Information Technology Reference
In-Depth Information
In an arbitrary coordinate system, we have the matrix equation:
R
)]
−
1
[
T
][
S
][
Z
R
][
h
]
−
1
[
R
(
[
Z
S
]
=
[
R
(
R
)]
,
(3
.
54)
where
R
is the regional strike angle measured clockwise from the
x
-axis. In the full
form
st
)
˜
st
)
˜
h
yy
(
s
h
xx
(
s
˜
1
˜
R
1
R
2
R
R
2
(1
−
+
(1
+
−{
+
t
)
−
−
t
)
}
Z
1
=
,
h
xx
h
yy
˜
1
˜
R
R
2(1
+
2
)
t
)
˜
t
)
˜
h
yy
(1
h
xx
(1
˜
1
˜
1
2
2
(
s
+
−
(
s
−
+{
−
st
)
+
+
st
)
}
Z
2
=
,
h
xx
h
yy
˜
1
˜
2
)
2(1
+
st
)
˜
st
)
˜
h
yy
(
s
h
xx
(
s
˜
1
˜
−
1
−
+
2
+{
+
+
−
}
2
(1
(1
t
)
t
)
Z
3
=
cos2
h
xx
h
yy
˜
1
˜
R
2(1
+
2
)
t
)
˜
t
)
˜
h
yy
(1
h
xx
(1
˜
1
˜
R
1
R
2
R
R
2
(
s
+
+
(
s
−
−{
−
st
)
−
+
st
)
}
−
sin2
R
,
h
xx
h
yy
˜
1
˜
R
R
2(1
+
2
)
t
)
˜
t
)
˜
h
yy
(1
h
xx
(1
˜
1
˜
R
1
R
2
R
R
2
(
s
+
+
(
s
−
−{
−
st
)
−
+
st
)
}
Z
4
=−
cos2
R
h
xx
h
yy
˜
1
˜
2
)
2(1
+
st
)
˜
st
)
˜
h
yy
(
s
h
xx
(
s
˜
1
˜
−
1
2
2
(1
−
(1
+
−{
+
t
)
+
−
t
)
}
−
sin2
,
h
xx
h
yy
˜
1
˜
R
+
2
)
2(1
(3
.
55)
where
Z
xy
−
Z
yx
Z
xx
+
Z
yy
Z
1
Z
2
=
=
2
2
Z
xy
+
Z
yx
Z
xx
−
Z
yy
Z
3
Z
4
=
=
.
2
2
On single frequency we have an underdetermined system of eight equations in
nine unknowns:
t, s,
h
xx
,
h
yy
and Re
˜
Im
˜
Re
˜
Im
˜
2
. It can be solved
by least squares multifrequency fitting under the assumption that
t, s
,
1
1
2
,
,
,
,
R
R
,
h
xx
,
h
yy
˜
˜
1
2
differ
do not depend on frequency. Note that apparent regional impedances
,
2
not only in amplitude but in phase as
well. So, we take into account the local magnetic anomalies, but restrict ourselves
to determining the twist, shear, and regional strike.
1
from the true regional impedances
,
