Specifications

University of Pretoria etd – Combrinck, M (2006)
4.3.1 Layered earth behaviour
The objectives of this analysis are:
• to determine whether there is any straight line behaviour in the logarithmic domain
of a sounding data set;
• to determine the largest number of channels (and channel numbers) on which the
behaviour can be found;
• to test whether these slopes are close to either -2.5 or -4 and consequently
• to classify the sounding as half space or S-layer type.
Firstly, the time channels and corresponding absolute ∂B
z
/∂t values are transformed to the
logarithmic domain. The next step is to determine which channels (if any) approximate
straight line behaviour the best. The “best fit” is based on the correlation coefficient (R
2
);
the closer it is to one, the closer the data display power law decay behaviour. All possible
combinations of channels are tested starting with the user-specified minimum number of
channels, the default being four. The least squares fit for channels one to four is therefore
calculated, followed by two to five, three to six, etc. Then the number of channels is
increased by one and the whole process repeated, i.e. channels one to five are analysed,
followed by two to six, etc. This process continues until the number of data points
evaluated is equal to the number of points in the data set and only one least squares fit is
done, e.g. channels one to twenty. For every combination of channels the results are tested
to determine the “best fit”. The “best fit” combination will have a R
2
value that falls within
a specified range; it will have the slope closest to either -2.5 or -4; and if there are two
combinations having the same properties thus far priority is given to the value
corresponding to the largest number of channels and latest times (figure 4.2).
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