P1: OTA/XYZ P2: ABC
JWST061-11 JWST061-Caers April 7, 2011 13:26 Printer Name: Yet to Come
204 CH 11 VALUE OF INFORMATION
Many types of spatial decisions exist in the Earth Sciences. In oil recovery, different
development schemes (where to drill wells and what kind of wells) represent different
possible actions or alternatives a to the decision of how to develop a particular field. In
mining, several alternative mine plans represent such actions or several clean up strategies
for a polluted site. Therefore, the outcome expressed in terms of value will be a combina-
tion of the action taken (the chosen development scheme) and the Earth response to these
actions (the amount of oil/ore recovered). The possible alternative actions are indexed by
a = 1, ..., A, with A being the total number of alternative actions, and the action taken on
the Earth is represented as function g
a
. Since the true subsurface properties are unknown,
the action g
a
is simulated on the generated models z
(t)
() such that:
v
(t)
a
() = g
a
(z
(t)
()) a = 1,...,At= 1,...,T .
Note that the value v
(t)
a
is a scalar. As discussed in Chapter 4, value can be expressed
in a variety of terms; however, monetary units (usually expressed in net present value,
NPV) are conceptually the most straightforward.
For any situation, the decision alternative that results in the best possible outcome
should be chosen. However, this is difficult to determine in advance because of uncer-
tainty regarding how the Earth will react to any proposed action. The values in the above
equation could vary substantially due to such uncertainty. Based on that variation we de-
termine the value without data V
without data
in the case where has two categories
1
and
2
as follows:
V
without data
= max
a
⎛
⎝
2
i=1
P( =
i
)
1
T
i
T
i
t=1
v
(t)
a
(
i
)
⎞
⎠
a = 1,...,A
Analyzing this equation a bit more:
r
1
T
i
T
i
t=1
v
(t)
a
(
i
) is the average value (in $) for that action (e.g., clean up) and for that value
of (e.g., fluvial depositional system exists).
r
2
i=1
P( =
i
)
1
T
i
T
i
t=1
v
(t)
a
(
i
) is the expected value of that average because the prior prob-
abilities for may not be equal.
r
max
a
: takes the maximum over all the actions of this expected value.
P( =
i
) represents the prior uncertainty for geologic input parameter
i
and T
is
the number of Earth models generated when =
i
. The computation of V
prior
to N