Evaluation Models
17
population. Therefore, an adequate play defi nition would ensure that
the subsequent statistical analyses are valid.
A play might contain many, few, or no discoveries at the time of
evaluation. A play lacking discoveries (a conceptual play), or one containing few discoveries, is analyzed using the pool-size equation (see
Chapter 5). If a play has suffi cient discoveries (such as those shown
in the lower right-hand corner of Fig. 2.7), there are two statistical
approaches that can be applied to estimate the sizes of the remaining
undiscovered pools.
The fi rst approach, called the superpopulation approach (Baecher,
1979; Cassel et al., 1977; Cochran, 1939), is used to estimate the continuous pool-size distribution and the discrete number-of-pools distribution. The superpopulation approach views a play (the fi nite
population) as one of the possible cases from the geological model
(the infi nite population or superpopulation), and has been described
by Kaufman et al. (1975). The second approach is to estimate the play
(upper right-hand corner of Fig. 2.7) without using the superpopulation concept. The play has a fi nite number of pools and a discrete poolsize distribution. This approach is called the fi nite population approach.
Examples for adopting the fi nite population approach include the Arps
and Roberts method (Arps and Roberts, 1958); Kaufman’s anchored
method (Kaufman, 1986); Bickel, Nair, and Wang’s nonparametric
fi nite population method (Bickel et al., 1992); and the geo-anchored
method (Chen, 1993; Chen and Sinding–Larsen, 1992). In this book,
both the superpopulation and the fi nite population approaches are discussed in chapters 3, 4, and 7.
When the superpopulation pool-size distribution and the numberof-pools distribution have been estimated, the individual pool sizes of
the play can be estimated from order statistics, as shown in the lower
left-hand corner of Figure 2.7. The boxes that express the estimation
intervals can be matched with the current discoveries (shown in the
lower right-hand corner). This matching process is one of several feedback mechanisms provided by PETRIMES that allow geological interpretations to be combined with statistical analysis.
In the following chapters, PETRIMES evaluation methods are validated using tested populations generated by known population parameters such as means and variances. The procedure for generating a fi nite
number of pools from a superpopulation is described as follows:
A hypothetical superpopulation with known mean and vari•
ance is assigned a probability distribution, such as the Pareto,
17
population. Therefore, an adequate play defi nition would ensure that
the subsequent statistical analyses are valid.
A play might contain many, few, or no discoveries at the time of
evaluation. A play lacking discoveries (a conceptual play), or one containing few discoveries, is analyzed using the pool-size equation (see
Chapter 5). If a play has suffi cient discoveries (such as those shown
in the lower right-hand corner of Fig. 2.7), there are two statistical
approaches that can be applied to estimate the sizes of the remaining
undiscovered pools.
The fi rst approach, called the superpopulation approach (Baecher,
1979; Cassel et al., 1977; Cochran, 1939), is used to estimate the continuous pool-size distribution and the discrete number-of-pools distribution. The superpopulation approach views a play (the fi nite
population) as one of the possible cases from the geological model
(the infi nite population or superpopulation), and has been described
by Kaufman et al. (1975). The second approach is to estimate the play
(upper right-hand corner of Fig. 2.7) without using the superpopulation concept. The play has a fi nite number of pools and a discrete poolsize distribution. This approach is called the fi nite population approach.
Examples for adopting the fi nite population approach include the Arps
and Roberts method (Arps and Roberts, 1958); Kaufman’s anchored
method (Kaufman, 1986); Bickel, Nair, and Wang’s nonparametric
fi nite population method (Bickel et al., 1992); and the geo-anchored
method (Chen, 1993; Chen and Sinding–Larsen, 1992). In this book,
both the superpopulation and the fi nite population approaches are discussed in chapters 3, 4, and 7.
When the superpopulation pool-size distribution and the numberof-pools distribution have been estimated, the individual pool sizes of
the play can be estimated from order statistics, as shown in the lower
left-hand corner of Figure 2.7. The boxes that express the estimation
intervals can be matched with the current discoveries (shown in the
lower right-hand corner). This matching process is one of several feedback mechanisms provided by PETRIMES that allow geological interpretations to be combined with statistical analysis.
In the following chapters, PETRIMES evaluation methods are validated using tested populations generated by known population parameters such as means and variances. The procedure for generating a fi nite
number of pools from a superpopulation is described as follows:
A hypothetical superpopulation with known mean and vari•
ance is assigned a probability distribution, such as the Pareto,