Specifications

University of Pretoria etd – Combrinck, M (2006)
The numerical calculation of the S-layer transform was done using the following steps:
1. Input |V| values
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
2
1m ofarea receiver to normalised if
t
B
z
2. Calculate |V|’, i.e.
2
2
t
B
z
∂
∂
3. Calculate S from equation 4.1
4. Calculate d from equation 4.2
5. Calculate
σ =
∂
∂
d
S
Numerical differentiations are performed in steps 2 and 5. Smoothing filters are applied at
various stages in the algorithm cumulating up to the strategy proposed by Tartaras et. al.
(2000) which is smoothing before and after each differentiation. Figure 4-8 top shows the
results of three variations:
• smoothing of |V| before step 1
• smoothing of |V| before step 1 and S after step 3
• smoothing of |V| before step 1, S after step 3 and
σ after step 5.
As can be expected the successive smoothing slightly lowers the maximum amplitude and
widens the response curve. However, it is critical
not to smooth |V|’ (figure 4.8 bottom),
which introduces extensive noise. This is due to the ratios of |V| and |V|’ used to
calculate S and d.
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