Geoscience Reference
In-Depth Information
Class 1
0, 62
Class 2
62,80
Class 3
80,160
Class 4
160, 210
Class 5
210, 235
Class 6
235, 255
Digitalized
data
Mean
4
0,811
72,093
93,054
198,517
227,367
245,087
Standard-
d
eviation
9,761
4,432
11,085
4,945
4,626
5,558
H
value
Mean
0
,218
0,222
0,192
0,181
0,172
0,163
Standard-
deviation
0,090
0,107
0,095
0,071
0,070
0,070
Table 1. Statistical parameters estimated from the histograms (gray level and corresponding
H
values) related to the six classes.
6. Conclusion
In this study, the 2D-mBm has been successfully used for a local Hölder regularity-based
modeling of the core image. We have presented three methods for estimating the local
regularity. The first and the second ones are FFT-based algorithms using, respectively, the
Morlet wavelet and the Mexican hat, while the third method is obtained by extending the
one-dimensional multiple filter technique to 2 dimensions
(2D MFT). The application of
these methods on synthetic 2D-mBm paths showed that the 2D MFT yields the best
estimations of the
H
functions.
The analysis of profiles extracted from the digitalized core image data reveals a fractal
behavior. Furthermore, the regularity maps obtained by 2D MFT from the digitalized data
can characterize heterogeneities from the analyzed core. Although a Hölder exponent value
does not describe a specific geological facies, its local variation reflects the lithological
changes (faults, breaks, stratifications, etc.). The presented analysis must be undertaken on a
large number of cores in order to establish a relation between a geological facies, the
corresponding gray level and
H
values.
7. Acknowledgements
I would like to thank Mr. Tenkhi for his comments and suggestions.
8. References
Barrière, O., 2007. Synthèse et estimation de mouvements browniens multifractionnaires et
autres processus a régularité prescrite. Définition du processus auto-régulé
multifractionnaire et applications (
in french
). PhD thesis. Univ. of Nantes (France).
Benassi, A.; Jaffard, S. & Roux, D. (1997). Elliptic Gaussian random processes.
Rev. Mat.
Iberoamericana
, Vol. 13, No.1, pp. 19-90.
Bicego, M. & Trudda, A. (2010). 2D shape classification using multifractional brownian
motion.
Lecture Notes in Computer Science
, Vol. 5342, pp. 906-916.
Bourissou, A.; Pham, K. & Lévy-Véhel, J. (1994). A Multifractal Approach for Terrain
Characterization and Classification on SAR Images;
International Geoscience and
Remote
Sensing
Symposium
(IGARSS)
,
Vol.
3,
pp.
1609-1611.
doi :
10.1109/IGARSS.1994.399514. August 8-12, 1994.
Search WWH ::
Custom Search