Specifications

University of Pretoria etd – Combrinck, M (2006)
function, implying more than one S value for each depth and this is not accounted for in
re-sampling with the cubic spline method.)
(c)
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0 100 200 300
Depth [m]
Imaged Conductivity [S/m]
(d)
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0 100 200 300
Depth [m]
Imaged Conductivity [S/m]
(a)
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0 100 200 300
Depth [m]
Imaged Conductivity [S/m]
Lagrange Three-Point
Cubic Spline
Inverse o f Integr ati on
(b)
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0 100 200 300
Depth [m]
Imaged Conductivity [S/m]
Figure 4-13: S-layer differential transform results for Sounding 3.
For Sounding 3 (Figure 4-13) the same pattern holds. Here the advantage of smoothing is
very clear, especially on the “inverse of integration” method. In Sounding 4 (Figure 4-14)
even the unequally spaced, smoothed data become noisy with gaps (indicating negative
conductivities having no physical meaning). This is once again due to the cumulative
conductance curve not increasing monotonically, although the measured data is smooth
the algorithm might fail in this case as the assumption of cumulative conductance on which
the S-layer transform is based, is violated.
53