Information Technology Reference
In-Depth Information
The transverse impedance assumes the form:
⎧
⎨
m
2
e
y
dm
2
(
k
)
2
(
k
)
2
0
∞
−
Z
N
+
y
≤
0
)
2
(1
π
+
/
)
(
E
y
H
x
o
=
Z
⊥
=−
⎩
2
(
k
)
2
(
k
)
2
0
m
2
e
−
y
dm
−
∞
Z
N
−
y
≥
0
,
π
)
3
(1
(
+
/
)
(6
.
12)
where
H
x
o
=
√
−
Z
N
E
N
y
=−
/
o
,
i
H
x
o
=
√
−
E
y
/
Z
N
=−
i
o
,
=
√
/
,
E
N
E
N
y
Z
N
/
Z
N
=
y
/
are the normal impedances for the left and right quarter-spaces. Here the transverse
impedance consists of the normal impedance
Z
N
and a distortion term that at g
r
eat
distances from the vertical interface decays exponentially as
e
−
Im
k
|
y
|
=
e
−|
y
|
√
2h
eff
,
where h
eff
is the
effective penetration depth
|
Z
N
|
o
=
o
,
h
eff
=
which can be used as a scale parameter of the magnetotelluric anomaly.
We have obtained rather simple analytical expression for the TM-mode. It would
be interesting to supplement this result with numerical solution for the TE-mode.
The TE-problem was solved using the finite element method (Wannamaker et al.,
1987).
Figures 6.2 and 6.3 present the transverse and longitudinal apparent-resistivity
and impedance-phase curves,
observed at a site over the left
quarter-space. The dimensionless quantities h
eff
/
|
⊥
/
,
⊥
and
/
,
y
|
are plotted as abscissas. Here
h
eff
is the effective penetration depth and
is a distance from the vertical interface.
With increasing h
eff
(lowering frequency) and with decreasing
|
y
|
|
y
|
(going toward
, while the impedance
the vertical interface), the apparent resistivity departs from
45
o
. When
>
, the transverse resistivities,
⊥
, quickly
phase departs from
−
⊥
, have deep minima, while the longitudinal
descend and the transverse phases,
, slowly ascend and the longitudinal phases,
, have flattened max-
resistivities,
<
, the longitudinal resistivities,
, quickly descend
ima. And vice versa, when
, have deep minima, while the transverse resistiv-
and the longitudinall phases,
⊥
, slowly ascend and the transverse phases,
⊥
,
ities,
have flattened maxima. We
see that the transverse and longitudinal curves conflict with each other. They come
apart, so that descending of one curve corresponds to ascending of another curve.
This effect will be called the
divergence effect
. Distortions of the transverse curves
are of a galvanic nature, whereas the distortions of the longitudinal curves are of a
