 5 to the older stage
B (Table
3.1
). The measurement error was introduced by adding to
a normal
random number with zero mean and standard deviation equal to one. As a result of
this, each value of
˄
was changed into a date
t
. Some values of
t
ended up outside the
interval [0, 10], like 11.197 for Run 1 (Fig.
3.4
and Table
3.1
), and were not used
later. In Run 1, a single date for the younger stage (A) has
t
˄
>
5, and a date for B has
t
5. Suppose now, for example, that the trial age of the stage boundary
t
e
is set
equal to 4.6. Then there are three inconsistent ages for run No. 1 and these are
marked by asterisks in Table
3.1
. Each normalized date
x
<
¼
t
t
e
was converted into
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