Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 76 (2015) 436 – 443
European Geosciences Union General Assembly 2015, EGU Division Energy, Resources & Environment, ERE
Using two-dimensional anisotropic wavelet transform for exploring anisotropy from airborne spectrometric measurements Said Gacia*, Naima Zaourarb b
a Sonatrach- Division Exploration, IAP Bâtiment C, Avenue 1er Novembre, Boumerdès (35000), Algeria. Geophysics Department - FSTGAT- University of Sciences and Technology Houari Boumediene (USTHB)-Algiers, Algeria.
Abstract A natural process can be described as a mixture of several components of different scales. The two-dimensional anisotropic wavelet transform is shown to be appropriate to study such processes and to focus on details at a given analyzing scale. In this paper, we apply the normalized optimized anisotropic wavelet coefficient (NOAWC) method on airborne gamma ray recorded over the Hoggar area (Algeria) to characterize anisotropies of orientation, shape and spatial distributions of the radioactive sources at different scales. This technique may provide additional significant information to the conventional analysis. © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the GFZ German Research Centre for Geosciences. Peer-review under responsibility of the GFZ German Research Centre for Geosciences Keywords: Hoggar; anisotropic wavelet analysis; gamma ray
1. Introduction Physical processes present a complex spatial distribution resulting from interactions at different scales. The analysis of the process component corresponding to a specific (or a characteristic) scale contribute to understand the nature’s complexity.
* Corresponding author. Tel.: +213-696-470-613; fax: +213-24-818-942. E-mail address:
[email protected]
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the GFZ German Research Centre for Geosciences doi:10.1016/j.egypro.2015.07.865
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For that purpose, previous researches [14, 16, 17] has shown that the anisotropic wavelet transform can be successfully used to carry on a multi-scale analysis of multidimensional signals [14, 16, 17]. Thanks to its capacity to decode signal components combined at diverse scales, this technique is applied for identifying dominant orientations in geophysical systems. Kumar [15] performed a wavelet analysis using a two-dimensional Morlet wavelet to describe the anisotropic behavior of spatial rainfall fields. Furthermore, the normalized optimized anisotropic wavelet coefficient (NOAWC) method, initially suggested by Ouillon et al. [16] and developed by Gaillot et al. [10], using the anisotropic Mexican hat wavelet, was implemented to detect dominant orientations of different mineral types within rock fabric [10, 11], structural analysis of hypocentral distribution of an earthquake sequence [12]. The airborne spectrometric measurements are originated from gamma ray radiations emitted by radioelements contained in different rock types. The derived radioelements concentrations data allow to establish geological mappings and to localize radioelement anomalies corresponding to zones disrupted by a mineralizing system. Since different geological processes are superposed, the resulting radioactive rocks exhibit a complex system that the conventional analysis cannot perfectly apprehend. In this view, we suggest here a NOAWC-based multi-scale analysis to investigate anisotropy of airborne spectrometric anomalies. In this paper, the NOAWC method is briefly given. Then, its application on airborne spectrometric measurements recorded over the Hoggar area (Algeria) is presented. It is demonstrated that this technique provides the opportunity of identifying and characterizing (in terms of geometry, location, shape ratio and orientation) spectrometric anomalies at different scales. 2. Theory 2.1. Continuous Wavelet Transform The potential of the wavelet theory in image processing has been shown by Antoine et al. [2]. The wavelet transform is a decomposition of a signal into details at different scales and directions using a family of functions, called daughter wavelets, obtained from a mother wavelet \ V .
&
\ aT, b& ,V (r )
& &· 1 §1 \ V ¨ CT r b ¸ a ©a ¹
(1)
& where a is the scale, V is the anisotropy (or shape) ratio of the wavelet, r is the 2D-physical location rx , ry , and
CT is the counterclockwise rotation operator of angle (or azimuth) T with respect to the X-axis & CT (r )
rx cos T ry sin T , rx sin T ry cos T , with 0 d T 2S
(2)
&
The wavelet transform W f of a two-dimensional function f r is given by & W f ( a, r , V ,T )
&
³ f (r ) \
R
2
T &* a , b ,V
& & (r ) d 2 r
(3)
where the asterisk refers to the complex conjugate. The different operations (dilatation, translation and rotation) on the wavelet enable the wavelet transform to locally characterize the signal at diverse scales and directions (or azimuths). The value of the wavelet coefficients quantifies the local match degree between the signal and the analyzing wavelet in terms of scale, location, anisotropy ratio and orientation. Weak coefficients designate a poor correlation between the signal and the analyzing wavelet, while high coefficients indicate a good match.
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&
The wavelet transform is calculated for a range of scales and orientations at all the positions of f r definition 2 & & domain. The combination (a, r , V , T ) leading to large values of the scalogram, W f (a, r , V ,T ) , is related to the dominant scales, anisotropy ratios and orientations around the location orientation within the considered range, Kumar [15] defines a function as:
[ ( a, T )
& r . In order to calculate the dominant
K ( a, T )
³
(4)
K (a, T ) dT
where K (a,T )
³W
f
2 & & (a, r , V ,T ) d 2 r . At a given scale, [ (a, T ) function represents the energy distribution with
R2
respect to the direction T, and the large ȟ values correspond to the dominant orientations. Regarding its anisotropy properties, the anisotropic Mexican Hat is well adapted for the study of singularities in all directions, and motivates us to consider it in this study. Characterized by its anisotropy ratio V, this wavelet derives from a second derivate of a Gaussian function: § 1 § r2 § · ·· & r2 \ V (r ) \ V rx , ry ¨¨ 2 x2 ry2 ¸¸ exp¨ ¨¨ x2 ry2 ¸¸ ¸ ¨ ¸ V © ¹ ¹¹ © 2©V
(5)
2.2. NOAWC method The NOAWC method has been initiated by Ouillon et al. [16, 17] for the needs of detecting the multi-scale organization and the hierarchical geometry of faulting. Then, Gaillot et al. [10] introduced normalization and filtering of the analyzed data to enhance the quality of interpretation. The NOAWC method is described as follows: 1. Choose the resolution or scale parameter a, which control the multi-scale analysis; 2. Choose the limits of the possible integration scales (Va), which govern the shape anisotropy. The minimum and the maximum values correspond the sampling scale and the signal size, respectively; 3. Select the variation domain and increment of the angle (orientation) T, which control the angular exploration; & & 4. Compute at each position r the wavelet coefficient W f (a, r , V ,T ) for each couple (V ,T ) . 5.
Choose at each position, among all the calculated coefficients, the maximal normalized wavelet coefficient which corresponds to the local optimum parameters (a, V ,T ) of the wavelet. These parameters reveal the best correlation between the signal and the selected filters, thus perfectly define the geometry of the irregularity at scale a in terms of location, anisotropy ratio and orientation.
The steps (1-5) are reiterated for the scale values of the considered range. For each scale, the local optimum & parameters (V ,T ) and the corresponding optimum (maximal normalized) wavelet coefficient, for all the locations r , are saved in an output file. 3. Application on airborne gamma ray measurements
This section is devoted to show the results obtained using the NOAWC method from airborne natural radioactivity measurements recorded over the Hoggar (Algeria). The data under study is acquired during a magnetospectrometric survey performed between 1971 and 1974 for the needs of a regional cartography. The average flight heights of the airborne survey is approximately 150m, while the distance between observations points and lines are
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respectively about ǻx =46.2 m and ǻy=2000 m. More survey details on the airborne survey can be found in previous researches [1, 7, 9]. The Hoggar belongs to the Trans-Saharan Pan-African chain [6]. It consists of three longitudinal compartments: eastern, central and western, exhibiting various structural and lithological characteristics, separated by two main submeridian faults, located at longitudes 4°50’ and 8°30’. The complex geological configuration of the Hoggar is the consequence of the collision of two rigid plates: the Western African craton and the Eastern African craton [3, 4, 5] . Here, the NOAWC method is implemented on the Uranium (U) measurements related to a area defined by its UTM coordinates (zone 31): X(m): 604277- 793510 and Y(m): 2266937 -2778937. The spectrometric corrections are first applied on the considered measurements [7, 8, 13]. Then, the corrected data are interpolated using the kriging method (Fig. 1).
Fig. 1. Corrected gamma ray measurements (in cps) recorded in the U channel
Local spectrometric anomalies, characterized by large gamma ray measurements values, can be identified on Fig. 1. They are originated from pan-African Granites. The medium natural radioactivity values are mainly recorded over gneisses and basalts, while the weak values are assigned to sedimentary rocks. This application aims at highlighting the contribution of the anisotropic wavelet transform in detecting, and characterizing the local natural radioactivity sources. The resolutions are selected as multiples of the X-axis sampling rate (ǻx = 46.2 m): a § 92, 185, 739, 1478, 2957, 5914 and 11827m, while the V value is chosen between 0 and 10. For each couple (a, V ) , the angle T ranges between 0 and 180° by 5° increments. The implementation of the NOAWC method on the considered gamma ray measurements provides, for a particular resolution a , values of the local &optimum parameters (V ,T ) and the & corresponding optimum wavelet coefficient W f (a, r , V ,T ) at all the positions r . All these values are stored in files and employed to maps optimal orientations, anisotropy ratios and wavelet coefficients. Only the results corresponding to the resolution a= 1478 m are presented (Fig.2). For the small scale values (a§ 92 and 185m), the T maps illustrate local bright points, corresponding to non-null angle values, which are related to the punctual spectrometric anomalies. The anisotropy ratios map, in its turn,
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presents relatively small V values associated to the radioactivity sources characterized by large optimum wavelet coefficients values. The wavelet coefficients depict the natural radioactivity distribution in the studied area. By increasing the resolution, the optimal angle is scattered on larger piece-wise and its distribution becomes smoother. However on the anisotropy ratios map, the number of the locally small V -value points increases with the scale, and decreases as the scale value exceeds a§ 1478m. Regarding the wavelet coefficients map, the detected anomalies size depends on the selected resolution. The higher resolution, the larger identified anomalies dimension.
Fig. 2. (Continued)
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Fig. 2. Results obtained by the NOAWC method from corrected gamma ray measurements in Fig. 1 for the scale value a§ 1478m. From top to bottom: optimal normalized wavelet coefficients map, optimal orientation map (T, in degrees); optimal anisotropy ratio maps;
The analysis of the functions [ (a, T ) with respect to the angle T for the selected resolution allows to identify the dominant orientations of the natural gamma ray sources of the studied zone (Fig. 3). For the scales a§ 92 and 185 m, the spectrometric anomalies are mainly oriented following T 0q , while for a§ 739m the horizontal direction is still the most important, combined with a secondary direction T 180q . It can be also noted that for the a§1478m, the gamma ray sources are oriented following the major direction T 0q , and minor directions T 5, 10,130, 170q . For a§ 2957 and 5914m, the dominant orientations are respectively T 5, 175q and T 10, 85,110, 175q . Finally, the important dominant orientations are T 90,175q for a§ 11827m.
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Fig. 3. Representation of the functions
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4. Conclusion
This study illustrates that the NOAWC method can be used as a powerful tool to carry out a multi-scale investigation of spectrometric data, and to extract useful information regarding the spatial and geometrical patterns of the spectrometric anomalies, corresponding to radioactive sources, at different scales. It is shown that for a given resolution, using the optimal parameter (anisotropies of shape, orientation and spatial distribution of the sources) maps, the dominant parameters can be determined. Such obtained information is of high importance to apprehend the spatial distribution of the radioactive sources. References [1] Aeroservice Corporation. Aero-magneto-spectrometric survey of Algeria. Final report, 3 volumes, Houston, Philadelphia; 1975. [2] Antoine JP, Murenzi R, Piette B, Duval-Destin M. Image analysis with 2D continuous wavelet transform: detection of position, orientation and visual contrast of simple objects, in « Wavelets and applications», Y. Meyer Editor, Masson Paris; 1992. [3] Bertrand JML, Caby R. Geodynamic evolution of the pan-african orogenic belt: A new interpretation of the Hoggar shield (Algerian Sahara), Geologische Rundschau; 1978, 67: 357-388. [4] Black R, Caby R, Moussine-Pouchkine A. 1979. Evidence for late Precambrian plate tectonics in west Africa, Nature 278, 223-227. [5] Caby R, Bertrand JML, Black R. Pan-African closure and continental collision in the Hoggar-Iforas segment, central Sahara. in Kroner A (ed) Precambrian Plate Tectonics, Elsevier, Amsterdam; 1981, 407-434. [6] Cahen L, Snelling NJ, Delhal J, Vail JR. The geochronology and evolution of Africa, Clarendon Press, Oxford; 1984, 512 pp. [7] Gaci S, Zaourar N, Briqueu L, Hamoudi M. Regularity Analysis of Airborne Natural Gamma Ray Data Measured in the Hoggar Area (Algeria), Advances in Data, Methods, Models and Their Applications in Geoscience, Dongmei Chen (Ed.), ISBN: 978-953-307-737-6, InTech; 2011. p.93-108. [8] Gaci S, Zaourar N, Briqueu L, Djeddi M. Impact of the pre-processings on the fractal properties of the airborne Gamma Ray measurements: a case study from Hoggar (Algeria). Arabian Journal of Geosciences, DOI 10.1007/s12517-011-0407-3; 2011. p. 1-8. [9] Gaci S, Zaourar N. A new regularity-based algorithm for analyzing Algerian airborne spectrometric measurements, Proceeding of EGU 2014, Energy Procedia; 2014, 59: 36 – 43. [10] Gaillot P, Darrozes J, de Saint Blanquat M, Ouillon G. The normalized optimised anisotropic wavelet coefficient (NOAWC) method: an image processing tool for multi-scale analysis of rock fabric. Geophysical Research Letters; 1997, 24(14): 1819–1822.
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