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In-Depth Information
The internal apparent resistivities are:
Z
int
y
)
Z
int
y
)
2
2
xy
(
x
,
yx
(
x
,
int
int
xy
(
x
,
y
)
=
yx
(
x
,
y
)
=
.
(11
.
48)
o
o
where
0
.
5
Z
xx
(
x
,
y
)
M
xy
(
x
B
,
y
B
|
x
,
y
)
+
Z
xy
(
x
,
y
)
{
1
−
0
.
5
M
xx
(
x
B
,
y
B
|
x
,
y
)
}
Z
int
xy
(
x
,
y
)
=
−
.
,
|
,
+
.
,
|
,
1
0
5tr [
M
xx
(
x
B
y
B
x
y
)]
0
25 det [
M
xx
(
x
B
y
B
x
y
)]
0
.
5
Z
yy
(
x
,
y
)
M
yx
(
x
B
,
y
B
|
x
,
y
)
+
Z
yx
(
x
,
y
)
{
1
−
0
.
5
M
yy
(
x
B
,
y
B
|
x
,
y
)
}
Z
int
yx
(
x
,
y
)
=
.
1
−
0
.
5tr [
M
xx
(
x
B
,
y
B
|
x
,
y
)]
+
0
.
25 det [
M
xx
(
x
B
,
y
B
|
x
,
y
)]
Within the
S
1
−
interval
0
Z
int
≈
Z
int
xy
1
S
1
1
o
S
1
.
Z
int
Z
int
int
int
xy
≈−
yx
≈
xy
≈
yx
≈
(11
.
49)
Z
int
yx
0
The remarkable property of the internal apparent resistivities is that they are
robust to the induction effects as well as to some galvanic effects (for instance, to
flow-around and current-gathering effects). It is believed that in these cases the elec-
tric and internal magnetic fields are proportional to the same factor characterizing
the intensity of the magnetotelluric anomaly.
Figure 11.58 shows the longitudinal apparent-resistivity
−
curve, obtained
over the middle of the resistive central segment in the two-dimensional three-
segment
model.
This
curve
has
a
broad
minimum
caused
by
the
inductive
Fig. 11.58
The Obukhov
transformation in the
two-dimensional
three-segment model; the
apparent-resistivity curves are
obtained at the midpoint of
the resistive central segment:
- longitudinal apparent
resistivity,
int
-internal
longitudinal apparent
resistivity, ¨
n
- locally normal
apparent resistivity
