Specifications

University of Pretoria etd – Combrinck, M (2006)
Table 2: Summary of S-layer differential transform performance on synthetic models. (h =
thickness, d =depth, l= side length of square plate and prisms)
Model
Cumulative
Conductance vs depth
Imaged Conductivity vs
depth
Comments
Half space
σ = 0.02 S/m
Smoothly increasing
with depth
Good approximation (12%
error) to true conductivity in
“late time”
Two Layers
σ
1
= 0.02 S/m
σ
2
= 0.002 S/m
h
1
= 200 m
Smoothly increasing
with depth, layer
boundary clearly defined
Show decreasing trend with
depth; values close to true
conductivity;
layer boundary not clearly
defined
Decreasing conductivity,
low contrast
Two Layers
σ
1
= 0.02 S/m
σ
2
= 0.0002 S/m
h
1
= 200 m
Smoothly increasing
with depth, layer
boundary clearly defined
Show decreasing trend with
depth; second layer values
not close to true
conductivity; layer boundary
not clearly defined
Decreasing conductivity,
high contrast
Two Layers
σ
1
= 0.02 S/m
σ
2
= 0.2 S/m
h
1
= 200 m
Smoothly increasing
with depth, layer
boundary not clearly
defined
Show increasing trend with
depth (except for early time);
values close to true
conductivity for first layer
only; layer boundary defined
as “first increase” in
conductivity, especially on
linear scale
Increasing conductivity,
low contrast
Two Layers
σ
1
= 0.02 S/m
σ
2
= 2 S/m
h
1
= 200 m
Decreasing depths with
increasing times, layer
boundary not clearly
defined
Show increasing trend with
depth (except for early time);
values close to true
conductivity for first layer
only; layer boundary defined
as “first increase” in
conductivity, especially on
linear scale; negative
conductivities calculated
Increasing conductivity,
high contrast
“Reflecting smoke-ring”
behaviour
Conductive layer in
half space (varying
σ contrast)
σ
HS
= 0.02 S/m
σ
Layer
= 0.04 S/m
and
Smoothly increasing
with depth
Resolve layer position well
but with underestimation of
conductivity values.
Low contrast
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