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trajectory of a 2D-mBm. The obtained
H
maps highlight well the main fault F1, the break
and the mud films. However, the minor fault F2 is locally noticeable. We note that these
lithological changes are marked by local maxima of
H
values which are higher than those
characterizing the surrounding medium.
Now, we aim to establish a correspondence between the digitalized data values, which are
the gray levels values representing the geological facies, and the
H
value via a statistical
analysis. In order to avoid the abnormally high values of
H
due to the limits effects, we
consider the digitalized data corresponding to a central zone extracted from the core
image (X: 10.8671- 43.5047cm; Y: 0.9550- 10.2627 cm). Thereafter, six classes are
determined by fitting the results yielded by the application of the k-means method on the
selected data. The six classes of the gray levels resulted from this classification are: class
1 = 0, 62 , class 2 = 62,80 , class 3 = 80,160 , class 4 = 160, 210 , class 5 = 210, 235
and class 6 = 235, 255 .
From figure 8, it can be seen that the histograms of
H
values calculated by 2D MFT follow a
normal distribution. For each class, the statistical parameters (mean and standard-deviation)
are estimated from the histograms of the gray level values, and the corresponding
H
values
(Table 1). It is worth noting that for the six classes, the statistical parameters of
H
values,
estimated from the histograms, present very close values. These results show that the
Hölder exponent value can not characterize a geological facies represented by the gray level,
whereas its local variation reflects local lithological changes as explained earlier.
Fig. 8. Histograms of the digitalized data values extracted from the core image, and the
corresponding
H
values estimated by 2D MFT, for the six classes. The six columns from left
to right correspond respectively to the classes 1 to 6.
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