400
P. Z. Korondi et al.
Table 12.3 Typical variogram models
Variogram model Definition
Linear
γ (h) =
⎧
⎪ ⎨
⎪ ⎩
0
f o r h = 0
C 0 + C 1
h
L
for 0 < h < L
C 0 + C 1
for h ≥ L
Exponential
γ (h) =
⎧
⎨
⎩
0
f o r h = 0
C 0 + C 1
1 − e
−
h
L
for h > 0
Gaussian
γ (h) =
⎧
⎨
⎩
0
f o r h = 0
C 0 + C 1
1 − e
−
h 2
L 2
for h > 0
Circular
γ (h) =
⎧
⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎩
0
f o r h = 0
C 0 + C 1
2
π
h
L
1 −
h
L
2 +
2
π arcsin
h
L
for 0 < h < L
C 0 + C 1
for h ≥ L
Bessel
γ (h) =
0
f o r h = 0
C 0 + C 1
1 −
h
L K 1
h
L
for h > 0
Fig. 12.4 Typical variograms
(scaled to have range L = 1)