Specifications

University of Pretoria etd – Combrinck, M (2006)
.38180
offactor tionmultiplica correctiondepth a toleads this
1
3818.0
6192.2
1
.
S
d
FATOR
FACTOR
=
==
4.5.1.3 Correction factor: Possibility 3
The third possibility is that the equations used in the transform are indeed mathematically
sound but that the physical assumptions regarding current distributions made in the S-layer
transform lead to poor approximations of the models used. In figure 2.1 it was shown that
the equivalent current filament that was successfully used by Nabighian to calculate the half
space response, did not spaciously coincide with the actual maxima of the current
distribution in the sub surface. It was decided to test this same discrepancy on the S-layer
transform. In other words, it is assumed that the equivalent filament for the S-layer
behaviour, as with the equivalent filament for the half space behaviour, does not coincide
with the electric field maxima in the subsurface. In order to test this theory the cumulative
conductance was calculated, as is done by the S-layer transform, for the electric field
maxima and equivalent current filaments (smoke-rings) respectively. The depth expressions
given in equation 4.24(a),
(After Nabighian and Macnae, 1991) was used in equation
4.24(b) to calculate the cumulative conductances for a 30 ohm.m half space shown in
figure 4.17.
)(24.4.4
2
0
0
a
t
d
t
d
FilamentCurrentEquivalent
MaximumFieldElectric
πσµ
σµ
=
=
)(24.4].[)()(
11
bdddSdS
iiii
−⋅+=
++
σ
As can be expected, the cumulative conductance curves are straight lines with slopes
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
d
S
equal to the conductivity (Fig 4.17). It can be seen that although both curves will
give correct conductivity values the S and d values vary distinctly.
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