Geoscience Reference
In-Depth Information
with
Z
0
=
0
.
−
Z
0
Z
0
0
This equation is strictly valid for a vertically incident plane wave. But its
application proves to be valid in a wide range of incidence angles for highly
conductive geoelectrical cross-sections. These angles or the corresponding hor-
izontal wavenumbers can be estimated using a simple model of homogeneous
half-space with conductivity
σ
g
. The spectral impedances reduce to
1+
i
k
2
d
g
2
−
1
/
2
Z
h
(
ω
;
k
x
,k
y
)=
Z
0
,
1+
i
k
2
d
g
2
1
/
2
Z
e
(
ω
;
k
x
,k
y
)=
Z
0
,
(11.23)
where
Z
0
=
ω
(4
πσ
g
)
−
1
/
2
exp
i
π
4
−
and
d
g
is the skin depth. The spectral impedances coincide with the impedance
Z
0
, if the horizontal spatial scale of the field is much larger than the skin
depth (i.e.
kd
g
1) [34]. This approximation is widely used for deep ULF-
electromagnetic sounding of the Earth ([10], [32]).
With linear dependence of field components on coordinates, the integral
operator in (11.20) reduces to a matrix multiplication operator and condi-
tion (11.22) proves to be suitable for small-scale field perturbations as well.
Numerical estimations showed that integral operator (11.19) is indeed re-
duced to (11.22) for field perturbations on a wide range of horizontal scales
∞−
100-200 km and time scales 10-10
3
s ([12], [34]).
For low-conductivity cross-sections the applicability conditions of the
model of a vertically incident wave can be violated. The most critical, in
that sense, may be polar regions. Near the resonance magnetic shell the pul-
sation phase and amplitude are sharply changed at distances comparable to
the height of the ionosphereic conductive layer (
≈
100 km). In this case, this
model also fails.
Sounding Near an FLR-Shell
The amplitude of the azimuthal component of the magnetic field
b
(
g
)
of pul-
y
sations near the FLR-shell is given on the ground by
b
(
g
)
δ
i
+
h
y
b
0
=
x
r
(
f
)+
i
(
δ
i
+
h
)
+
C
1
k
y
log
k
y
(
x
x
−
−
x
r
(
f
)+
i
(
δ
i
+
h
)) +
···
,
(11.24)
Search WWH ::
Custom Search