Information Technology Reference
In-Depth Information
In the traditional log
−
representation
log
for
|
y
| ≥
a
⊥
(
y
log
,
)
=
log
N
(
)
+
(7
.
6)
log
for
|
y
| ≤
a
.
So, the MTS-distortion defined in accordance to (1.101) is
⊥
=
⊥
−
log
log
N
=
log
.
It is evident that electric charges accumulated at the inclusion surface produce the
galvanic anomaly, which manifests itself in the vertical
static shift
of the transverse
apparent-resistivity curves. The magnitude log
of the static shift is defined by
1
/
1
. This effect goes under the name of
-
effect
. Beginning with a critical fre-
quency that depends on the inclusion size, the
−
effect shifts the low-frequency
⊥
−
⊥
−
branches of the
curves up or down. It does not change the shape of shifted
curves and does not affect the corresponding impedance-phase curves.
Let us consider a model with
1
10
5
=
10 Ohm
·
m,
h
1
=
1km,
2
=
Ohm
·
m
,
1
h
2
=
124 km,
3
=
0, and
a
=
10 m,
=
100 Ohm
·
m (“resistive” inclusion)
or 1 Ohm
m (“conductive” inclusion). The semicylinder radius
a
is several orders
less than the effective penetration depth
h
eff
required for the sufficiently complete
information on
·
N
(
z
). Look at the graphs of
and the apparent-resistivity curves
⊥
presented in Fig. 7.1. In the vicinity of the resistive inclusion we see a dras-
tic fall of
of
caused by deconcentration of currents flowing under the inclusion.
Here
⊥
-curve with its ascending and descending branches is shifted
downward. Over the resistive inclusion
<
1 and the
>
1 and the
⊥
−
curve with its ascending
and descending branches is shifted upward. But note that
does not exceed 4
1
is infinitely large. Exactly the converse situation is characteristic of the
conductive inclusion. In its vicinity we have a rise of
even if
caused by concentration of
>
1 and the
⊥
−
currents flowing into the inclusion. Here
curve with its ascend-
ing and descending branches is shifted upward, but
does not exceed 4 even if
1
is infinitesimal. Over the conductive inclusions we see a drastic fall of
and
⊥
−
the
curve with its ascending and descending branches is shifted profoundly
downward.
Similar effect is observed in a model with a prismatic outcropped conduc-
tive inclusion (Fig. 7.2). The computations have been performed using the finite-
element method (Wannamaker et al., 1987). Look upon the apparent-resistivity and
impedance-phase curves obtained over the middle of the inclusion (
y
0). The
⊥
-curve with its ascending and descending branches is shifted downward more
than by one decade. But in form it is almost identical to the normal
=
N
-curve. This
⊥
-curve, whose ascending and descending branches
static effect does not affect the
merge with the normal
N
-curve.
The immediate interpretation of the
⊥
-curve distorted by the
effect would
yield dramatic errors in the sediments conductance and depth to the conductive
mantle. Fortunately the distorted TM-mode is accompanied by the TE-mode that
is hardly distorted: the ascending and descending branches of the curves for
−
,
merge with the normal
N
- and
N
-curves.
