Information Technology Reference
In-Depth Information
Fig. 1.11
A superimposition model with a near-surface resistive cylinder and a 2D deep regional
conductive prism; O-observation site. Model parameters:
1
=10Ohm
·
m,
h
1
=0.5km,
=∞
,
L
m,
h
2
=10km,
a
= 0.125 km,
2
=∞
,
h
2
= 100 km,
=
10 Ohm
·
h
=10km,
v
=20km,
3
=0
R
below the near-tangential
y
x
-curve. This relationship can be readily explained
by effect of current flowing around the resistive cylinder L. On the other hand,
the relationship between the near-radial and near-tangential phase curves is rather
strange: the near-tangential
y
x
-curve does not leave the fourth quadrant, whereas
the near-radial
x
y
-curve passes over all the quadrants, making a total phase
rotation.
The Kramers-Kronig transforms of the first kind relating the real and imaginary
parts of the near-tangential and near-radial impedances are shown in Fig. 1.13.
We see that relations (1.98) provide for rather accurate transition from the real
part of the impedance to its imaginary part and vice versa. Here the dispersion
relations of the first kind obviously hold and we can say that the near-tangential
and near-normal impedances have no poles in the upper half-plane of the complex
frequency
.
Now we turn to Fig. 1.14 that presents the Kramers-Kronig transforms of
the second kind relating the apparent resistivities and impedance phases. The
