Information Technology Reference
In-Depth Information
2)]
S
E
S
1
2
[
R
(
1
2
[
R
(
H
A
S
1
E
R
=
−
π/
2)]
J
=
−
π/
−
(1
.
82)
1
2
[
R
(
[
h
]
E
R
S
1
[
I
])
E
R
=
−
π/
2)] (
S
[
e
]
−
=
,
where
1
2
[
R
(
[
h
]
=
−
/
2)] (
S
[
e
]
−
S
1
[
I
])
and [
R
], [
I
] are rotationl and identity matrices:
0
10
00
1
10
−
[
R
(
−
/
2)]
=
,
[
I
]
=
.
Finally, with account for (1.68) and (1.70), we write
H
S
[
h
]
H
R
=
,
(1
.
83)
where
[
h
][
Z
R
]
=
+
.
.
[
h
]
[
I
]
(1
84)
The components of magnetic distortion tensor [
h
]are
1
2
(
Se
yy
−
1
2
Se
yx
Z
S
1
)
Z
⊥
h
xx
=
1
+
h
xy
=−
(1
.
85)
1
2
Se
xy
Z
⊥
1
2
(
Se
xx
−
S
1
)
Z
.
h
yx
=−
h
yy
=
1
+
At the final stage, we go to (1.74) with (1.79), (1.80), (1.84) and synthesize the
LR-decomposition:
[
Z
S
]
[
e
][
Z
R
][
h
]
−
1
=
.
The truncated decomposition, [
Z
S
]
[
e
][
Z
R
] , is admissible if
=
2
(
Se
yy
−
S
1
)
Z
⊥
<<
1
2
S
e
yx
Z
<<
1
1
1
(1
.
86)
2
(
Se
xx
−
S
1
)
Z
<<
1
2
S
e
xy
Z
⊥
<<
1
1
1
.
The arithmetic suggests that near-surface magnetic anomalies can be neglected
in the period range
T
>
≤
2
≥
·
,
100 s
providing
S
300S and
1000 Ohm
m
h
2
≤
,
3
≤
·
.
100 km
100 Ohm
m
