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xx
xy
[Re
Z
]
−
1
[Im Z]
[
]
=
=
.
yx
yy
The pseudo-topography of the apparent phase
arctan
xx
+
yy
2
A
=−
is constructed. At the surface of a horizontally homogeneous Earth, we have
.
Figure 11.49 shows the pseudo-topography of Wiese-Parkinson matrix invariant
A
=−
arg
Z
,
where
Z
is the 1D Tikhonov-Cagniard impedance
constructed in the range of periods from 0.16 to 10000 s. The near-surface,
crustal, and mantle prisms are clearly recognizable here as edge maxima of
W
delineating the prisms. With increasing period, these maxima become smoother and
broaden because the resolution of the Wiese-Parkinson matrix drops with depth.
Examining the pseudo-topography of the invariant
W
, we can identify periods
at which the effects of various prisms are superimposed on each other and periods
at which each prism is seen as a separate body unaffected (or almost unaffected)
by the other prisms (the effects of the prisms are not superimposed). Thus, the
period
T
W
16 s demonstrates the pure effect of the near-surface prism, while, at
longer periods, the effects of the crustal (
T
=
0
.
10000 s) prisms
are predominant. At these periods, we can change projections of the near-surface,
crustal, and mantle prisms and find their azimuths (0, -45
◦
, and -90
◦
). Moreover,
each of these prisms can admit a trial 2D inversion performed in a more or less
narrow interval of periods around 0.16, 40, or 10000 s excluding the presence of
other prisms. It is evident that the pseudo-topography of the invariant
=
40 s) and mantle (
T
=
of the
Wiese-Parkinson matrix provides a good basis for the choice of adequate interpre-
tation model.
We arrive at the same conclusion, examining the pseudo-topography of the invari-
W
ant
M
of the magnetic tensor [
M
] shown in Fig. 11.50. The pseudo-topography
of
is constructed in the same range of periods from 0.16 to 10000 s. The
high resistivity near-surface prism is observed at the period
T
M
=
.
16 s as a 2D
“graben” framed by maxima that arise due to the external skin effect in the con-
ductive medium surrounding the prism (at high frequencies, the longitudinal elec-
tric current concentrates near the vertical faces of the high resistivity prism). With
decreasing frequency, the effect of the near-surface prism decays, giving room to
the effect of the conductive crustal prism (
T
= 1 and 6.3 s) which manifests itself as
2D “horst” with side maxima arising due to the internal skin effect. The effect of the
crustal prism prevails at the period
T
0
40 s, so that this prism can be regarded as a
separate body almost free from the influence of the near-surface and mantle prisms.
The further decrease in frequency reveals the mantle prism resolved in the form of
a flat maximum. The effects of the mantle and crustal prisms are superimposed at
T
=
10000 s, the effect of the mantle prism becomes predominant,
while the effect of the crustal prism is nearly unrecognizable. In the vicinity of the
=
250 s. At
T
=
