Geoscience Reference
In-Depth Information
15
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0
0
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500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
0
0
0
0
0
0
0
0
500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
500 1000 1500 2000
Distance (m)
500
500
500
500
500
500
500
500
1000
1000
1000
1000
1500
1500
1500
1500
2000
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2000
Distance (h)
Distance (h)
Distance (h)
Fig. 2. Visualization of a generic variogram
(h)
. The left-hand panel corresponds to three
distinctive cases of geological continuity: single, average characteristic direction of
continuity (red curve), minimum and maximum direction of continuity (blue and green
curves, respectively). The black line represents the true variance of the data and is referred
to as
sill
. The right-hand panel depicts the variogram polar plot, with the major ellipse axis,
corresponding to maximum and the (perpendicular) minor ellipse axis, to the minimum
direction of continuity.
Z
3
Z
3
Z
2
Z
2
3
3
2
2
1
1
Z
1
Z Z Z
1
Fig. 3. Principles of kriging, the geostatistical interpolation method. The value of the
unsampled location
Z
0
, is estimated based on linear combination of measurements at
locations
Z
1
to
Z
3
, where weights
i
at locations
Z
i
are calculated from the variogram model.
Among the numerous interpolation methods, the geostatistical kriging algorithm is
commonly used in the geosciences. Kriging is an unbiased, linear, least-square regression
technique that automatically “de-clusters” data to produce best local or block estimates with
minimized error variance. Figure 3 depicts the principles of linear, weighted estimation of
the value at location
Z
0
, based on measured values at locations
Z
1
to
Z
3
:
n
Z
(2)
0
ii
i
1
where the weights
i
at locations
Z
i
are calculated from the variogram model. Unlike the
more conventional linear weighting estimators, the kriging weights,
i,
account for distance
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