Introduction

Fault systems in the basement have played a major role during the genesis of the Poland Kupferschiefer deposit (Fig. 1). First, these structures have driven fluid migration from brines in deeper parts of bedrock (Jowett 1986; Blundell et al. 2003; Muchez et al. 2005; Wedepohl and Rentzsch 2006; Hitzman et al. 2010). Second, relative high permeability and porosity, required for circulation and accumulation of metals during mineralization, occurred near to basement fault systems (Forster and Smith 1989; Rentzsch et al. 1997; Wagner et al. 2010). Rentzsch and Franzke (1997) have shown several examples of close relationship between major tectonic structures and Kupferschiefer ores in central Germany. To identify the fault systems related to Kupferschiefer-ore locations is an important issue in present day exploration campaigns. However, to recognize these ore-controlling structures sometimes requires huge cost surveys. A first exploration challenge is that buried basement faults are not easily detected, or subject to uncertainty inherent to data interpretation (Lecour et al. 2001; Bond et al. 2007). A second challenge is due to deformation (folding and faulting developed during the structural evolution), which can blur links between a given mineralized location and its corresponding basement fault system. Indeed, fault activity may vary trough time and space, with possibly strong impact on rock permeability and mineralized fluid circulation. Even in cases where fault systems are identified, it is necessary to establish their role and timing of activity to understand their role for a given mineralized locality. To overcome this, we propose to use curvature values obtained from a sequential surface-restoration process for inferring the existence and activity of basement-faults related to Cu mineralization. Curvature, as geometric attribute measurable in horizons of a surface-structural model, can reveal internal deformation in those horizons due a faulting event (Mallet 2002; Moretti et al. 2007). Curvature, computed after several sequential restorations, can be translated as the signal of basement faults presence and also indicates their activity over the geologic record. Estimating correlation between curvature and mineralized locations, it is possible to deduce fault-fractures linked to Kupferschiefer-ores. Finally, we evaluated the usefulness of curvatures as a predictor in the Fore-Sudetic Monocline (FSM), SW of Poland, with the application of a multivariate data-driven predictive method. Particularly, we chose logistic regression (LR) analysis to obtain a predictive model as a combination of curvatures acquired in the restorations. The results show that in locations with high curvature values the predicted probability to host a Cu mineralization increases considerably. We suggest that this methodology provides useful evidence for the Cu potentials assessments in the FSM region.

Fig. 1
figure 1

Simplified geological cross section across the Fore-Sudetic Monocline

Full size image

General Geology

The Kupferschiefer is a metal-bearing black shale, broadly spread across central Europe (from Ireland to Belarus), with very well- known high Cu-grade locations in SW Poland and central Germany (Rentzsch and Franzke 1997; Oszczepalski and Speczik 2011). The Kupferschiefer-ore exploitation in the Legnica-Głogów Copper Belt Area (LGCB), located within the FSM, is one of most important sources of Cu and Ag in the world (KGHM Polska Miedź 2012). This layer was formed at the end of the Permian, overlying volcaniclastic sequences (Rotliegendes and Wessliegendes) of Saxonian age (Oszczepalski 1999), and overlain by sedimentary products (mainly evaporites) of eustatic variations during the Guadalupian to Lopingian (Zechstein Formation) (Lefebvre 1989).

Geologic Settings of the FSM

The Kupferschiefer Formation overlies a group of Early Permian sub-basins covering Paleozoic rocks affected by Caledonian and Variscan tectonics (Karnkowski 1999). The post-Permian sediments correspond to continental successions and shallow marine sediments of Triassic age followed by a Jurassic succession of shallow marine sediments. Basin analysis shows subsidence rates in the Late Permian-Early Triassic superiors to 80 m/m.y. (Central Basin) (Karnkowski 1999; Resak et al. 2008). This rate decreased substantially in Late Triassic and is maintained through to the Jurassic (Karnkowski 1999). At the end of the Jurassic, the top Rotliegend surface in the Lower Silesian basin was at a depth of up to 4 km (Blundell et al. 2003). At the Jurassic–Cretaceous boundary, the Lower Silesian basin was inverted and uplifted, creating the Fore-Sudetic block, bounded by NW-SE trending faults extending from the basement to the post-Permian successions (Blundell et al. 2003). The Cretaceous sediments, present in the eastern part of the Fore-Sudetic Monocline, comprise mainly of sandstones, conglomerates and marls. These rocks unconformably cover older strata (Pieczonka et al. 2008). Northern-Europe was affected by a Late Cretaceous-Early Paleocene tectonic inversion, probably linked to an early Alpine orogeny phase. This event produced the most intensive tectonic movements in the Fore–Sudetic Monocline (Pieczonka et al. 2008), provoking the erosion of hundreds to thousands meters of sediments (Mazur et al. 2005; Scheck-Wenderoth and Lamarche 2005; Resak et al. 2008; Narkiewicz et al. 2010). In the Lubin region, the uplift is estimated to be >1,000 m (Stephenson et al. 2003), eroding rocks from Triassic to Cretaceous. The pre-Cenozoic rocks were tilted \(3^{\circ }\)–\(6^{\circ }\) to the NE, probably during the Alpine orogeny. The post-Variscan cover of Permian–Cenozoic formations is subdivided into the Kimmerian (Permian, Triassic, Jurassic ), Laramide (Cretaceous), and post-Laramide stages (Tertiary, Quaternary) (Oszczepalski 1999).

Mineralization

Three main mineralized sulfide levels both as grains and veinlets can be identified within the shales: a lower dolomite level, an intermediate bituminous black shale level and an upper dolomite black shale level. The main minerals in the polymetallic Kupferschiefer ore in the Fore-Sudetic area are Cu(Cu-Ag) sulfides and other mineral species such as arsenides, sulphosalts, thiosulfates, arsenates and precious metals (Oszczepalski 1999; Piestrzyński et al. 2002). At least three stages are involved in the ore-Kupferschiefer formation (Vaughan et al. 1989; Wodzicki and Piestrzyński 1994; Speczik 1995; Wagner et al. 2010), which represent broadly the main post-Permian tectono-magmatic events in central Europe (Schmidt Mumm and Wolfgramm 2004). The first stage is associated with diagenesis during a Triassic to Early Jurassic rifting event (Ziegler 1982; Bechtel et al. 1999). A second stage is related to the Late Jurassic extensional tectonic event that formed the nearby North German Basin, reactivating Variscan basement faults and extending them upwards through the overlying strata (Symons et al. 2011). Finally, basin inversion and uplifting occurred in northern Europe in the Late Cretaceous-Early Paleocene. This led to erosion of several hundred meters of the Triassic to Cretaceous sedimentary formations (Resak et al. 2008). This last erosion event likely provoked increase of fluid/lithostatic pressure ratio, and hydraulic fracturing allowing circulation of mineralizing fluids, remobilization of elements and replacement and enrichment of Cu-sulfides (Mejia and Royer 2012).

Modeling the Fore-Sudetic Monocline

Modeling Outlines

The surface-based modeling of the FSM is established on cartographic and interpreted subsurface data, which were integrated in a SKUA ® -2011 framework, resulting in a consistent model that honors the input data. The management of data and the main model-building tasks were realized as suggested by Caumon et al. (2009) and PARADIGM (2012). The topographic information was obtained from the SRTM 90m digital elevation data freely provided by the International Centre for Tropical Agriculture (Jarvis et al. 2008). The subsurface data were introduced picking the lithological contacts and faults from regional cartographic information (Dadlez et al. 2000; Pawlak et al. 2008; Oszczepalski and Speczik 2011). Interpreted cross-section from wells and seismic surveys (Wodzicki and Piestrzyński 1994; Krzywiec 2006; Mazur et al. 2010) were used to establish thicknesses and shapes of the main rock units (Fig. 2).

Fig. 2
figure 2

Fore-Sudetic Monocline 3D model built using the structure and stratigraphy SKUA ® -2011 workflow. a The input data comprise cross-sections, a regional geological map of the study area and the interpolated Kupferschiefer depth. The contacts and unit limits are introduced by picking both the map and the cross-sections (see Sect. 3.1). b The meshed domain necessary for the implicit modeling has a resolution of 2,000 and 500 m horizontal and vertical, respectively. The sedimentary units overlaying the pre-Triassic rocks are considered as conformable in the structure and stratigraphy workflow, except for the Post-Cretaceous units deposited upon the eroded Upper Cretaceous units. The Upper Permian units are considered deposited in baselap mode. The crosses represent the borehole locations from Oszczepalski et al. (1997)

Full size image

Outcome FSM 3D Model

The resulting model covers a surface of >31,000 \(\hbox {km}^{2}\) extending from the Fore-Sudetic Block to Świebodzin at north and Kluczbork at east. The vertical extension is down to 6.3 Km mbsl in the deepest part. The grid resolution used in the implicit modeling was about 2 km and 0.5 km horizontally and vertically, respectively. 17 horizons from Cenozoic to the top of Precambrian rocks were created, corresponding to five main depositional periods: Upper Permian to Triassic, Triassic, Jurassic, Cretaceous, and Oligocene to present day. The geometry of the FSM consists of gently NE-dipping strata except for the sub-horizontal Cenozoic units. In general, the final model is similar to an inclined layer cake horizontally eroded in the upper part, lightly folded in the central region with a NE strike fold axis (Fig. 3). Finally, we extracted surfaces representing the top of the main sedimentary units namely: pre-Rotliegend, Rotliegend, Zechstein, Triassic, Jurassic, erosion Cretaceous-Paleocene and post-Oligocene. The top of the Cretaceous (now eroded) was extrapolated following the shape and morphology of the preserved units.

Fig. 3
figure 3

Location of the study area and resulting model of the FSM

Full size image

Detecting Fault Activity from Restoration

Restoration Goals

Restoration aims at reconstructing the original geometry from the current structural geometry. For example, in deformed sedimentary rocks restoration is used to find the original depositional state at a given time. The first attempts to restore a starting geometry were conducted more than 100 years ago by Chamberlin (1910) using an areal preservation criterion in cross-section analysis. Later, his concepts were extended in a volume constant criterion in foreland compressive belts by Dahlstrom (1969). In the last decade, restoration methods integrating the mechanical properties of rocks have been proposed (De Santi et al. 2002; Maerten and Maerten 2006; Moretti et al. 2006; Moretti 2008; Guzofski et al. 2009; Durand-Riard et al. 2013). Although it is proved that accounting for rock mechanic parameters in the restoration offers greater precision and provides better accuracy for describing strain and stress fields (Durand-Riard et al. 2010; Vidal-Royo et al. 2012; Durand-Riard et al. 2013), 3D conformable mesh generation is a significant challenge at large scale. Mesh generation is often time-consuming and requires a very large number of elements to honor fine-scale structural features, especially in complex faulted contexts (Moretti 2008; Caumon 2010; Durand-Riard et al. 2010; Botella et al. 2013). Thus, in this work, we use simple geometric analysis to restore layers to their original depositional states applying surface restoration (also called 2.5D restoration). In the next sections, we explain the basis and methods of 2.5D structural restoration, focusing on detecting faults presence and estimating their activity.

Surface Restoration

The aim of 2.5D restoration is to remove fault slip and unfold deformed surfaces. The unfaulting aims at matching horizon cutoff lines on either side of a fault that compound a given surface. The simplest unfaulting procedure consists in a rigid-body displacement, generally acomplished by domino-block and circular-fault methods (Rouby 1994; Groshong 2006). The unfolding aims to flatten a surface, considering that the continuous part of a surface can return to its original geometry following one of these methods: (i) Simple-shear slip on closely spaced parallel planes (Verrall 1981); (ii) Flexural slip slip parallel to bedding (Dahlstrom 1969).

Because these concepts were initially defined in cross-sections, their applications to map restorations of faulted, and possibly non-developable surfaces, call for specific algorithms, among which are triangle adjustment (Gratier and Guillier 1993), extrapolation of parallel cross-sections (Moretti et al. 2007) and parameterization (Mallet 2002; Moretti 2008). In this work we applied flexural slip, which is achieved by parameterization, preserving the global area of folded and restored surfaces.

Iterative Restoration

In sequential-surface restoration, the horizons are restored iteratively from top to bottom. When a horizon is restored, the deformation is propagated to the underlying horizons (Mallet 2002). This implies that two parallel horizons are flattened at once when restoring the upper horizon only. If this is not the case, it probably means that a deformation event (or several) occurred before the deposition of the layer represented by the upper surface (Fig. 4a). After removing the upper restored reference surface and decompacting the entire stack of sediments using an isostatic approach (Sclater and Christie 1980), which is called back-stripping, sequential, deterministic, surface restoration is applied to simulate iteratively from youngest to the oldest sediment layer (Fig. 5a). Although the iterative surface restoration cannot describe the detailed structural evolution of a study area, it is a useful method in the reconstruction of ancient structural stages (Moretti et al. 2007; Titeux 2009).

Fig. 4
figure 4

a Schematic surface-restoration workflow. The flattening of the upper surface removes the deformation caused by fault activity at the corresponding time. This flattening is propagated on the underlying surfaces. b The curvature, obtained at each restoration, is higher in the folded neighborhood than in the rest of the surface. c For the overall restoration process, the regions affected by several faulting events are highlighted by high curvature values. In this example, the fault \(F_{1}\) has been active for a longer period than \(F_{2}\)

Full size image

Internal Deformation and Fault Activity

Although the main restoration aim is to get the original geometry at a given time, other outputs can be obtained by unfolding and unfaulting. Three common outputs correspond to strain, dilation and curvature which account for surface variations between deformed and restored geometry. The strain corresponds to the deformation tensor at each point of the reference surface before and after restoration. In 2.5D restoration, the strain considers only geometric deformation and does not generally reflect mechanical layering. The dilation is trace of strain tensor and corresponds to local area variation between the restored and current geometry. Finally, curvature is a second order tensor defined on the surface. It is a static geometric measure corresponding to the inverse of the radius of all tangent circles orthogonal to the surface. If reversed, the direction in which the radius is smaller corresponds to the maximum curvature, which relates to folding/faulting (Fig. 4b). Assuming surfaces have correct geometry, curvature reveals high deformation zones in horizons (Lisle 1994; Roberts 2001). For each restoration, the curvature analysis on a selected horizon highlights the most deformed regions at the corresponding geologic time. Other attributes from geometric analysis (e.g., curvature gradient using 3D seismic data (Gao 2013)) can express high deformed areas related to faulting.

Continuous-Surface Representation

In this study, horizons were modelled as smoothed-continuous surfaces for two reasons:

Fault uncertainty In the absence of direct fault observations, it could be hazardous to cut horizons with inferred faults. This work aims to correlate mineralization process with fault activity. If we introduce an inferred fault that does not corresponds to the geologic record then the results will be biased. Wrong modeled faults can be the product of bad interpretation, missing data or noise in the raw data (Cherpeau et al. 2010). Instead, it is possible to represent horizons as smoothed continuous surfaces and then use geometric attributes to detect fault activity (see previous section) (Fig. 4c).

Forced-extensional folds Normal extensional faulting in the basement may develop folding in the sedimentary cover (Finch et al. 2004). This is especially observed when a salt layer above the basement introduces a mechanical decoupling between the basement and the overlying rocks (Withjack et al. 1990; Withjack and Callaway 2000). This is the case in the Fore-Sudetic region, where the thick evaporite-rich Zechstein Formation is deposited directly above the basement (see Fig. 1 and Sect. 3). In the FSM, the present day known faults in the cover may correspond to active basement faults. In early to medium stages of the structural evolution of the region, the faulting in the basement could develop forced extensional folding rather than faulting in the above layers. Examples of salt-related folding due to Zechstein presence have been documented in several locations of Europe (Krzywiec 2006; Kane et al. 2010; Duffy et al. 2013). Therefore, we address the problem of detection of fault zones in the basement and their time activity by studying internal deformation in cover horizons depicted as continuous surfaces (Fig. 5b).

Fig. 5
figure 5

a Synthetic case of structural restoration. Faulted horizons are represented by smoothed-continuous-triangulated surfaces. After flattening, the upper restored horizon is removed and the restoration process starts again. b The high Kmax values, stored in the nodes of the oldest layer, reveal the fault activity. Fault \(F_{1}\) starts its activity before deposition of the middle layer, contrary to \(F_{2}\) whose activity is evidenced only after deposition of the middle layer

Full size image

Restored Models

The restoration of the FSM is achieved as a multi-sequential surface flattening. Taking as reference the horizon at the top of the stack, unfolding is applied on the hanging wall of this horizon, thus obtaining the field of restoration vectors for this horizon. Then, deformation on the stack is achieved applying the field of restoration vectors on the bottom horizons. Finally, the top layer is removed and the unfolding process starts again (Mallet 2002). We chose the flexural slip method KINE3D-2®, available in SKUA, looking for preserving thickness and the global area of the layers. After each restoration, we decompacted the sedimentary units applying the methodology suggested by Sclater and Christie (1980). A total of six restoration routines were realized using the KINE3D-2® workflow. During the restoration, some surface inconsistencies (e.g., unrealistic folding, wrong thickness variations, underlying horizons crossing upper horizons) are adjusted manually. In practice, structural restoration is an iterative process which imposes eventually the reconstruction of the initial surface model attempting to correct these inconsistencies. It was achieved by modifying the initial surface shapes honoring the input data. These corrections are performed before making any new restoration operation (Fig. 6).

Fig. 6
figure 6

Cartoon showing some discrepancies that may arise in the unflattened surfaces for a given restoration. These discrepancies are corrected before starting a new restoration routine on the remaining horizons

Full size image

Restoration Outputs

For each of the five restoration outputs simulating the main depositional phases (Cenozoic, Cretaceous, Jurassic, Triassic and Upper Permian), we obtained the restoration vectors, the strain tensor, the dilation and the curvature. We defined the variable K as the ratio of: the maximum curvature found in the mineralized horizon \((K_{max}=max(K_{i}, K_j)\), \(i, j\) orthogonal main directions) as positive values \((|K_{max}|)\), and the maximun value of \(|K_{max}|\) over the surfaces. The more deformed areas are then highlighted as function of the K magnitude between 0 and 1 (Fig. 7).

Fig. 7
figure 7

Maximum curvature corresponding to each restoration from Cretaceous to Upper Permian a Cretaceous, b Jurassic, c Triassic and d Upper Permian. e Horizontal distance to Fore-Sudetic Block. f Depth of the Zechstein base at Late Cretaceous. Some locations related to mining activities are highlighted. Cu-potential areas from Oszczepalski and Speczik (2011) are the result of several exploration programs accounting for more than 370 archival boreholes outside of the LGCB district

Full size image

Curvature and Cu Assessments

Potentials Assessments and Predictors Variables

In mineral potential modeling, the analytical or empirical relationships between descriptive features and a mineral target express the possibility to predict a given mineral concentration in a location as function of descriptive features (e.g., Quadros et al. 2006; Cheng 2008; Zuo and Carranza 2011; Schaeben 2012). Let evidences denote the set of observed features that are directly related to the mineralization process (e.g., mineral alterations in rocks during a hydrothermal event, or sorting of heavy-minerals grains during a depositional process). Let geo-variables denote the set of features that control the system during mineralization (e.g., pressure, temperature, pH, Eh). Then, in principle, it is possible to build a potential model for a given mineralization integrating (as predictors) evidential geo-variables in terms of multivariate statistical analysis (Agterberg et al. 1993; Kerrich 1993; Araújo and Macedo 2002). Several mathematical methods are available to accomplish this, logistic regression (LR) being one of the most employed. Compared to other popular methods (e.g., weight-of-evidence), LR has the advantage of dealing with conditional independence assumptions and works with both continuous and discrete variables (Schaeben 2013, 2014). Specifically, the LR determines a relationship between the linear combination of predictors and the logit-transformed conditional mean using the logit transform as link function (Eq. 1) (McCullagh and Nelder 1989):

$$\begin{aligned} \begin{array}{ccc} {{log(Odds)}}=\beta _{0} + \beta _{l}x_{1} + \beta _2x_2 +,\ldots ,+\beta _{m}x_{m} \\ x_{1m} : {\mathrm{{predictors}}} \\ \beta _{0m} : {\mathrm{{coefficients}}} \end{array} \end{aligned}$$
(1)

Thus, using curvature as a predictor in LR analysis, it is possible to test the relevance of this restoration output in Cu-potential predictive models.

Cu Potentials and Selected Predictors

We digitized the Cu-potential areas reported by Oszczepalski and Speczik (2011) in Lower Silesia, including the Legnica–Głogów Copper Belt district. These areas are the result of several exploration programs accounting for more than 370 archival boreholes outside of the LGCB district (Oszczepalski et al. 1997; Speczik et al. 2007). Subsequently, we created a binary attribute of 1 for the highest potentials and 0 for the rest. Then, we generated LR predictive models using the logits of these higher Cu-potentials. The K, estimated in the mineralized horizon after each restoration, is added in the predictive models. Curvature of the top of Cenozoic restoration was not taken into account as it is posterior to the mineralization. Thus, four predictors \(K_{l=0:4}\) (l: restoration from Cretaceous to Upper Permian) were integrated in the LR models. Looking to obtain more accurate predictions, we added two other variables in the analysis: horizontal distance from the Fore-Sudetic Block (HFB) and depth of Zechstein base at Late Cretaceous (ZBK), both as continuous predictors. These two attributes were selected among other continuous variables (e.g., distance to current faults, layer thickness, restored depths) due to their good correlation coefficients (0.430 and 0.339, respectively) with the Cu distribution showed by Oszczepalski et al. (1997). The LR models of Cu-potentials per predictor are shown in Tables 1 and 2 and Figure 8.

LR Models by Predictor

The LR models per show that high curvature values, obtained at each restored time, increase the log Odds of having a Cu-potential locality (versus not having a Cu-potential locality). These positive coefficients obtained by the K models indicate a positive link between deformation in the horizons, highlighted by curvature, and the Cu-potential zones defined by Oszczepalski and Speczik (2011). Another tendency is observed in relation to the restorations, where the coefficient obtained for K increases by restored time. This trend is observable in Figure 8 where predicted probabilities increase by geologic-time-restoration. In contrast, the negative coefficients for distance HFB and depth ZBK show that the log Odds to have a Cu-potential location (versus non Cu-potential) decrease where these variables increase.

Table 1 LR model by restoration step curvature
Full size table
Table 2 LR model by complementary predictors
Full size table
Fig. 8
figure 8

Predicted probabilities from the LR models by predictor. Each image corresponds to the predicted probability of having a Cu-potential location according to the predictor individually (HFB and ZBK in km)

Full size image

Predictive Model and Conditional Independence

Attempting to build a general predictive model of Cu-potentials with the above predictors, we integrated all predictors in a single LR model. Because \({ K}_{(1, 2, 3, 4)}\), HFB and ZBK appear to be mutually dependent conditionally to Cu-potentials (Fig. 9), the interaction terms for them are integrated as predictors trying to yield true conditional probability (Schaeben 2014, 2013; Schaeben and Schmidt 2013). Table 3 shows the LR predictive model integrating all predictors and interaction terms. The resulting LR general model was applied to the study region, thus obtaining the predicted probability map for Cu-potential locations (Fig. 10.)

Fig. 9
figure 9

Graph of the conditional independence test for \({ K}_{l}\) (\(l=1\): Cretaceous, 2: Jurassic, 3: Triassic, 4: Upper Permian), HFB and ZBK given Cu-potentials. Each arc represents the lack of the conditional independence for the predictors in the corresponding nodes. For the test we used the bnlearn-R package (for more details about the conditional independence test see Scutari 2010)

Full size image
Table 3 LR model coefficients with interaction terms
Full size table
Fig. 10
figure 10

Predicted probabilities of Cu-potentials (P) in the FSM. Some main structures and Cu potential locations are highlighted. The match between high P and the Cu-potential areas are close to main regional structures as the Pogorzela elevation, the Sieroszowice graben and the Odra fault system among others

Full size image

Perspectives

High curvature values obtained during all restorations match locally with known mineralized zones. The most important correlations correspond to the present day exploitation area of LGCB, and also in the adjacent Cu-potential locations of Luboszyce, Ścinawa and Śłubów. Other Cu-potential areas that are related to high curvature for all restorations are: Mirków, Sułmierzyce, Czeklin and Kȯzuchów. The areas of Janowo, Kaleje, and Florentyna are related to high curvatures in the Upper Permian (Top Zechstein) and Cretaceous restored steps. In the Milicz area, good potential may exist in the northern part (Fig. 7).

For the Triassic restoration, the distribution of high curvature values shows strong differences in relation to the Permian restoration. Outside of LGCB, high curvature values are found in the Żary Pericline and Zielona Gora depression. The Cu-potentials areas of Kulów, Wilcze and Zarków appear linked to the increase in curvature values for this restoration step (Fig. 7c). In contrast, Triassic and Jurassic restorations show a similar feature in the obtained curvature, except for the LGCB and Sułmierzyce areas. (Fig. 7b, c). The Cretaceous restoration gives high curvature values on the central part of the study area and close to the border with the Fore-Sudetic Block. The Paproć and Borzȩcin areas present similar curvature values and distribution as in the Jurassic.

In relation with deformation stages, mineralization and Cu-enrichment times, the Odra Fault system may have played a significant role during the Late Permian and Cretaceous at locations such as the LGCB, the north part of the Żary Pericline, and in the Wrocław proximity (Fig. 7d and Fig. 10). In contrast, fault systems associated to the Pogorzela elevation seem to have controlled the Cu mineralization during the Triassic. The Cu-potentials on the Zielona Góra depression suggest a link to active structures during the Triassic and Jurassic and less strongly during the Cretaceous (Fig. 7d, c and b). Finally, the Cretaceous restoration indicates a relationship between the fault systems of Sieroszowice graben with proximal potential areas for this period (Fig. 7a and 10).

Several attempts have been made to determine the age of the Kupferschiefer mineralization (Jowett et al. 1987; Bechtel et al. 1999; Michalik 1997). The wide range of different ages obtained in those and similar works (from Late Permian to Late Jurassic) have been explained in terms of multi-stage mineralization (Speczik 1995). The curvature obtained at each time-restoration step reveals a strong spatial correlation between high curvature values and Cu-potentials. This association between high curvature and Cu-mineralization/enrichment could help in understanding of timing and structural mechanisms involved in ore formation. Table 4 presents synthetically the geodynamic setting, the dominant tectonic process that occurred in the region and the Cu-potential areas with high curvature values for each restoration. The method exposed in this work may improve metallogenic models for this kind of ore-deposit, relating geodynamic evolution, fluid pathways, and mineralized areas.

Table 4 Restoration steps, geodynamic setting, and high curvature in Cu-potential areas
Full size table

Discussion

In this work we model horizons overlying the Zechstein Formation as continuous surfaces, assuming that the different tectonic events that occurred before the Alpine orogeny have caused folding rather than faulting in these horizons. The resulting surface geometry depends on the interpretive points used as input data for the 3D modeling, on the way interpolation is done between these points and on the mesh resolution used to model the surface. All three elements are potential sources of uncertainty and inaccuracy in the final structural geometry, which could possibly affect the potential mapping results. More precisely, we used discrete smooth interpolation (DSI) (Mallet 2002) for creating these continuous triangulated surfaces. In DSI, the nodes of the triangular mesh are placed so as to minimize data misfit and roughness (Laplacian). Given the data spacing and the chosen surface resolution, the interpolation error due smoothing is considered minimal. The error due to the limited surface mesh resolution is likely more significant in high-curvature areas. Therefore, the detection of fault activity using curvature analysis may be under-estimated due to the limited surface mesh resolution. In the final potential map, this means that basement faults having a slight displacement may remain undetected due to negligible curvature in the overlying horizons. This effect could easily be mitigated by refining the mesh in the neighborhood of the faults (Caumon et al. 2009).

We nonetheless chose a constant resolution to avoid overfitting effects. Indeed, we believe the main source of uncertainty in the results stems from the depth maps and interpreted seismic sections used for the structural modeling. The geometry of these “data” and of the associated fault locations is well constrained close to boreholes but is obviously more uncertain in sparsely drilled areas. Structural uncertainty assessment methods (Wellmann et al. 2010; Cherpeau et al. 2010) could be used to address these sources of uncertainty. In the present study, we consider that bias due to possible interpretation errors may be present in areas with low borehole density, especially in the NE and SE parts of the study area (Fig. 2b).

The map of predicted probabilities for Cu-potential areas using curvature values with interaction terms (Fig. 10) shows several regions with medium to high potentials. The predictive model applied to obtain this map only considers geometric parameters relating fault systems that may have played a role with the Kupferschiefer formation. However, the Kupferschiefer ore creation has involved other factors such as passage of metalliferous fluids (Oszczepalski 1999), amount of organic matter in the Kupferschiefer Formation (Bechtel et al. 2001; Gouin 2008) and the presence of meteoric recharge systems (Brown 2011), among others. In this sense, a predictive model accounting only for structural parameters is incomplete. Future work could, thus, consider these other sources of information as additional predictors (if they can be extrapolated with limited uncertainties) or as a means to locally test the predictability of the proposed potential model.

Conclusions

Curvature from the FSM restorations are related spatially with the Cu-potential areas established in previous works. This relation probably expresses the impact of fault systems active during the mineralization process. Upward migration of thermal fluids along deep faults and damaged areas in the rocks mass could directly influence the Cu-sulfides formation. The Cu distribution patterns in the FSM were caused by variation of the stress regime during the tectonic evolution from Late Permian to Late Cretaceous. The Odra fault system has controlled the mineralization at Late Permian times, but during the Triassic and Jurassic other fault-systems ruled the mineralization, especially the faults related to the Pogorzela elevation, the Sieroszowice graben and the Zielona Góra depression.

The utility of curvature as a predictor is evidenced from the LR analysis, completing the set of structural parameters also obtained from the restoration modeling. We believe that the above ideas and methods can be applied in similar cases where fault systems are sealed by an impermeable cap and the occurrence of hot brines expulsion events from the basement.