Introduction

Because of the limits of the conventional methods based on traditional manual overlay processes, mineral exploration require nowadays the use of updated and innovative geomatic approaches. In fact, these methods are focused on the integration and combination in a Geographical Information System (GIS) environment of various geodatasets to identify efficiently new mineral targeting zones. Recent years have witnessed a great deal of interest for the application of GIS-based predictive spatial analysis techniques in order to integrate several exploration datasets in the framework of different deposit models for mineral potential mapping.

Based on a manner of weighting evidence, Bonham-Carter (1994) described predictive analysis techniques as knowledge-driven and data-driven models. Knowledge-driven models are more suitable for underexplored or unexplored areas characterized by few number of deposits (Porwal et al. 2006a; Bonham-Carter 1994; Carranza 2009). They use mathematical theories (e.g., Boolean operators, fuzzy logic, and Dumpster-Shafer belief functions), centered on the knowledge of the geologist explorer, where weighting evidence depends on experts’ opinions. However, in data-driven models, the weights are calculated using statistical methods that quantify the spatial relationships between the evidential layers and the training sites (control points). These models, more appropriate for moderate to well-studied areas with a reasonably large number of known deposits (Porwal et al. 2006b; Carranza 2009), are based on several techniques such as logistic regression, artificial neural network, and weights of evidence (Harris et al. 2001).

The weights of evidence model is a Bayesian statistical method that uses the conditional probabilities to predict a hypothesis about the occurrence of an event based on the combination of known information in a study area where sufficient data are available to estimate the relative importance of each the information. In the recent years, it has been applied in several domains such as archeology (Diggs and Brunswig 2010), landslide susceptibility analysis and hazard (Mathew et al. 2007; Barbieri and Cambuli 2009; Hyun-Joo and Saro 2010), biology (Wildman and Peters 2008), geothermal potential (Yousefi and Kamkar-Rouhani 2004), and forests and fires (Romero-Calcerrada et al. 2008; Fagin and Hoagland Bruce 2010). It has also been used to map mineral potential of a variety of mineral resources such as Cu-Pb-Zn (Benomar and Fuling 2006), VMS Cu-Au (Partington 2010), gold potential (Carranza 2009; Ziaii et al. 2009; Nykänen and Salmirinne 2007; Nykänen et al. 2011), and magmatic nickel sulfide (Porwal 2010). In this work, it will be used to map mineral potential of tin-wolfram (Sn-W) and rare metal mineralization in the Laouni area (Hoggar shield, Algeria).

The Laouni region, also known as “Laouni rare metal province,” is characterized by the abundance of rare metal mineralization associated with peraluminous rare metal granitoïds (RMGs). Over the past decades, discoveries and prospecting breakthroughs have received a significant attention. The study area encloses several known mineral occurrences represented by deposits and prospects. However, previous works are focused mainly on conducting intensive geochemical testing of the surface by collecting a grid of samples over the areas which are amenable to soil geochemistry testing. In addition, conventional methods are based on personal experience and interpretation of existing geological, geochemical, or geophysical data (e.g., Lelubre 1952; Boissonnas 1973; Benazouz-Fezoui 1989; Chalal 1989; Azzouni-Sekkal 1990; Djadoun 1993; Chillak et al. 1986; Al 1990; Kesraoui 2006).

The main purpose of this study is the application of the weights of evidence modeling by combining multi-source geospatial data in a GIS environment for the assessment of Sn-W and rare metal potential. The aim is to increase the chances of finding deposit sites within the Laouni region. This outcome has a great number of advantages, including maximizing processing efficiency, easy interpretability, and improved decision making.

The method encloses also some disadvantages such as the use of binary maps which may result in loss or distortion of valuable information. This is corrected by the introduction of the “extended weight of evidence (WofE)” (Porwal et al. 2001) and fuzzy WofE (Porwal et al. 2006) and modified fuzzy WofE (Zhang et al. 2014). In recent years, the uncertainty of mineral potential map (MPM) due to missing evidence was advantageously studied (Zuo et al. 2015).

This article goes through the following three crucial aspects: first, various types of geodatasets are selected carefully and are processed for building the WofE model. Second, quantitative analysis of spatial association between evidential layers and the known Sn-W-rare metal (RM) mineralization is exposed for better understanding of the ore-controlling factors. Last but not least, the resultant mineral prospectivity map is validated using “test deposits.”

Geological background of the study area

The Laouni study region is located at the southern part of Hoggar, in south Algeria. It is bounded by latitudes 20–21°N and longitudes 5–6°E. Geologically speaking, it belongs to the central part of Hoggar which constitutes the Air and the Adrar of Iforas of the Tuareg shield interpreted as the result of a complete Wilson cycle which occurred between 800 and 600 Ma (Black et al. 1979; Caby et al. 1981). Previous studies (Black et al. 1994; Liegeois et al. 2003) show that the Hoggar shield is made of 23 terranes limited by mega-shear zones and basal thrusts. Four of them, namely, Laouni, Azrou-N’Fad, Tefedest, and Egéré-Aleksod, grouped under the acronym “LATEA” (Liegeois et al. 2003), are made principally of Proterozoic basement with basic features (Bertrand et al. 1986). Our study region is part of this large structural unit (Fig. 1).

Fig. 1
figure 1

Tuareg shield terrane map (Black et al. 1994): Djanet (Dj), Edembo (Ed), Aouzegueur (Ao), Barghot (Ba), Assode-Issalane (As-Is), Tchilit (Tch), Tazat (Ta), Serouenout (Se), Egere-Aleksod (Eg-Al), Azrou-n-Fad (Az), Tefedest (Te), Laouni (La), Iskel (Isk), In Teidini (It), Tin Zaouatene (Za), Tirek (Tir), Ahnet (Ah), In Ouzzal (Ou), Iforas granulitic unit (Ugi), Tassendjanet (Tas), Kidal (Ki), Tilemsi (Til), and Timetrine (Tim)

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The simplified geological map of the Laouni area (Fig. 2) shows eight main geological units. Units (i) and (ii) correspond to Paleoproterozoic metamorphic series made mainly of gneiss and metasediments metamorphosed under amphibolite or granulite facies. Unit (iii) consists of Neoproterozoic rocks enclosing volcano-clastic series bounded generally by tectonic contacts (Bertrand and Caby 1978). Units (iv) and (v) are essentially composed by Pan-African migmatites and syn-kinematic granitic batholiths (>70 % surface), intruded in metamorphic country rocks with sub-horizontal foliation dated between 600 and 630 Ma (Bertrand et al. 1986). Unit (vi) consists of mafic-ultra-mafic rocks, interpreted as ophiolitic remnants (Black et al. 1994) intrusive into syn-kinematic granites and Neoproterozoic metamorphic rocks and emplaced between 600 and 520 Ma (Cottin et al. 1998). Unit (vii) is post-orogenic albite-topaz bearing granitic intrusions related to the “Taourirt magmatism” dated at 525 Ma and all linked to late movements along mega-shear zones (Black et al. 1994) that are relatively abundant in the Tuareg shield and to which Sn-W and rare metal mineralization are strongly associated. Unit (viii) is represented by Paleozoic sedimentary covers of platform type.

Fig. 2
figure 2

Simplified geological map of Laouni region

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Weights of evidence theory

The WofE is a Bayesian statistical method that uses conditional probabilities to determine the relative importance of occurrence “evidence.” An exhaustive explanation of the mathematical formulation of the WofE modeling method is revealed in Bonham-Carter (1989, 1994), Wang and Al (2002), and Carranza (2009).

WofE calculations are based on prior and posterior concept of probabilities. Prior probability, noted P (D), is defined as the probability of a given number of unit cells N (D), containing a mineral deposit D, in the study area consisting of total cells N (T), without taking into account any other information. It can be expressed as

$$ P(D)=N(D)/N(T) $$
(1)

Posterior probability is a revised original probability (prior probability) with the introduction of a new information called evidence. According to Bayesian theorem, it is defined as the probability of occurrence of mineral deposit “D” given the presence of the condition B1 and noted P (D|B1).

$$ \begin{array}{cc}\hfill P\left(D/B1\right)=P(D)*\frac{P\left(B1/D\right)}{P(B1)}\hfill & \hfill \left(\mathrm{Bayes}\ \mathrm{theorem}\right)\hfill \end{array} $$
(2)

For “n” variables (evidences), Bayesian theorem is expressed in its general form as

$$ P\left(D/B\right)=P(D)*\frac{P\left(B1/D\right)}{P(B1)}*\frac{P\left(B2/D\right)}{P(B2)}*\frac{P\left(B3/D\right)}{P(B3)}\cdot \cdot \cdot \cdot \cdot *\frac{P\left(Bn/D\right)}{P(Bn)} $$
(3)

The WofE method generally uses a log-linear form of the Bayesian probability to assess the importance of evidence by a pair of weights; the positive weight (W +) expresses the presence of the evidence B, and the negative weight (W −) its absence denoted \( \overline{B} \).

$$ {W}^{+}=\mathrm{L}\mathrm{n}\cdot \frac{P\left(B/D\right)}{P\left(B/\overline{D}\right)}=Ln\frac{N\left(B\cap D\right)/N(D)}{N\left(B\cap \overline{D}\right)/N\left(\overline{D}\right)} $$
(4)
$$ {W}^{-}=\mathrm{L}\mathrm{n}\cdot \frac{P\left(\overline{B}/D\right)}{P\left(\overline{B}/\overline{D}\right)}=\cdot Ln\frac{N\left(\overline{B}\cap D\right)/N(D)}{N\left(\overline{B}\cap \overline{D}\right)/N\left(\overline{D}\right)} $$
(5)

The pairwise of weights (W + and W −) shows the character of the relationship between the training points and the evidential theme B. They are calculated for each evidential theme.

The difference between the two weights, known as the contrast, C, is also calculated.

$$ C={W}^{+}-{W}^{-} $$
(6)

The contrast represents an overall measure of spatial association between the set of deposits D and the evidential theme B, combining the effects of the two weights. For a positive correlation, C is positive and C is negative in the case of negative spatial correlation.

The studentized contrast or confidence (stud(C)) is also necessary and expresses a useful measure of the significance of the contrast C and provides an approximate test of the spatial association, i.e., as an informal test that the contrast C is likely to be “real” (Bonham-Carter 1994). It is defined as the ratio of the contrast C to its standard deviation (σ).

$$ \mathrm{Stud}(C)=C/\sigma $$
(7)

The basic idea in the weight of evidence processing is to see which predictor theme shows more deposits in order to suggest that the selected evidential pattern is more predictive and coherent.

Datasets and modeling methodology

Datasets and deposit recognition criterion selection

Datasets used in the current study were mainly extracted from systematic research and geological mapping report (Chillak et al. 1986; unpublished report) enclosing mineral occurrences (deposits, prospects, and mineralized zones), geological map, geochemical anomalies, and tectonic map, whereas airborne radiometric and magnetic data are acquired from “Aéro Service Corporation” (1974) works. All collected raster datasets are georeferenced, digitized, and integrated in GIS environment in order to extract required evidential geoinformation for weights of evidence analysis.

Sn-W-RM mineral occurrences were integrated into the prospectivity analysis as “training sites.” Forty-eight mineral occurrences which fall within the study area (Appendix 1) are collected from several bibliographic documents (Armines 1977; Syntchouk et al. 1984; Chillak et al. 1986).

The geochemical anomalies are used to create a “mineralization density map” in order to assess mineral fertility of hosted rock. This map is produced from the distribution of 324 anomalies. The lithological units and tectonic and magmatic layers are derived from various geodatasets and maps. The geophysical data are part of the nationwide airborne magnetic and radiometric coverage of Algeria, flown with line spacing of 2 km. The data were acquired at an elevation of 150 m to provide information about the near-surface geology.

The study area encloses several rare metal deposits such as Nahda, Rechla, Sedis, Tit N’Enir, and Tamazaror. Spatially and genetically, they are associated with the peraluminous related to post-orogenic granitoid, so-called RMGs. The Sn-W-RM mineralization (Appendix 2), enclosing Sn-W, Ta-Nb, Be-Li, La-Ce, Zr, and Bi, are controlled by five ore-controlling factors (deposit recognition criteria): (i) geology (lithological units) including gneiss, migmatites, métasédiments, and volcano-clastic rocks; (ii) tectonic structures, particularly NE and NW faults, as well as circular structures (Chillak et al. EREM 1986; Al 1990); (iii) plutonic rocks, in view of the fact that all Sn-W-RM mineral occurrences are spatially genetically related with “hyper aluminous post-orogenic granites”; (iv) geochemistry, because Sn-W-RM geochemical anomalies seem to be an important factor in showing the link between geochemistry fertility and hosted deposit rocks; and (v) geophysical parameters given that magnetic and spectrometric signatures (U, Th, and K) can be successfully used to map RMG plutons and identify circular structures. Thus, the following features representing the basic recognition criteria for our model are

  • Location within the appropriate geological unit.

  • Location within or around RMG plutons.

  • Location near or at the intersection of NE and NW faults and within circular structures.

  • Location around or within geochemical Sn-W-RM anomaly zones

  • Association with favorable geophysical parameters.

From the existing geodatasets, we have built a GIS database including mineral occurrence layer that represents the training sites and four thematic layers characterizing the geological ore-controlling factors (Fig. 3).

Fig. 3
figure 3

Geological evidential themes digitized from raster datasets

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Evidential map generation and spatial analysis

The pixel size used in the present analysis is 1 × 1 km, which is imposed by the scale and the resolution of available geospatial data for the study area. However, the pixel size is considered adequate to represent lateral extension of individual prospects and ensures representation of only one prospect per pixel.

The study area measures 11,570 km2 or N{T} = 11,570 pixels. Multi-class evidential maps were produced for each exploration factor. Most of continuous data were classified into equal-value classes, while to the categorical data, such as the “geological units,” a unique attribute value was set to each class.

A proximity analysis (buffering) was performed on faults, circular structures, and RMG plutons where the weighting of a particular feature in the analysis decreases with increasing distance from the feature. Features in each of the evidential maps were buffered at variable intervals. All the evidential maps used in this study that provide information related to the deposit recognition criterion model are given in Figs. 4 and 5.

Fig. 4
figure 4

Binary predictor maps derived from geological data

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Fig. 5
figure 5

Binary predictor maps derived from airborne geophysical data

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The spatial association between the derived multi-class evidential layers and the known mineral occurrence were quantitatively analyzed to determine thresholds for binary reclassification. Only classes showing the strongest values of weights and characterized by good confidence were retained as predictor pattern.

The following table shows an example of the calculated weights related to the spatial association between the “lithological units” and training sites (Table 1).

Table 1 Summary of “lithological units” of WofE calculation parameters
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As expected, the strongest positive values of W +, contrast and confidence, correspond to RMG class (class 2). Thus, RMG can be taken as the best predictive geological unit, in addition to the “ migmatite PR1” unit (class 4) which seems also to be a suitable lithological predictor unit as expressed by a positive contrast (0.6335) and a good value of confidence (2.1193). In the reclassified lithological evidential binary theme, these two units were assembled together to form a single predictive class, and the weights of evidence parameters were recalculated (Table 2).

Table 2 Weights of the binary reclassified lithological theme
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In the same way, all of the themes were treated, and after analyzing their weights of evidence statistical parameters, the other binary predictor themes have been weighted, analyzed, and reclassified into binary maps.

Weights of evidence modeling results

The WofE modeling requires the combination of all generated binary predictor maps. Modeling without checking with statistical test of conditional independence (CI), a preliminary generated MPM causes an overestimation or underestimation of posterior probability induced by conditional dependence between maps.

In practice, the combined maps are not completely independent and always present some degree of dependence to one another (Bonham-Carter 1994; Mihalasky 1999; Porwal and Halle 2003). Thus, CI is always violated to some degree. Therefore, the geomodeler must assess the severity of the violation and try to identify the maps that are causing CI problems so they can be rejected from the final analysis. To overcome such a problem, various tests for CI were suggested; the first one is pairwise test for CI that calculates χ 2 (chi-squared) statistic value where for 1 df and 95 % of probability level χ 2 = 3.8 rejects the CI test (Bonham-Carter 1994). The second one is the original overall test (OT). If 95 > OT > 0.85, CI is not violated seriously. The last one is the new omnibus test (NOT) that is more effective, not subject to limitation, and is applied even in areas with large or small number of training points (Bonham-Carter et al. 1989; Paganelli et al. 2002; Agterberg et al. 1993; Wright and Bonham-Carter 1996; Carranza and Hale 2000, 2002; Thiart et al. 2007). In this case, the CI hypothesis is accepted if 85 < NOT < 95 %.

CI test results, obtained for the preliminary model, cannot be represented here because of its voluminous contingency table which indicates a number of CI problems between some layers. To overcome this difficulty, we separate the predictor maps into two intermediate models, geological and geophysical predictor maps.

Geological predictor patterns and CI tests

The geological model consists of seven binary predictor maps which have been checked with the CI test. The contingency table results, given in Table 3, illustrate clearly some degree of dependence between predictor maps 1 and 2 (“intersection fault point density pattern” and “fault density pattern”) and other maps as shown by the calculated high values of χ 2 and low values of its corresponding probability. Then, the final modeling requires the rejection of these two maps.

Table 3 Contingency table for CI test for the geological model
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Geophysical predictor patterns and CI tests

The geophysical predictor patterns consist of ten predictor patterns including uranium (U), thorium (Th), potassium (K), U/Th, U/K, and Th/K, all well expressed by their respective binary predictor maps (Fig. 5). These patterns were also assessed using the CI test. The CI contingency table results (Table 4) show clearly that “circular structure density” (map 9) causes a serious CI problem as well as the U/K theme (map 6) as shown by the high values of χ 2 and their low corresponding probability values. Their rejection from the final model seems to be necessary.

Table 4 Contingency table for CI test for the geophysical model
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WofE modeling and cross validation

Modeling without CI problematic layers, we obtain a more coherent model enclosing only 11 evidences. The CI test contingency table indicates acceptable values of probabilities and chi-squared (Table 5). The MPM, obtained from this model and represented in Fig. 6, was reclassified into the following three classes: prospective, less prospective, and not prospective areas.

Table 5 Contingency table for CI test without problematic predictor maps
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Fig. 6
figure 6

Mineral prospectivity map for Sn-W-RM of Laouni study area

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Control of the modeling results using “deposit tests”

In order to test the predictive accuracy of our exploration modeling pattern, a control model was generated using only 40 of the 48 training sites previously used. Eight mineral occurrences (no. 28, 29, 30, 31, 32, and 34; bold in Table 6), representing the best deposits of Nahda region, were retired from training sites in this analysis. The posterior probability map, obtained from this model (Fig. 7), shows comparable results as the previous MPM, and efficiently predicts the locations of the well-known deposits of Nahda, validating the consistency and effectiveness of the used exploration model. This reveals a large success of the weights of evidence modeling applied for Sn-W-RM prediction in this region.

Fig. 7
figure 7

MPM control indicating the prediction of the well-known deposits of Nahda

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Conclusions and perspectives

The GIS-based “weights of evidence” approach, carried out step by step using MapInfo-SDM, was successfully applied in the Laouni area. The existing deposits are used as training sites and geodatasets as predictor patterns describing the deposit recognition criterion model of Sn-W-RM of RMG deposit-type sought.

According to the WofE modeling: (1) we have built a digital database including a training site layer including 48 mineral occurrences and five thematic layers representing the RMG deposit recognition criterion model (lithology, faulting, magmatism, geochemistry, and geophysics), all collected from diverse geodata, digitized, and integrated into a GIS environment. (2) Seventeen binary predictor maps were derived from the thematic layers, weighted to select the best of them, and are combined to generate a preliminary posterior probability map. (3) The obtained model was checked for the CI test, and six problematic layers were deleted from the final modeling. (4) The retained coherent evidential layers were combined in the final model to generate a valid posterior probability map representing the “mineral prospectivity map” for Laouni, showing the following three main areas: predictive, less predictive, and not predictive areas. (5) The permissive areas, reduced to a small surface, include more than 30/48 mineral occurrences and represent the most predictive zones for Sn-W-RM in our region. (6) The MPM generated shows several underexplored areas (Zazir S, Zazir N, Fort Laouni, North Rechla, South Ouenni, Akeboum, and Tedjerine region) and unrecognized favorable areas such as the Mounts of Tessalit.

In order to assess the accuracy of the WofE modeling, we have produced a controlling model where eight of the top deposits of Nahda region were excluded from this model. The MPM reveals similar results: (1) the location of the permissive area is globally comparable with the previous model, (2) the permissive area includes several known deposits (more than 20 deposits) and strongly predicts the known mineralized zone of Nahda region, and (3) the control WofE model can be extended to the adjacent regions of the study area which enclose a small number of deposits.

In the light of these evident results, the GIS-based WofE modeling, combining known mineral deposits and geodatasets, provides an improved tool for mineral potential mapping of Sn-W and rare metals of the Laouni region. This modeling allowed the demonstration of the capability of the multi-source spatial analysis and the accuracy of the data-driven methods applied to a region where deposit recognition criteria are well known. The suitability of the results is equally supported by the location of the well-known deposits of Nahda, Sedis, Rechla, and Tit N’Enir and by the prediction of underexplored areas such as Ouenni, Akeboum, and Tessalit Mount regions.

On the other hand, the WofE modeling led to confirm the use of some adequate ore-controlling factors by the quantitative analysis of their spatial association with the known deposits. A number of them (e.g., association with RMG plutons and NE-NW faults) are well known and previously used by mineral explorers as main ore-controlling factors, whereas other new possible features are recognized (association with migmatitic rocks and association with specific values of magnetic susceptibility). Therefore, the WofE approach is highly recommended in the future for mineral exploration projects of Sn-W and rare metal mineralization in the Hoggar area, especially where airborne geophysical data exists.