More about Discovery Process Models
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and shifted Pareto, Weibull, one-parameter exponential, and twoparameter exponential.
The Beaverhill Lake Play
For the Beaverhill Lake play, all distributions were hypothesized
and fi tted to the nonparametric equation as displayed previously in
Figure 3.6, line B. The Q–Q plot results for these tests are displayed in
fi gures 4.20 and 4.21. The assessment of the distributional assumption
is summarized as follows:
The Beaverhill Lake data set has a longer tail than that of the
1.
distributions of normal, power normal (with power = 0.5), uniform, gamma (with shape factor = 5 to 0.01), one-parameter
exponential, and two-parameter exponential.
The Q–Q plots for the truncated and shifted Pareto distribu2.
tion display an S shape. This means that the tail of the distribution is longer than that of the data set.
The lognormal, Weibull, and power normal (with
3.
power = 0.001) distributions might have a slightly longer tail
than that of the data set. However, the lognormal is a better
choice if one has to use a prior distribution. Statistics for
the straight line fi tted to various distributions are listed in
Table 4.6. From this, one can judge which one or two distributions are better for a specifi c play. The nonparametric
discrete distribution of Figure 3.6, line B is approximated by
a continuous lognormal distribution that is used to estimate
individual pool sizes.
Furthermore, PETRIMES can estimate the ratio from the empirical pool-size distribution by computing the shape factor, θ, value. An
example is presented by Lee and Gill (1999).
Plays from Worldwide Basins
The Western Canada Sedimentary Basin provides a vast and valuable
information source to test the adequacy of probability distributions.
Gas plays that have been tested by the nonparametric model include the
Devonian (Reinson et al., 1993), Mississippian and Permian (Barclay
et al., 1997), Triassic (Bird et al., 1994), and Foothills (Lee et al., 1995;
Osadetz et al., 1995). More data sets obtained from worldwide basins
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