42
Statistical Methods for Estimating Petroleum Resources
of a pool. If the porosity has no impact on the order of discovery, β 3
would be close to zero. In principle, many different functional forms
can be included here for the magnitude. Time-dependent factors, such
as the price of oil, land availability, company, and level of geological
knowledge about the play can also be included.
Under the successive sampling discovery model, the play under study
is considered to be a statistical population consisting of N oil and gas
pools with magnitudes W 1 , W 2 , … , W N . First, it assumes that the W 1 ’s
are generated independently and identically according to a superpopulation distribution F that is assumed to be lognormally distributed in
this case. Second, given the magnitudes, W i , i = 1, 2, … , N, the model
assumes that the probability of discovering pools with magnitudes
W 1 , … , W n fi rst and in that order is
=
+ +
∏
1
···
n
j
j
j
N
W
W
W
. The magnitude is
usually taken to be the area or the volume of a pool.
Let y 1 , … , y N with y i = ( y i1 , … , y ik )
T be the values associated with
the N pools of a fi nite population that are available for discovery. We
assume that the y i ’s are generated independently and identically from
a multivariate lognormal distribution F θ with θ = ( μ, Σ). Let F θ denote
the cumulative function and f θ denote the density function. The aim is
to estimate the unknown parameter θ.
Table 3.2. Examples of Various Plays Characterized by the Parameters μ,
σ
2 , and N
Population parameters
Plays
μ
σ
2
N
Large Large Large
Cretaceous plays, West Siberia Basin
Devonian plays, Volga–Ural Basin
Large Small Large
Middle Jurassic play, Viking Graben, North Sea
Small Large Small
Beaverhill Lake and Rimbey–Meadowbrook reef
plays, Western Canada Sedimentary Basin
Small Small Large
Mannville plays, Keg River plays, Western
Canada Sedimentary Basin
Small Small Small
Jurassic and Triassic plays, Western Canada
Sedimentary Basin
Small Large Large
Devonian clastic play, Western Canada
Sedimentary Basin
Statistical Methods for Estimating Petroleum Resources
of a pool. If the porosity has no impact on the order of discovery, β 3
would be close to zero. In principle, many different functional forms
can be included here for the magnitude. Time-dependent factors, such
as the price of oil, land availability, company, and level of geological
knowledge about the play can also be included.
Under the successive sampling discovery model, the play under study
is considered to be a statistical population consisting of N oil and gas
pools with magnitudes W 1 , W 2 , … , W N . First, it assumes that the W 1 ’s
are generated independently and identically according to a superpopulation distribution F that is assumed to be lognormally distributed in
this case. Second, given the magnitudes, W i , i = 1, 2, … , N, the model
assumes that the probability of discovering pools with magnitudes
W 1 , … , W n fi rst and in that order is
=
+ +
∏
1
···
n
j
j
j
N
W
W
W
. The magnitude is
usually taken to be the area or the volume of a pool.
Let y 1 , … , y N with y i = ( y i1 , … , y ik )
T be the values associated with
the N pools of a fi nite population that are available for discovery. We
assume that the y i ’s are generated independently and identically from
a multivariate lognormal distribution F θ with θ = ( μ, Σ). Let F θ denote
the cumulative function and f θ denote the density function. The aim is
to estimate the unknown parameter θ.
Table 3.2. Examples of Various Plays Characterized by the Parameters μ,
σ
2 , and N
Population parameters
Plays
μ
σ
2
N
Large Large Large
Cretaceous plays, West Siberia Basin
Devonian plays, Volga–Ural Basin
Large Small Large
Middle Jurassic play, Viking Graben, North Sea
Small Large Small
Beaverhill Lake and Rimbey–Meadowbrook reef
plays, Western Canada Sedimentary Basin
Small Small Large
Mannville plays, Keg River plays, Western
Canada Sedimentary Basin
Small Small Small
Jurassic and Triassic plays, Western Canada
Sedimentary Basin
Small Large Large
Devonian clastic play, Western Canada
Sedimentary Basin