Geology Reference
In-Depth Information
When this tangent cuts the line
Y
=
c
at the point of intersection, the
values of (
x
,
y
) are common for both the lines, which can be obtained
by equating them.
3
2
c
a
A
2
3
Yc
h
a
Question 3.4
Show that the spherical variogram has the same behaviour at the origin
as the linear variogram with the following equation:
3
c
()
h
h
2
a
Answer
3
h
a
At the origin,
term is so small that it can be neglected for practical
3
purposes. Hence the equation of the variogram can be considered as
3
h
3
c
B =
()
hc
=
h
2
a
2
a
But this is nothing but the linear variogram. Hence it is proved that
spherical variogram has the same behaviour at the origin as the linear
3
c
variogram with the equation
()
h
h
.
2
a
Exponential Model
(
h
) =
C
[1 - exp (- |
h
|/
a
)]
Question 3.5
Trace the variogram curve when sill
c
= 2 and range
a
= 30 m. Make
a comparison with those of the questions 3.1 and 3.2.
Answer
h
h
dh
()
1
c
a
a
'( )
h
=
c
(
e
)
e
dh
a
a
We can get the slope near the origin by differentiating the Gamma
function and substituting
h
= 0 in the differential.
0
c
c
c
2
30
/ 0
0
e
a
e
(0) =
a
a
a
0
30
e
(0) =
21
0
