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The transverse impedance assumes the form:
⎧
⎨
e
−
(
|
y
|−
v
)
dm
cos h
v
+
2
(
k
)
2
(
k
)
2
0
v
−
∞
m
2
sin h
Z
N
+
|
y
| ≥
v
π
(
)
3
sin h
v
Z
⊥
=
⎩
2
(
k
)
2
(
k
)
2
0
m
2
ydm
−
∞
cos h
Z
N
−
|
y
| ≤
v.
v
+
π
(
)
2
cos h
sin h
v
(6
.
20)
Here, similar to the vertical-interface model, the transverse impedance consists
of the normal impedances
Z
N
Z
N
and distortion terms. At great distances fro
m
the
,
e
−
y
/
√
2
h
eff
,
, the distortion terms decay exponentially as
e
−
Im
k
y
dike,
|
y
|
>> v
=
is the distance from the dike edge and
h
eff
where
y
= |
y
| −
v
is the effective
penetration depth.
Again, as in the vertical-interface model, we supplement the analytical solution
with numerical solution using the finite element method (Wannamaker et al., 1987).
We consider a dike 1 km wide in the half-space of resistivity
=
10 Ohm
·
m.
The dike of restivity
=
100 Ohm
·
m is said to be “resistive” and the dike of
=
resistivity
m is said to be “conductive”.
Figures 6.9 demonstrates the apparent-resistivity, impedance-phase and tipper
curves obtained on the left of the dike. The observation site is located at the distance
1Ohm
·
100 m from the dike. Let us compare the apparent-resistivty and
impedance-phase curves with locally normal curves of ˙
y
= |
y
| −
v
=
2
n
=
Z
N
o
=
and
arg
Z
N
=−
45
o
characterizing the homogeneous vicinity of the dike. Look at
the apparent-resistivity curves. At high frequencies the longitudinal
n
=
˙
−
curves and
⊥
−
the transverse
n
-curve. The induction
and galvanic effects of the dike become evident at frequencies, on which the effec-
tive penetration depth exceeds the distance to the dike,
h
eff
>
curves coincide with the locally normal ˙
100 m. With lowering
frequency these effects attenuate and the apparent-resistivity curves merge again
with the locally normal ˙
n
-curve. The resistive dike manifests itself in the bell-type
−
⊥
−
curve and the bowl-type
curve, whereas the conductive dike manifests itself
−
⊥
−
in the bowl-type
curve and the bell-type
curve. Similar divergence effects
⊥
. We can say that in the vicinity
of the dike the magnetotelluic sounding reflects the horizontal resistivity distribu-
tion. Come now to the tipper curves. It is notable that the conductive dike causes
more intensive magnetovariational anomaly than the resistive one. Note also that
the Re
W
zy
−
and
are characteristic of the phase curves,
curve is bell-type on the left of the resistive dike, while it is bowl-type
on the left of the conductive dike. At the same time, Im
W
zy
varies in sign, and with
lowering frequency it may go from one quadrant to another.
Next examine the magnetotelluric response functions, obtained over the middle
of the resistive and conductive dikes (Fig. 6.10). Compare the apparent-resistivty
and impedance-phase curves with locally normal curves of ¨
2
n
=
Z
N
o
=
,
