Complexity of the Geological Framework and Use of Mathematics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 36

Fig. 1.22 Examples of ˉ ijk : ˉ ¼ 2 ʳ 121 , and ˉ ¼ ʳ α 27 ( cf . Fig. 1.20 and Table 1.1 )

121 127 127

(Source: Agterberg 1994 , Fig. 6)

polygon become short. In that situation, the solution is almost entirely determined
by the relation

r ij h ik ! ˉ ijk ¼ 0 ; r ij > ˉ ijk ¼ ʸ ik

An example of application is given in Figs. 1.23 and 1.24 . It is concerned with
the Leduc Reef Complex-Windfall Play in Alberta ( cf . Reinson et al. 1993 ; Kauf-
man and Lee 1992 ). This play has 249 wildcats including 52 gas discovery wells.
The play boundary was digitized in vector mode yielding a data set with coordinates
for 249 vertices (Agterberg 1994 ). The area enclosed by the polygon is 12,861 km 2
(15,616 km 2 if the smaller polygon in the center is included in the play). Figure 1.24
shows the function L 2 ( r ) which is for the 52 gas discovery wells only. This function
deviates significantly from a straight line through the origin that dips 45
representing complete random distribution of the gas wells within the play area.
Obviously they are strongly clustered. This is brought out by the 95 confidence belt
for the Poisson model that would probably contain the entire L 2 ( r ) curve if the
spatial random distribution model would be satisfied.