Specifications

University of Pretoria etd – Combrinck, M (2006)
data, (c) equally spaced points without smoothing of data and (d) equally spaced
points with smoothing. ..............................................................................................................46
Figure 4-6: A summary (in ascending order) of the average error over twenty data points
for each of the alternatives in Figure 4.5. (ES: equal spacing, US: unequal spacing) .....47
Figure 4-7: Synthetic data and model for three-layer earth.............................................................47
Figure 4-8: Effects of smoothing at different points in S-layer transform algorithm................49
Figure 4-9: Comparison of S-layer differential transform results for the three numerical
differentiation methods applied on (a) unequally spaced data points without
smoothing of data, (b) unequally spaced data points with smoothing of data, (c)
equally spaced data without smoothing and (d) equally spaced data with
smoothing.....................................................................................................................................50
Figure 4-10: Four field data soundings; 1 to 4 are very smooth and considered to be
clean data, while 5 & 6 contains noise. ...................................................................................51
Figure 4-11: S-layer differential transform results for Sounding 1. ...............................................51
Figure 4-12: S-layer differential transform results for Sounding 2. ...............................................52
Figure 4-13: S-layer differential transform results for Sounding 3. ...............................................53
Figure 4-14: S-layer differential transform results for Sounding 4. ...............................................54
Figure 4-15: Half space resistivities compared to resistivities from S-Layer differential
transform. .....................................................................................................................................56
Figure 4-16: Values for S and d corrections giving correct resistivity values and the
effective depth correction resulting from each pair. (from Excel: summary of
depth conversion factor models) .............................................................................................58
Figure 4-17: Cumulative conductance curves for late time halfsapce approximations. ...........60
Figure 4-18: Cumulative conductance curves for late time half space and S-layer
approximations............................................................................................................................61
Figure 4-19: Comparison of S-layer differential transform (SLDT) solutions using
different depth factors and layered earth inversions of synthetic data for a two
layer earth. ....................................................................................................................................63
Figure 4-20: Comparison of S-layer differential transform (SLDT) solutions using
different depth factors and layered earth inversions of synthetic data for a three
layer earth (thin conductive layer)............................................................................................64
Figure 4-21: Comparison of S-layer differential transform (SLDT) solutions using
different depth factors and layered earth inversions of synthetic data for a three
layer earth (thick conductive layer). Top: negative values included; Bottom: no
negative values. ............................................................................................................................65
Figure 4-22: Comparison of S-layer differential transform (SLDT) solutions using
different depth factors and layered earth inversions of synthetic data for a thin
conductive plate in a resistive half space. ...............................................................................66
Figure 4-23: Comparison of S-layer differential transform (SLDT) solutions using
different depth factors and layered earth inversions of synthetic data for a
conductive prism in a resistive half space...............................................................................67
Figure 4-24 Cumulative conductance versus depth, 0.02 S/m (50 Ω.m) half space...................69
Figure 4-25 Conductivity versus depth, 0.02 S/m (50 Ω.m) half space......................................69
Figure 4-26: Cumulative conductance versus depth for two layers of decreasing
conductivity; first layer thickness 200m..................................................................................70
iv