Geology Reference
In-Depth Information
h
h
dh
()
1
c
'( )
h
=
c
(
e
a
)
e
a
dh
a
a
0
c
c
/ 0
c
0
'(0)
e
a
e
The slope near the origin =
a
a
a
Yh
a
The equation of the tangent near the origin is
Since it cuts the line
Y
=
c
, both can be equated near point of
intersection. In other words:
c
hc
a
or
.
ha
Gaussian Model
2
2
h
a
22
()
hc e
1
c
[1 Exp(
ha
/
)]
Question 3.8
Trace the curve of the Gaussian variogram, when Sill
c
= 2 and the
Range
a
= 50. Make a comparison of the curves in questions 3
=
5 and
3=1.
Answer
We can get the slope near the origin by differentiating the Gamma
function and substituting
h
= 0 in the differential.
2
2
h
a
hc
e
()
1
2
2
h
h
dh
()
2
h
2
h
2
2
')
h
.
c
e
a
c
.
e
a
2
2
dh
a
a
!
"
0
20
.
2
a
'(0)
c
=
e
0
2
a
/
0
2
2
/
0
21 Exp( 0 /50 )
0
21 Exp( 1/25)
0.08
(0) =
(10) =
(20) = 2(1
Exp ( 4 / 25))
0.30
(30) = 2(1
Exp ( 9 / 25))
0.60
(40) = 2(1
Exp ( 16 / 25))
0.95
(50) = 2(1
Exp ( 25 / 25))
1.26
(60) = 2(1
Exp ( 36 / 25))
1.53
(70) = 2(1
Exp ( 49 / 25))
1.72
(80) = 2(1
Exp ( 64 / 25))
1.85
(90) = 2(1
Exp ( 81/ 25))
1.92
(100) = 2(1
Exp ( 100 / 25))
1.96
