12
Statistical Methods for Estimating Petroleum Resources
outcome and a small number for an unlikely one). In other words, all
the porosity values of a formation will be associated with a probability
that describes their likelihood of occurrence. All these values and their
probabilities form a probability distribution.
We know the probability associated with each value, but we may not
be able to explain the process that leads to the distribution. This class
of physical phenomenon (a so-called random phenomenon), behaves
“randomly” according to a probability distribution. Therefore, if a
specimen from a given formation is sampled and we wish to predict
the value of a particular variable for that sample, then the probability
distribution of that variable must be known.
One of the steps in resource evaluation is to estimate the probability distributions of geological random variables. There are two types of
distributions: discrete and continuous. Let us take, for example, a fi nite
number of pools in a play. Certainly all pools constitute a fi nite population and will exhibit a discrete distribution (Fig. 2.4A). On the other hand,
pool values can be thought of as coming from an infi nite population that
has a continuous probability distribution. This continuous probability
distribution is called a superpopulation distribution (Fig. 2.4B).
In cases when we have a random sample or a very large sample
set collected from a geological population, normal statistics can be
used to construct a probability distribution of the population. For
example, 406 porosity values have been obtained from the Lower
Mannville Formation of the Western Canada Sedimentary Basin. This
0.001
0
50
100
A
B
0.01 0.1
POOL SIZE, 10 6 m 3
1
1.0
0.001
0
50
100
0.01
0.1
POOL SIZE, 10 6 m 3
1
10
100
CUMULATIVE FREQUENCY
GREATER THAN
Figure 2.4. Examples of probability distributions. (A) Discrete distribution.
(B) Continuous distribution.
Statistical Methods for Estimating Petroleum Resources
outcome and a small number for an unlikely one). In other words, all
the porosity values of a formation will be associated with a probability
that describes their likelihood of occurrence. All these values and their
probabilities form a probability distribution.
We know the probability associated with each value, but we may not
be able to explain the process that leads to the distribution. This class
of physical phenomenon (a so-called random phenomenon), behaves
“randomly” according to a probability distribution. Therefore, if a
specimen from a given formation is sampled and we wish to predict
the value of a particular variable for that sample, then the probability
distribution of that variable must be known.
One of the steps in resource evaluation is to estimate the probability distributions of geological random variables. There are two types of
distributions: discrete and continuous. Let us take, for example, a fi nite
number of pools in a play. Certainly all pools constitute a fi nite population and will exhibit a discrete distribution (Fig. 2.4A). On the other hand,
pool values can be thought of as coming from an infi nite population that
has a continuous probability distribution. This continuous probability
distribution is called a superpopulation distribution (Fig. 2.4B).
In cases when we have a random sample or a very large sample
set collected from a geological population, normal statistics can be
used to construct a probability distribution of the population. For
example, 406 porosity values have been obtained from the Lower
Mannville Formation of the Western Canada Sedimentary Basin. This
0.001
0
50
100
A
B
0.01 0.1
POOL SIZE, 10 6 m 3
1
1.0
0.001
0
50
100
0.01
0.1
POOL SIZE, 10 6 m 3
1
10
100
CUMULATIVE FREQUENCY
GREATER THAN
Figure 2.4. Examples of probability distributions. (A) Discrete distribution.
(B) Continuous distribution.