Specifications

University of Pretoria etd – Combrinck, M (2006)
(c)
1.E-03
1.E-02
1.E-01
1.E+00
0 100 200 300 400
Depth [m]
Imaged Conductivity [S/m]
(d)
1.E-03
1.E-02
1.E-01
1.E+00
0 100 200 300 400
Depth [m]
Imaged Conductivity [S/m]
(a)
1.E-03
1.E-02
1.E-01
1.E+00
0 100 200 300 400
Depth [m]
Imaged Conductivity [S/m]
Lagrange Three-Point
Cubic Spline
In ve rse of Inte grati o n
(b)
1.E-03
1.E-02
1.E-01
1.E+00
0 100 200 300 400
Depth [m]
Imaged Conductivity [S/m]
Figure 4-14: S-layer differential transform results for Sounding 4.
4.4.5 Concluding remarks on numerical differentiation
The S-layer differential transform (and other imaging techniques) are useful tools in
automated interpretation of TDEM data because it is fast and do not require a starting
model. It is not as accurate as inversion methods but remains useful in providing starting
models for these more time consuming procedures. As numerical differentiation is very
unstable, it is important to take great care when applying this operator in the S-layer
transform. When working with field data, data have to be smoothed but with cognizance
of the influence on the final result. Even though time-effectiveness can be increased in
using algorithms for equally spaced data points it produces very poor results when applied
to the S-layer transform. As for the method of differentiation, the “inverse of integration”
performed best on synthetic data but it is arguable whether the 0.4% increase in accuracy is
worth the additional effort compared to the Lagrange three-point formula. However, the
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