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feature of the induction anomalies is the horizontal skin effect: high-frequency elec-
tric currents are concentrated in the vicinity of resistive zones.
This simple classification of magnetotelluric anomalies is built on phenomeno-
logical base. Can we construct a self-consistent theory of galvanic and induction
effects?
Turn back to the model shown in Fig. 1.1. According to (1.6) the anomalous field
meets the equations
curl
H
A
=
N
E
A
+
j
curl
E
A
o
H
A
=
i
,
where
j
(
M
)
=
E
M
∈
V
j
(
M
)
=
0
M
∈
V
is the density of excess electric current filling the inhomogeneous domain
V
.
Let us divide the excess current into potential,
j
p
, and solenoidal,
j
s
, parts:
j
=
j
p
+
j
s
,
(1
.
103)
where
curl
j
p
=
curl
j
s
=
0
curl
j
(1
.
104)
di
v
j
p
=
di
v
j
di
v
j
s
=
0
.
The parts
j
p
and
j
s
are readily determined.
We will start with the potential part
j
p
.Define
j
p
as
−
grad U
(
M
)
M
∈
V
j
p
(
M
)
=
(1
.
105)
0
M
∈
V
.
Here
U
is the scalar potential of the field
j
p
. It satisfies the equation
U
(
M
)
=−
di
v
j
p
(
M
)
=
di
v
j
(
M
)
M
∈
V
(1
.
106)
with condition
U
0 on the surface
S
bounding the inhomogeneous domain
V
.
Solving (1.106), we find
|
S
=
U
(
M
)
=
G
(
M
,
M
v
)
di
v
j
(
M
v
)
dV
,
(1
.
107)
V
,
where
G
(
M
M
v
) is the Green function for the Dirichlet problem:
