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[ Z S ]
[ e ][ Z R ]
=
.
(1
.
75)
It would be instructive to evaluate, at least roughly, the frequencies that allow
for truncating the LR-decomposition. Let us consider a three-layered K-type
model describing a one-dimensional normal background with
2 >> 1 ,
h 2 >>
h 1
3 =
0. According to (1.45) and (1.46),
1
S 1
in the S 1
interval
E x
H y
Z
=
(1
.
76)
i
o h
in the h
interval
,
whence
1
E x S 1
H y
J 1
H y =
in the S 1
interval
J 1
=
(1
.
77)
i
o S 1 h 2
in the h
interval
,
J 1 is its normalized
where J 1 =
E x S 1 is the current induced in the upper layer and
value. From (1.77), taking into account (1.48), we get
J 1 ( h
interval)
T max
T
,
(1
.
78)
J 1 ( S 1
interval)
where T max is a period of the maximum of the apparent resistivity curve. To esti-
mate the magnetic anomalies caused by a near-surface inhomogeneity, we assume
that their intensity varies proportionally with the normalized current J 1 induced
in the first layer. Within the S 1 - interval, anomalies in horizontal components of
the magnetic field do not usually exceed 25
÷
50%. Thus, according to (1.78), at
T
>
10 T max we observe negligibly small magnetic anomalies (2.5
÷
5%) allowing
for the truncated decomposition.
For more precise estimates we have to examine the superimposition models
numerically. To this end, an approximate hybrid method suggested by Berdichevsky
and Dmitriev (1976) can be used.
Let us examine a (3D + 2D)-superimposition model shown in Fig. 1.6. It consists
of three layers: conductive sediments (
1 ), resistive lithosphere (
2 ) and highly con-
ductive mantle (
3 ). The model contains a local three-dimensional inhomogeneous
inclusion L of width w in the sediments and a regional two-dimensional homoge-
neous prism R of width w R in the lithosphere, the strike of the prism being along the
x
axis. Here w L << w R so that the regional field can be assumed uniform in the
area of the local inclusion.
The problem is solved in three stages.
At the first stage, we solve the two-dimensional problem for the prism R in the
absence of the inclusion L and over the middle of the prism determine the regional
impedance with longitudinal and transverse antidiagonal components:
 
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