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is the local spectral exponent which is related to the local Hurst (or Hölder) exponent,
. The spectral exponent
in each point
x,y
is computed as the slope of the
scalogram versus the wavenumber in the log-log plan, the
Hx,y
x,y
Hx,y
value is then derived
using the equation (11).
The implementation of the wavelet-based algorithm, using the generalized multiple filter
technique, allows to establish regularity maps from the interpolated GR measurements
recorded in the three channels (K, Th and U) (Fig. 7). In order to interpret the resulting maps
in terms of geology, a geological map of the studied zone is considered.
The results show that the
H
maps, derived from the measurements of all the channels,
exhibit almost an identical image of the local regularity. By reporting the faults affecting the
studied zone on the obtained regularity maps, we remark that the faults locations
correspond to local minima of
H
values. The main accident (the 4°50' fault) is noticeable on
almost all the regularity maps. However, the regularity maps present local minima of
H
values in some places, probably due to less important faults which have to be checked on
updated detailed geological maps.
26°
23°
20°
5°
7°
3°
(a) A geological map of the studied zone
1
- Archaean granulites;
2
- Gneiss and metasediments, series of Arechchoum (Pr1);
3
- Gneiss with
facies amphibole, series of Aleskod (Pr2);
4
- Indif. gneiss (Pr3);
5
- Pharusian Greywackes;
6
- Arkoses
and conglomerates, series of Tiririne (Pr4);
7
- Volcano-sediments of Tafassasset (Pr4);
8
- Molasses
(purple series) of Cambrian;
9
- Pan-African syn-orogenic granites;
10
- Pan-African Granites;
11
- Pan-
African post-orogenic granites;
12
- Granites of Eastern Hoggar;
13
- Late pan-African Granites;
14
- Basalts and recent volcanism;
15
- Paleozoic cover;
16
- Fault.
Fig. 7. (Continued)
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