Information Technology Reference
In-Depth Information
m
−
1
T
min
,
>
T
m
=
1
,
m
∈
[1
,
M
]
.
(10
.
93)
Then,
ln
arg
Z
(ln
T
1
)]
2
2
Z
(ln
T
1
)
Z
(ln
T
1
)
Z
(
T
)
1
2
ln
2
R
Z
(
T
)
[arg
Z
(ln
T
1
)
−
=
+
−
ln
arg
Z
(ln
T
m
)]
2
2
M
−
1
Z
(ln
T
m
)
Z
(ln
T
m
)
[arg
Z
(ln
T
m
)
+
ln
+
−
m
=
2
ln
arg
Z
(ln
T
M
)]
2
2
Z
(ln
T
M
)
Z
(ln
T
M
)
1
2
ln
[arg
Z
(ln
T
M
)
+
+
−
,
(10
.
94)
where ln
is a distance between adjacent measurements.
Similarly, we can define
R
- norm for the admittance:
R
L
2
=
L
2
+
L
2
.
.
=
|
|
Y
(
T
)
ln
Y
(ln
T
)
ln
Y
(ln
T
)
arg
Y
(ln
T
)
(10
.
95)
The admittance metric (misfit) is defined as
Y
(
T
)
2
R
Y
(
T
)
−
ln
Y
(ln
T
)
−
arg
arg
Y
(ln
T
)
2
L
2
2
L
2
Y
(ln
T
)
|
|
=
ln
Y
(ln
T
)
+
−
(10
.
96)
ln
arg
Y
(ln
T
)
2
dT
2
T
max
Y
(ln
T
)
Y
(ln
T
)
+
arg
Y
(ln
T
)
=
−
T
,
T
min
where
Y
(
T
) and
Y
(
T
) are admittances obtained from the field measurements and
model computations. In discrete representation we write
ln
arg
Y
(ln
T
1
)]
2
ln
2
Y
(ln
T
1
)
Y
(ln
T
1
)
Y
(
T
)
−
Y
(
T
)
1
2
T
2
T
1
2
R
[arg
Y
(ln
T
1
)
=
+
−
ln
+
[arg
Y
(ln
T
m
)
−
arg
Y
(ln
T
m
)]
2
ln
2
M
−
1
Y
(ln
T
m
)
Y
(ln
T
m
)
1
2
T
m
+
1
T
m
−
1
+
m
=
2
ln
arg
Y
(ln
T
M
)]
2
ln
2
Y
(ln
T
M
)
Y
(ln
T
M
)
1
2
T
M
T
M
−
1
,
(10
[arg
Y
(ln
T
M
)
+
+
−
.
97)
where
T
1
=
=
T
min
and
T
M
T
max
. On a logarithmic uniform grid (10.93), we have
