Specifications

University of Pretoria etd – Combrinck, M (2006)
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E-05 1.E-04 1.E-03 1.E-02 1.E-01
Time [s]
Resistivity [Ohm.m]
10 Ohm.m
WJ Botha
Late Time
50 Ohm.m
WJ Botha
Late Time
100 Ohm.m
WJ Botha
Late Time
500 Ohm.m
WJ Botha
Late Time
1000 Ohm.m
WJ Botha
Late Time
5000 Ohm.m
WJ Botha
Late Time
Figure 4-15: Half space resistivities compared to resistivities from S-Layer differential
transform.
The 10 ohm.m full solution shows distortions in the first time channels when the late time
has not been reached. Distortions are also visible on the late channels of the 5000 ohm.m
data. The correlation of the full solution data to the late time approximation results is as
expected – in times adhering to the late time approximations the values are equal. From
the figure it is immediately obvious that the resistivities produced by the S-Layer transform
are consistently higher than that of the input values.
It was found that the ratio of the resistivities calculated from the S-layer transform divided
by the modelled resistivity yielded a constant of 2.6192. Since the conductivities
(1/resistivities) are calculated in the algorithm as the derivative of conductance (S) to depth
(d), this “error” could be produced either in the calculation of S or d, since depth (d) is a
function of S (eq. 4.2). Correction factors can be applied in either the S or d formulae and
will yield “correct” (i.e. equal to half space) conductivities as long as the following
relationships hold.
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