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on the lower side of the Earth's surface
E
z
0 and, according to (1.51), get a
simple boundary condition, for the TM-mode,
H
x
|
z
=
0
=
const
. The constant is
taken as double primary magnetic field 2
H
p
and thus it fits with the normal (one-
dimensional) magnetic field observed at a great distance from the inhomogeneous
region.
The horizontal directions along and across the strike of the 2D-model are labeled
as the
longitudinal direction
(notation “
=
||
” ) and the
transverse direction
(notation
“
” ). It is plain that any transverse vertical plane is a plane of the mirror symmetry.
Then,
J
E1
y
⊥
J
E2
x
J
H1
x
J
H2
y
,
,
,
and according to (1.14),
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
Z
e
Z
Im
Z
0
0
0
0
Z
xy
⎣
⎦
=
⎣
⎦
=
⎣
⎦
+
⎣
⎦
,
[
Z
]
=
i
Z
⊥
Re
Z
⊥
Im
Z
⊥
0
−
0
−
0
−
0
Z
yx
(1
.
54)
where
Z
=
Z
xy
is the longitudinal impedances (TE-impedance) and
Z
⊥
=−
Z
yx
is the transverse impedance (TM-impedance):
J
E2
y
J
E1
x
Z
N
−
Z
N
+
Z
=
Z
⊥
=
,
.
1
+
J
H1
y
1
+
J
H2
x
Here, D = 2 and
n
4.
Considering longitudinal and transverse impedances, we can calculate the longi-
tudinal and transverse apparent resistivities and phases:
=
Z
Z
⊥
2
2
=
⊥
=
o
o
(1
.
55)
=
arg
Z
⊥
=
arg
Z
⊥
.
Now rotate axes
x
,
y
clockwise through an angle
. With (1.27) we obtain
Z
−
Z
⊥
Z
xx
(
)
=
sin 2
2
Z
+
Z
⊥
Z
−
Z
⊥
Z
xy
(
)
=
+
cos 2
2
2
(1
.
56)
Z
+
Z
⊥
Z
−
Z
⊥
=−
+
Z
yx
(
)
cos 2
2
2
Z
−
Z
⊥
Z
yy
(
)
=−
sin 2
,
2
whence, with account for (1.29
a
),
+
=
=
I
1
=
,
.
Z
xx
(
)
Z
yy
(
)
tr [
Z
]
0
(1
57)
