Information Technology Reference
In-Depth Information
are the major and minor semi-axes of the ellipse. Here
AB
=
ad
−
bc
=
det [Re
S
τ
(
r
|
r
B
)]
.
(4
.
109)
The slope of the major axis is
2(
ac
+
bd
)
tan
=
+
(
a
2
a
2
+
b
2
−
c
2
−
d
2
+
b
2
+
c
2
+
d
2
)
2
−
4(
ad
−
bc
)
2
−
(
a
2
a
2
+
b
2
−
c
2
−
d
2
+
b
2
+
c
2
+
d
2
)
2
−
4(
ad
−
bc
)
2
(4
.
110)
=
−
2(
ac
+
bd
)
+
2(
ac
+
bd
)
−
(
a
2
a
2
+
b
2
−
c
2
−
d
2
+
b
2
+
c
2
+
d
2
)
2
−
4(
ad
−
bc
)
2
+
(
a
2
4(
ad
−
bc
)
2
.
=
a
2
+
b
2
−
c
2
−
d
2
−
2(
ac
+
bd
)
+
b
2
+
c
2
+
d
2
)
2
−
Similarly we construct the perturbation ellipse for the Schmucker tensor [Im
S
τ
].
Substituting
a
=
Im
S
xx
(
r
|
r
B
)
,
b
=
Im
S
xy
(
r
|
r
B
)
,
c
=
Im
S
yx
(
r
|
r
B
)
,
d
=
Im
S
yy
(
r
|
r
B
)
into (4.108) and (4.110), we get the semi-axes and the slope of the major axis of the
imaginary perturbation ellipse
associated with the imaginary perturbation vectors
Im
p
and Im
q
.
The same technique can be used for constructing the real and imaginary ellipses
of the horizontal magnetic tensor [
M
].