Specifications

University of Pretoria etd – Combrinck, M (2006)
LIST OF FIGURES
Figure 2-1 The use of equivalent current filament concept in understanding the
behaviour of TEM fields over a conducting half space (after Nabighian and
Macnae, 1991)................................................................................................................................8
Figure 2-2 Conductive sheet parameters.............................................................................................9
Figure 2-3 Equivalent current filaments (images) for a conducting thin sheet at various
times after current interruption in the transmitter loop (after Nabighian and
Macnae, 1991)..............................................................................................................................10
Figure 2-4 Sphere currents at various times (a – surface currents; b-d – equatorial/plane
currents) (after McNeill, 1980). ................................................................................................12
Figure 2-5 A permeable conducting sphere embedded in a conducting infinite space.
The dipolar source is located at S(r
0
,0,0) outside the sphere (after Singh 1973). ............14
Figure 2-6 Time characteristic of h
v
1rr
(t) for r/a=2, µ
2
/µ
1
=1, and variable σ
1
/σ
2
(after
Singh 1973)...................................................................................................................................14
Figure 2-7 Time characteristic of h
v
1
θ
r
(t) for r/a=2, µ
2
/µ
1
=1, and variable σ
1
/σ
2
(after
Singh 1973)...................................................................................................................................15
Figure 2-8 Time characteristic of h
u
1
θθ
(t) for r/a=2, µ
2
/µ
1
=1, and variable σ
1
/σ
2
(after
Singh 1973).
..................................................................................................................................15
Figure 2-9 “Reflected” smoke-rings. Electric field intensity is presented as sections for
20 consecutive time channels. The cyan and black contour lines present the
electric field intensity for a homogeneous 50 Ohm.m half space and indicate the
well-known diffusive smoke-ring behaviour. The colour contours indicate
electric field intensity of currents for a 5 Ohm.m prism (black rectangle) in a 50
Ohm.m half space as percentage of the half space response. The “reflected”
currents are clearly visible in channels 13 to 20. ...................................................................16
Figure 3-1 Comparison of apparent conductivity (calculated by differentiating the fitted
slowness with respect to reference depth curve) with the actual conductivity for
four three-layer models (after Macnae and Lamontagne, 1987). .......................................25
Figure 3-2 Cross-section of the model (top); Conductivity-depth image obtained by
differential S-transformation (centre); Conductivity-depth image obtained by
regularized S-inversion (bottom). (After Tartaras et. al., 2000)..........................................26
Figure 4-1 In (a) the raw data are presented in a contoured log-scale. In (b) the data
were normalised using the half space value used in the forward model. In (c) the
data were normalised as discussed above.
..............................................................................30
Figure 4-2 Flow diagram for decay curve slope analysis. ...............................................................32
Figure 4-3 Percentage errors for differentiation in different domains of TDEM data for
a 10 Ohm.m half space. .............................................................................................................38
Figure 4-4 A Lagrange interpolating polynomial fitted to the data points outlining the
back of a duck (top) and a cubic spline curve fitted to the same data points
(bottom). (From Burden and Faires, 1993, Figures 3.11 and 3.12) ...................................40
Figure 4-5: Comparison of differentiation methods applied to (a) unequally spaced
points without smoothing of data, (b) unequally spaced points with smoothing of
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