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and
arctan
e
yx
e
xx
arctan
e
xy
e
yy
x
=
y
=−
(3
.
13)
−
/
2
<
x
<
/
2
−
/
2
<
y
<
/
2
.
Returning to (3.1), we get apparent amplitudes
1
and
2
of the principal regional
˜
˜
R
R
impedances:
Z
xy
Z
xx
1
=
e
(
y
)
1
=
+
Z
yy
2
=
e
(
x
)
2
=
+
Z
yx
2
2
2
2
˜
˜
R
R
R
R
.
(3
.
14)
As is easy to see, moduli of the principal values of [
Z
R
] can be found in the insepara-
ble conjunction with frequency-independent factors
e
(
x
)
and
e
(
y
)
that define intensity
of static distortions of
2
caused by near-surface local inhomogeneities.
To distinguish between longitudinal and transverse regional directions,
1
,
R
R
and
⊥
, and between longitudinal and transverse regional impedances,
Z
and
Z
⊥
,we
have to use an additional geological or geophysical indication.
Along with characteristics of regional structure, the Bahr method may give some
information on local structures. Let us show that the vector components
e
(
x
)
and
e
(
y
)
of the electric distortion tensor [
e
] coincide with electric fields that arise when a
local inhomogeneity is excited by the unit electric fields linearly polarized in the
x
-
and
y
-directions:
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
e
xx
e
xy
1
0
e
xx
e
yx
e
xx
e
xy
0
1
e
xy
e
yy
⎣
⎦
⎣
⎦
=
⎣
⎦
,
⎣
⎦
⎣
⎦
=
⎣
⎦
.
e
(
x
)
e
(
y
)
=
=
e
yx
e
yy
e
yx
e
yy
(3
.
15)
Thus, the angles
x
,
y
indicate how a local inhomogeneity deflects the observed
electric fields from the exciting field. In regional coordinates, according to (3.1) and
(3.13),
arctan
Z
yy
arctan
Z
xx
arctan
e
yx
arctan
e
xy
x
=
e
xx
=
Z
xy
,
y
=−
e
yy
=−
Z
yx
.
(3
.
16)
In practice, we take into account the phase inaccuracies and to avoid the complex
angles use approximate formulae
arctan Re
Z
yy
arctan Re
Z
xx
x
=
Z
xy
,
y
=−
Z
yx
.
(3
.
17)
Looking upon a map that represents the orientation of vectors
e
(
x
)
and
e
(
y
)
,wemay
reveal the current concentration (current concentrates in a conductive body) or cur-
rent flow around (currents flow around a resistive body) and thereby classify the
near-surface structures by their conductivity.
