Application of 3D Euler deconvolution and improved tilt angle to the ...

Arab J Geosci (2016) 9: 508 DOI 10.1007/s12517-016-2536-1

ORIGINAL PAPER

Application of 3D Euler deconvolution and improved tilt angle to the aeromagnetic data of In Ouzzal terrane, western Hoggar, Algeria Lakhdar Harrouchi 1,2 & Mohamed Hamoudi 1 & Abderrahmane Bendaoud 3 & Lilia Beguiret 2

Received: 30 June 2015 / Accepted: 31 May 2016 / Published online: 8 June 2016 # Saudi Society for Geosciences 2016

Abstract The study area is located in the western Hoggar Shield (southern Algeria). It includes the In Ouzzal terrane, which consists of Archaean metamorphic rocks. By contrast to other rocks of the Hoggar Shield, the In Ouzzal terrane represents an exception of being neither deformed nor metamorphosed during the Pan-African event, remaining as a rigid block since 2 Ga. Although, previous geophysical works in the area include an airborne magnetometer and gamma-ray spectrometric survey as well as ground gravity and magnetotelluric survey structurally, the study area has not been very well understood. In this paper, we present the interpretation results of the airborne magnetic data by using the 3D Euler deconvolution and the improved Tilt-angle methods. These results reveal the existing of fault systems (FS) occurring within the center of the study area and along the latitude of 22°; the results also suggested that the deepest fault system is oriented NE–SW and is represented by parallel major faults splitting the In Ouzzal terrane into two different parts: northern and southern. The northern part moved northwards, whereas the southern part moved southwards colliding with the Iforas unit. The interpretation confirms that the In Ouzzal terrane and the surrounding Pan-African structures are bound two by two sub-vertical lithospheric faults with the existence

* Lakhdar Harrouchi [email protected] 1

Geophysics Department, FSTGAT/USTHB, P. O., Box 32, Bab Ezzouar, 16111 Algiers, Algeria

2

Sahara Geology Laboratory, Kasdi Merbah University, P. O., Box 511, 30000 Ouargla, Algeria

3

Geology Department, FSTGAT/USTHB, P. O., Box 32, Bab Ezzouar, 16111 Algiers, Algeria

of dextral and sinistral faults in the west and east of the terrane, respectively. Keywords Euler deconvolution . Improved tilt angle . Aeromagnetic data . In Ouzzal terrane . Hoggar

Introduction Euler’s equation has been used by a number of authors for analyzing both magnetic and gravity data. Hood (1965) showed that Euler’s relation could be used to calculate depth to point pole or point dipole, given a measured vertical gradient. Thompson (1982) developed the technique and applied it to profile data. Reid et al. (1990) developed the technique more widely used version for grid-based data. Also, recent improvements in the technique had occurred which includes the estimation of the structural index (Barbosa et al. 1999). Hansen and Suciu (2002) developed a multiple-source generalization of Euler deconvolution (ED), which is capable of handling complex systems that the single-source algorithm can only deal with approximately. In this present study, we will implement the ED, the tilt angle derivative (TAD), and the improved tilt angle (ITA), to a synthetic magnetic model with the purpose of having the good choice of the parameters which offer a better interpretation, before their implementation to a real case of the aeromagnetic data of the In Ouzzal terrane. The analytical method ED is based on a mathematical development represented by the Euler’s homogeneity equation (Thompson 1982). The TAD has the attractive property of being positive over the sources. It crosses through zero at or near the edge of a vertical sided source, and it is negative outside the source region (Miller and Singh 1994). Salem et al. (2007) have shown that half-distance between +45° and −45° contours

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Fig. 1 a Plan view of synthetic magnetic model composed of dyke (a) and prism (b). The top of the dyke (a) is located at a depth of 3.5 km and the top of the prism (b) at a depth of 4.5 km. b Total magnetic intensity (TMI) anomaly map for synthetic model described in text. The inducing field has an inclination of −10° and a declination of 30°

provide an estimate of the source depth for vertical contacts. The TAD overcomes the problem of the shallow and deep sources by dealing with the ratio of the vertical derivative to the horizontal derivative. The ITA is defined as being the inverse of the tangent of the ratio of the magnetic field module over the square root of the square of the sum of Hilbert transform in the x and y directions. Instead of using the derivatives of the magnetic field, the method uses its Hilbert transform.

Methodology The ED method applied to the potential field data finds the location of parameters of the local magnetic sources. It is based on a mathematical method represented by Euler’s homogeneity equation (Thompson 1982). If we consider a magnetic source, located at the point of local coordinates (x0, y0, z0), the total magnetic intensity at the point (x, y, z) can be written in the form: K M ðx; y; zÞ ¼ rhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi iN ðx−x0 Þ2 þ ðy−y0 Þ2 þ ðz−z0 Þ2

ð1Þ

where K is a parameter independent of (x, y, z) and N is structural index, in the case of the magnetic data. Thompson (1982) and Reid et al. (1990) showed that N takes the values of 0, 1, 2, and 3 (N = 0 for a contact, N = 1 for a dyke, N = 2 for a horizontal or vertical cylinder, and N = 3 for a sphere). According to Reid et al. (1990), the expression (1) of Euler’s homogeneity equation is given in the form: Table 1 Physical parameters of the dyke model

Depth Magnetic susceptibility Magnetization Total magnetic field Declination Inclination

3.5 km 0.015 SI units 3 A/m F = 37,000 nT D = −10° I = 30°

ðx−x0 Þ

∂M ∂M ∂M þ ðy−y0 Þ þ ðz−z0 Þ ¼ N ðB−M Þ ∂x ∂y ∂z

ð2Þ

where B represents a local constant which characterizes the regional field and are first-order derivatives magnetic field M in the x, y, and z directions, respectively. The principle of the ED is based on the resolution of the preceding equation (2) which contains four unknown parameters (x0, y0, z0, B). Within a selected window, there are n data points available to solve the four unknown parameters (Zhang et al. 2000). We consider a square window size w × w = n on the grids of the gradients of field. This window gives a system of n linear equations. Solutions of the equation system in the sense of least square are derived by resolving the inverse problem (Menke 1989). Detailed numerical development may be found in (Mushayandebvu et al. 2004; Reid et al. 1990). Let ∂M/∂x, ∂M/∂y, and ∂M/∂z be the partial derivatives of the magnetic field M. Following Miller and Singh (1994) and Verduzco et al. (2004), briefly recall that this TAD transformation is given by: 2 3 ∂M 6 7 ∂z TAD ¼ tan−1 4 q"ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ # " ∂M #2 5 ∂M 2 þ ∂x ∂x

All tilt angles obtained belong to the [−π/2, π/2] range. This transformation has many interesting properties (Cooper and Cowan 2006; Salem et al. 2007). An important application for the 3D Analytic signal defined by Roest et al. (1992) is calculating the total gradient. As described above, the analytic

Table 2 Physical parameters of the prism model

Depth Magnetic susceptibility Magnetization Total magnetic field Declination Inclination

4.5 km 0.010 SI units 1 A/m F = 37,000 nT D = −10° I = 30°

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Arab J Geosci (2016) 9: 508 Fig. 2 a Gaussian noise with standard deviation of 0.4 nT. b Gaussian noise with standard deviation of 0.4 nT contaminated TMI anomaly. c Gaussian noise with standard deviation of 2.0 nT. d Gaussian noise with standard deviation of 2.0 nT contaminated TMI anomaly. e Gaussian noise with standard deviation of 6.0nT. f Gaussian noise with standard deviation of 6.0 nT contaminated TMI anomaly

signal amplitude (ASA) can replace the total gradient, which is defined as (Luo et al. 2011; Cooper 2015):

Synthetic magnetic model

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ASA ¼ M 2 þ H x 2 ðM Þ þ H y 2 ðM Þ

The preceding methods ED, TAD, and ITA were implemented on a synthetic magnetic model composed of two sources with simple geometry (Fig. 1a): the first source is represented by a thick vertical dyke (A), at 3.5 km depth. It has a magnetic susceptibility and magnetization of 0.015 SI units and 3 A/ m, respectively (Table 1). This source simulates dykes or fault systems. The second source is represented by a rectangular prism (B), having a depth of 4.5 km and the large depth extension to be regarded as infinite, its magnetic susceptibility is 0.010 SI units, the value of magnetization is 1 A/m (Table 2). The dyke and contact models can be said to represent two extreme, simplified models of real geologic structures (Beiki and Pedersen 2010). This model simulates geological contact

ð4Þ

where M is a total magnetic intensity (TMI) and Hxy are the Hilbert transforms of the TMI in the x and y directions, respectively. The ITA based on the ASA can be expressed as (Luo et al. 2011; Cooper 2015). 2

3

M 6 7 ITA ¼ tan−1 4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 2 2 H x ðM Þ þ H y ðM Þ

ð5Þ

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Fig. 3 The depths obtained by the ED method for the synthetic magnetic model using different structural index N (Gaussian noise with standard deviation of 6.0 nT contaminated TMI anomaly). a Estimated depths using by N = 0. b Estimated depths using by N = 0.25. c Estimated depths using by N = 0.5. d Estimated depths using by N = 0.75

and tectonic block which are often met in the study area. The magnetic response TMI of the synthetic magnetic model has been calculated (Fig. 1b), by using the value of the declination, the inclination, and the total magnetic field of −10°, 30°, and 37,000 nT, respectively. In this study, the synthetic magnetic model data (Fig. 2b, d, f) has been corrupted by Gaussian noise with standard deviations of 0.4, 2.0, and 6.0 nT (Fig. 2a, c, e), respectively. The higher noise levels are included to allow us to demonstrate the stability of the method. Note that calculating the ED (requiring first derivatives) amplifies the noise. These data were processed to estimate the structural index and depth using a moving window size. The ED method has been applied assuming two models (dyke and prism) were performed using various structural indices; (N = 0, N = 0.25, N = 0.5, N = 0.75, N = 1, N = 1.25, N = 1.50 and N = 1.75) by choosing a window size of 11 × 11 grid points (Figs. 3 and 4). In case of N = 0 and N = 1, the ED method gives poor depth estimates, showing that N = 0 and N = 1 are the wrong structural index (Figs. 3a and 4a). For N = 0.25 and N = 1.25, this method gives good grouping and acceptable depths as shown in Figs. 3b and 4b, respectively. Using N = 0.5 and N = 1.5, we got bad solutions depths as illustrated by Figs. 3c and 4c while using N = 0.75 and N = 1.75, we got bad clustering around the theoretical model (Figs. 3d and 4d). The solutions

corresponding to the parameters of ED are represented in Figs. 3b and 4b for contact and dyke structure, respectively. For the dyke (A), we obtained the average depth of 3.47 km (Fig. 3b and Table 3) whereas the depth of prism (B) is about 4.47 km (Fig. 4b and Table 3). The magnetic improved tilt angle (ITA) map generated from the data is shown in Fig. 5. The region enclosed by the 45° and −45° contours is gray, and the zero contour shown by the dashed line indicates an approximate location of the source edges. The contact coincides with the zero crossing and the part of the ITA between ±45° is highlighted (Salem et al. 2007), the new ITA method is less sensitive to noise than the method for TAD (Fig. 5a, b). Figure 5c represents ITA solution applied to the reduced to the pole (RTP) upward continued to a distance of 1 km. The RTP simplified the interpretation because for subvertical prisms or subvertical contacts (including faults), it transforms their asymmetric responses into simple symmetric and antisymmetric forms. The examination of the derived solutions gives an estimate depth close to the theoretical values (Figs. 3b and 4b). Synthetic magnetic examples (prism and dyke) have shown the high resolving power of the proposed technique. This approach has also given very good results when applied to the aeromagnetic data of In Ouzzal terrane.

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Arab J Geosci (2016) 9: 508 Fig. 4 The depths obtained by the ED method for the synthetic magnetic model using different structural index N (Gaussian noise with standard deviation of 6.0 nT contaminated TMI anomaly). a Estimated depths using by N = 1. b Estimated depths using by N = 1.25. c Estimated depths using by N = 1.5. d Estimated depths using by N = 1.75

Field data Geological setting The In Ouzzal terrane, also known as In Ouzzal Granulitic Unit (IOGU) is located in the western Hoggar, southern Algeria, about 300 km to the west of Tamanrasset (Fig. 6). It is one of the 23 (Roest et al. 1992) terranes, defined by Black et al. (1994) in the Tuareg shield, which includes Hoggar (Fig. 7b). The Hoggar is composed of both juvenile Neoproterozoic terranes and Archaean/Paleoproterozoic blocks variably remobilized during the Pan-African (850– Table 3 Tentative structural index and estimated depth for prism and dyke model, respectively

550 Ma) orogeny (Black et al. 1994; Caby 2003; Liégeois et al. 2003). The In Ouzzal terrane consists of two Archaean units, a lower crustal unit made up essentially of enderbites and charnockites, and a supracrustal unit of quartzites, banded iron formations, marbles, Al–Mg and Al–Fe granulites commonly associated with mafic (metanorites and garnet pyroxenites) and ultramafic (pyroxenites, lherzolites and harzburgites) lenses (Ouzegane et al. 2003). It forms an elongated N–S trending block, 450-km long and 70 to 80-km wide in the north around the In Hihaou massif (Fig. 7a). It is separated into two parts by cretaceous formations making more than 1.5-km thickness deposited in a Mesozoic basin.

Structural Index (N)

Estimated depth for prism model (km)

Estimated depth for dyke model (km)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75

3.18 4.47 4.83 5.59 6.36 7.05 7.15 8.39

1.99 2.54 3.00 3.16 3.27 3.47 4.50 5.51

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Fig. 5 a Tilt angle derivative (TAD) map from Gaussian noise with standard deviation of 6.0 nT contaminated TMI anomaly, projected on synthetic model from (1a). b Improved tilt angle (ITA) map from Gaussian noise with standard deviation of 6.0 nT contaminated TMI anomaly The new ITA method is less sensitive to noise than the method for TAD shown in Fig. 3a. c Solutions from ITA applied to the RTP of the synthetic model and upward continued by 1 km, dashed lines show the 0° contour of the tilt angle. Solid lines are contours of the tilt angle for −45° and 45°

Aeromagnetic data Aeromagnetic data of the study area (Fig. 8a) is a subset of an airborne geophysical survey covering the whole Algerian territory which was carried from 1969 to 1974 by the Aeroservice Corporation, in order to give information on the regional geology of the country and the possibilities of prospection for minerals and oil (Aeroservice 1975). Design parameters of the airborne aeromagnetic survey over the In Ouzzal terrane were constrained by the geology. The E-W flight-line direction was perpendicular to the geological Fig. 6 Location of In Ouzzal terrane, southern Algeria, in northern Africa

structures. The distance between lines varies from 2 to 5 km according to the areas, but on average it is about 2 km. The NS tie-line spacing varies from 25 to 40 km. The average of the flying height was fixed at approximately 150 m above ground level. Along a flight line, the sampling interval of the observation points is approximately 46.2 m. The Cesium optically pumped magnetometers used during the survey achieved 0.02 nT resolution (Aeroservice 1975). The raw data plotted on Fig. 8a is actually preprocessed one. Indeed, in the In Ouzzal area, the magnetic field intensity is around 37,000 nT on average. One can notice that the measured field is of

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Fig. 7 a Geological map of the study area (after Caby 1996), 1 Mesozoic sediments, 2 Paleozoic sediments, 3 Cambrian molasse, 4 Cambrian volcanics, 5 Granites intruding the IOGU, 6 PanAfrican metamorphics and granitoides, 7 Neoproterozoic andesites, 8 Late Paleoproterozoic sediments and magmatics, 9 Paleoproterozoic basement, 10 Major shear zone. b Geological map of the Hoggar, southern Algeria (after Black et al. 1994), Tim (Timetrine), Til (Telemsi), Ki (Kidal), Tas (Tassendjanet), Ugi (Iforas), Ou (In Ouzzal), Tir (Tirek), Tch (Tchilit), Ta (Tazat), Se (Serouenout), Eg-Al (EgereAlekzod), Az (Azrou-N’Fad), Is (Issalane), Te (Tefedest), La (Laouni), Ba (Barghot), Ao (Aouzequeur), Ed (Edembo)

the order of 34,000 nT. The difference of ~3000 nT is probably related to a constant value subtracted by Aeroservice Co from raw measurements in order to keep the anomaly field Fig. 8 a Total magnetic intensity map (raw) of the study area. b The polynomial P(x, y) of the first degree

always positive in the area relatively to the reference field. Taking into account the low accuracy of the IGRF models of the preMAGSAT era (Langel and Estes 1982), of the order of

508 Page 8 of 11 Table 4 Estimates of the first degree coefficients

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A

34,076 nT

B C

0.04818 nT/m −0.04722 nT/m

hundred nT especially for geographically limited area like In Ouzzal, we determined the aeromagnetic anomaly field using polynomial approximation of the core field and longwavelength regional field (Hamoudi et al. 2011). In this study, we calculated a first-degree polynomial surface P(x, y), the trend function (Fig. 8b), is given by P(x, y) = a + bx + cy: where a, b, and c are coefficients to be determined by adjustment using the least-squares method (Martínez-Moreno et al. 2015). The results of the least squares procedure applied to first degree are summarized in Table 4; (x, y) are UTM coordinates of the observation points. The residual anomaly (Fig. 9a) is then obtained by subtracting the regional P(x, y), values from the preprocessed Aeroservice data (Fig. 8a). In order to consider an analytic method and in particular, this technique assumes the residuals to be random errors with zero mean (Fig. 9b). Unlike the gravity field which is vertical, the shape of the magnetic anomaly is closely related to the combination of two vectors: (1) the normal core field vector direction which is vertical only at the magnetic poles and (2) the magnetization vector of the magnetic crustal sources. Baranov (1957) introduced a mathematical transformation called the reduction to the pole (RTP) to correct the distortion of the magnetic anomaly field. In this study, we derived the RTP anomaly map using an inclination of 27° and a declination of 4.7°W for the normal field in the center of the area assuming that the magnetization is induced Fig. 9 a The magnetic residual anomalies obtained by subtracting the regional P(x, y), values from the original of the Aeroservice data of the In Ouzzal terrane. b Histogram of the estimated assumes the magnetic residual anomalies

(Blakely 1995). The magnetic anomaly field was also upward continued to a height of 0.5 km (Fig. 10a). The comparative study of the RTP anomaly map and the geological map of the study area showed a good correlation, this indicates that the magnetic structures generally follow the direction of the geological structures. The analysis of energy spectrum allows identification of three cutoff frequencies related to the change of spectrum slope (Fig. 11), so it is possible to classify magnetic anomalies in three categories, according their wavelengths and correspond to distinct geological units; the first one is characterized by short-wavelength: Depth (Z) ≺ 2.5 km (green solid line), the second one is characterized by middle-wavelength: 2.5 km ≺ Depth (Z) ≺ 6 km ( red solid line). The last one is characterized by long-wavelength: Depth (Z) ≻ 6 km (blue solid line).

Results and discussion Figure 12 represents Euler solution, projected on geological map of In Ouzzal terrane shows a perfect accordance of the positions of the Euler solutions with anomalies of short and large wavelengths related to several tectonics events and lithological formation. In this study, we calculated two types of solutions; prism (geological contact, tectonics blocks…) and dyke (lineaments, fault systems...), by using Euler parameters (Fig. 12a, b), respectively. In this part, we get the following results: lithologic contact the In Ouzzal terrane and the adjacent terranes coincide with the solution of medium depth (14 km). According to the

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Fig. 10 a Reduced to the pole (RTP) magnetic anomaly data from In Ouzzal terrane using a magnetic inclination of 27° and a declination of 4.7°W, and upward continued to a distance of 0.5 km. b Improved tilt angle (ITA) map of the study area. White solid lines are the major faults of the study area, WOF West Ouzzalian Fault, EOF East Ouzzalian Fault, AF Adrar Fault, TF Tirek Fault, IOF Intra-Ouzzalian Fault, and FS Fault Systems

ITA map (Fig. 10b), the edges of In Ouzzal terrane (EOF and WOF) with the branches of the Pan-African structures which surround it are delimited by two subvertical major shear zones. In part NW of In Ouzzal terrane, there is excellent agreement between the Pan-African magmatism (granites) and Cambrian volcanic with sources surface (blue). The western limit of In Ouzzal terrane with Tassendjanet terrane (Tas) shows solutions of great depth (more than 6 km); probably Fig. 11 Energy spectrum applied to the RTP of the aeromagnetic data of the study area

is a subduction area. Solutions located in the NE of In Ouzzal terrane are limited by Ahnet terrane (Ah), characterized by a very major structure which corresponds to granites PanAfrican on the level of the contact between the crystalline basement and the sedimentary cap, and also at the volcanic formations in the west of central area of In Ouzzal terrane, due probably to magnetic deeply sources. In this part, sources surface up to 3–4.5 km (blue and green) underline part of the Adrar fault (AF) area which limits it In Ouzzal to the east

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Fig. 12 Solutions of the ED projected on geological map of In Ouzzal terrane. 1 Mesozoic sediments, 2 Paleozoic sediments, 3 Cambrian molasse, 4 Cambrian volcanics, 5 Granites intruding the IOGU, 6 Pan-African metamorphics and granitoides, 7 Neoproterozoic andesites, 8 late Paleoproterozoic sediments and magmatics, 9 Paleoproterozoic basement, 10 major shear zone. a Solutions of the ED of contact model using by structural index N = 0.25. b Solutions of the ED of dyke model using by structural index N = 1.25

the major sources are concentrated in the southern part (red), where they underline in particular the two faults EOF and WOF, respectively. The AF which located in the east of the In ouzzal terrane is vertical (Fig. 10b). The center of north part is characterized by almost absence of Euler solution due to an important lack of the magnetic anomalies in this area. In the western central area (along the latitude of 22°), a couple of solutions of medium depth, in a real form, is characterized the contact between the adjacent terranes pit and the In Ouzzal. In the central part of the study area (along the latitude of 22°) is affected by sets of fault systems (FS), which are mainly trending the NE–SW directions (Fig. 10b), with a high depth (more than 10 km). According to the ITA map (Fig. 10b), the FS of the adjacent areas are subverticals, it can be interpreted as a major fault that separates In Ouzzal terrane into two compartments: northern and southern, with the existence of dextral and sinistral faults from the west to the east of the terrane, respectively. Another important concentration of major sources is located within the cretaceous basin which separates In Ouzzal into two parts. This event suggests that the constitution of this graben was accompanied by the installation by an

important magmatic. One of the discoveries of these results is the identification of the prolongation of the EOF (the southern part) under the cover cretaceous of this basin. The surface sources (blue) are primarily intra-ouzzalian. They are correlated for example with the Pan-African granites and the basic ultrabasic complex of In Allarene. In the two parts of In Ouzzal, the surface sources show alignments (NNE–SSW with NE–SW) which correspond to faults and lineaments.

Conclusion The application of the analytical method of the ED and ITA to the aeromagnetic data of In Ouzzal terrane led to the very interesting results in the geological cartography. The solution obtained with ED gives better-focused depth estimates, which are closer to the real position of sources; In the central part of the study area; existence of a fault system oriented NE–SW rather more deep with the lower parts of the Paleozoic cover. This system separates the In Ouzzal terrane in two parts: this last interpretation confirms that In Ouzzal terrane, the setback

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is dextral, while in the west, it acts rather of a sinister setback. According to the method of ITA, the edges of In Ouzzal with the branches of the Pan-african structures which surround it are delimited by two subvertical fault systems, probably lithospheric. They are very clear in the southern part which includes the northern part. Acknowledgments The authors would like to thank the Draria Nuclear Research Center (CRND), Algeria, for providing the aeromagnetic data shown in Fig. 8a. Thanks are due to the anonymous reviewers who helped improving the final version of this paper. Thanks to GRJ Cooper from University of the Witwatersrand, South Africa, for their help. Sincere thanks to N Bournas from Geotech Ltd. for his constructive comments on the manuscript. Thanks to the Editor of AJGS for his kind cooperation and help.

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