Specifications
University of Pretoria etd – Combrinck, M (2006)
• Speed
• No need for an initial model
• Although it is based on the same imaging principles as the CDI transform it is
easier to implement with fewer empirical factors that need to be included
• The late time approximation used in the algorithm is very applicable to the impulse
response, central-loop configuration this work is based on
• For the specific case of a conductive host rock environment the S-layer differential
transform shows good resolving capabilities
• As mentioned by Tartaras et. al. (2000) the main drawback of this method is the
fact that it requires a numerical differentiation scheme which tends to introduce
noise in the interpretation results. The implementation of a robust, yet accurate
numerical differentiation scheme based on the specific properties of TEM data
therefore receives high precedence. Further enhancements include a noise filter
based on data points satisfying the theoretical conditions for the S-layer transform.
The S-layer differential transformation results in two equations that have to be solved for
every time channel obtained at every station. Originally derived by Sidorov and Tikshaev
(1969) these are summarised by Tartaras et. al. (2000) as:
()
)2.4(
4
0
1
)1.4(
3
4
3
5
3
4
0
3
1
3
3
1
16
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
′
−=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
′
⎟
⎟
⎠
⎞
⎜
⎜
⎝
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∑
=
t
V
V
S
d
V
V
nM
S
µ
µ
π
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