Tectonophysics 470 (2009) 129–146 Contents lists available at ScienceDirect Tectonophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t e c t o Paleostress states at the south-western margin of the Central European Basin System — Application of fault-slip analysis to unravel a polyphase deformation pattern Judith Sippel a,⁎, Magdalena Scheck-Wenderoth a,1, Klaus Reicherter b,2, Stanislaw Mazur c,3 a b c GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam, Germany RWTH Aachen, Lochnerstrasse 4-20, 52056 Aachen, Germany Institute of Geological Sciences, University of Wrocław, Maxa Borna 9, 50-204 Wrocław, Poland A R T I C L E I N F O Article history: Received 25 July 2007 Received in revised form 19 February 2008 Accepted 2 April 2008 Available online 18 April 2008 Keywords: Paleostress inversion Heterogeneous fault-slip data Central European Basin System Multiple Inverse Method PBT-Method A B S T R A C T We analyse the deformation pattern along the south-western margin of the Central European Basin System (CEBS) where Upper Carboniferous–Mesozoic rocks are uplifted due to the Late Cretaceous basin inversion. The geometry of mesoscale faults and associated striae are used to calculate the stress state(s) responsible for the observed deformation. Each reduced stress tensor obtained comprises (i) the directions of the principal stress axes σ1, σ2, and σ3 (σ1 ≥ σ2 ≥ σ3) and (ii) the ratio of principal stress differences R = (σ2 − σ3) / (σ1 − σ3). We present a stress inversion technique that allows each stress state inherent in a heterogeneous fault population to be identified by integrating the results of the PBT-Method [Turner, F.J., 1953. Nature and dynamic interpretation of deformation lamellae in calcite of three marbles. American Journal of Sciences, 251(4): 276– 298; Sperner, B., Ratschbacher, L. and Ott, R., 1993. Fault-striae analysis: a Turbo Pascal program package for graphical presentation and reduced stress tensor calculation. Computers & Geosciences, 19: 1361–1388] and the Multiple Inverse Method [Yamaji, A., 2000. The multiple inverse method; a new technique to separate stresses from heterogeneous fault-slip data. Journal of Structural Geology, 22(4): 441–452]. This comprehensive approach not only facilitates the separation of complex data sets into homogeneous subsets but also guarantees that each stress state derived fulfils both the criteria of low-misfit angles (Wallace–Bott hypothesis) and high shear-to-normal-stress ratios (Mohr–Coulomb criterion). The reliability of our technique is confirmed by the fact that irrespective of (i) the number of fault-slip data from an outcrop, (ii) the number of subsets they represent and (iii) the proportion of newly formed and reactivated faults, we obtain consistent results from outcrops of variously aged rocks. This consistency concerns both calculated stress states as well as locally observed deformation sequences. Such local chronologies are derived from cross-cutting relationships and superimposition of different fault-slip data which individually are assigned to a consistent stress state. A synthesis of results from different locations of the study area argues for the superposition of two main deformation events. Most prominently, the area was affected by a stress state with a horizontal N–S- to NE–SWdirected maximum compression (σ1) and a low stress ratio which induced reverse and strike-slip faulting. A pure strike-slip regime of E–W- to NW–SE-directed compression with moderate stress ratios is less prevalent and probably younger. The age of the youngest rocks documenting these two phases proves the stress fields to correspond to the polyphase Late Cretaceous–Tertiary basin inversion of the CEBS during post-Cenomanian times. The youngest tectonic imprints detected in the study area correspond to locally appearing extensional stress states with varying directions of σ3. At many sites, the youngest derived paleostress state coincides with the present-day stress field in terms of the direction of the maximum horizontal stress axis, SHmax. The only stress state detected which pre-dates the basin inversion corresponds to an extensional regime with an WNWESE- to NW–SE-directed σ3-axis observed only locally in the N–S striking Leine Graben and its prolongation to the North. The fact that the majority of variously aged rocks exhibit only the traces of the latest deformation phases indicates a high degree of fault plane reactivation in the study area. © 2008 Elsevier B.V. All rights reserved. ⁎ Corresponding author. Tel.: +49 331 2881342; fax: +49 331 2881349. E-mail addresses: sippel@gfz-potsam.de (J. Sippel), leni@gfz-potsam.de (M. Scheck-Wenderoth), k.reicherter@nug.rwth-aachen.de (K. Reicherter), stm@getech.com (S. Mazur). 1 Tel.: +49 331 2881345; fax: +49 331 2881349. 2 Tel.: +49 241 8095722. 3 Present address: GETECH, Kitson House, Elmete Hall, Elmete Lane, Leeds LS8 2LJ, UK. 0040-1951/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2008.04.010 130 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 1. Introduction The Central European Basin System (CEBS) covers an area extending from the southern North Sea across Denmark, The Netherlands and northern Germany to Poland (Fig. 1). Studies that investigate the structural evolution of the CEBS on a basin scale (ScheckWenderoth and Lamarche, 2005) or on the scale of sub-basins (Clausen and Pedersen, 1999; Scheck and Bayer, 1999; Hansen et al., 2000; Baldschuhn et al., 2001; Scheck et al., 2002a,b; Evans et al., 2003; Lamarche et al., 2003) argue for a recurrently changing stress field affecting this area. A main conclusion of these studies is that two major types of structural elements, striking NW–SE and N–S, respectively, experienced repeated and selective reactivation during basin history. NW–SE-trending basins like the Norwegian Danish Basin, the North German Basin, and the Polish Basin document localized deformation in terms of subsidence during the Permian and the Mesozoic and in terms of uplift during the Late Cretaceous–Early Cenozoic inversion phase. In the North German Basin, for instance, the most important inversion-related uplift took place along the SW margin of the basin, i.e. along the Elbe Fault System (Fig. 2; Mazur et al., 2005). N–S trending grabens (Central Graben, Horn Graben, Glückstadt Graben), on the other hand, indicate localized subsidence during the Mesozoic and in parts during the Cenozoic. Concerning the geodynamic history of the CEBS, five main phases can be distinguished: (1) an initial rift phase with volcanic activity most intense along both NW–SE and N–S striking zones; (2) a phase of thermal subsidence along NW–SE oriented basin axes during the Early Permian and Early Triassic; (3) Late Triassic and Jurassic extensional tectonics with the formation of N–S-striking grabens and localized subsidence in NW–SE-oriented sub-basins along the margins; (4) a phase of inversion mainly affecting NW–SE striking blocks during the Late Cretaceous–Early Cenozoic in response to the build-up of Alpine collision-related intra-plate compressional stresses, opening of the North Atlantic and mantle plume activity (Ziegler, 1990; Dezes et al., 2004); and (5) a final phase of subsidence during the Cenozoic with mainly N–S striking subsidence axes and a major depocentre in the Central North Sea. Whereas the present-day stress field of the CEBS is well known — it is mainly characterized by a maximum horizontal stress direction SHmax that rotates from a NW–SE direction in the NW German Basin, to a N–S direction in the North German Basin, and a NE–SW direction in the NE German Basin (Roth and Fleckenstein, 2001; Kaiser et al., 2005; Reinecker et al., 2005) — there are only few studies on the evolution of paleostresses in North Central Europe (Delvaux, 1997; Vandycke, 1997; Lamarche et al., 1999, 2002; Vandycke, 2002). We analyse the deformation pattern from outcrops distributed along the south-western margin of the CEBS (Fig. 3). Here, several NW–SE striking, marginal sub-basins of the CEBS (e.g. Lower Saxony Basin, Subhercynian Basin) have been uplifted during the Late Cretaceous–Early Tertiary phase of inversion. In particular, we investigate mesoscale faults to use associated striae as kinematic indicators (Doblas, 1998, Fig. 4). In this context, a fault-slip datum is composed of the fault plane orientation, the slip orientation, and the sense of slip. Knowing the fault-slip attitudes of numerous faults, it is possible to calculate the corresponding causative stress state (Carey and Brunier, 1974). With such a fault-slip analysis, we obtain the reduced stress tensor which comprises (1) the orientations of the three principal stress axes σ1, σ2, and σ3 with σ1 ≥ σ2 ≥ σ3 and (2) the ratio of principal stress differences R = (σ2 − σ3) / (σ1 − σ3) (Angelier, 1979). This study presents a new strategy towards stress inversion of heterogeneous fault populations which originate from polyphase deformation. By combining different commercial (TectonicsFP 1.6.5 by Reiter and Acs, 1996–2003) and open-source (MIM Software Package by Yamaji and Sato, 2005, Yamaji et al., 2005a) computer programmes, our approach integrates the results of the “PBT-axes-method” (Turner, 1953; Sperner et al., 1993) and the “Multiple Inverse Method” (Yamaji, 2000). The derived optimal stress states fulfil both, the criterion of Fig. 1. Depth to top pre-Permian illustrating the major structural elements of the Central European Basin System which strike NW–SE (e.g. Elbe Fault System, Ringkøbing Fyn High, Tornquist Zone; modified after Scheck-Wenderoth and Lamarche, 2005). A second set of structures trends N–S (e.g. Glückstadt Graben (GG), Horn Graben (HG), and Central Graben (CG)). The area of current investigations is indicated by a black rectangle. SL: Seismic line (Fig. 2). Coordinates: UTM, Zone 33 N. J. Sippel et al. / Tectonophysics 470 (2009) 129–146 131 Fig. 2. Regional geological profile across the SW part of the North German Basin (see Fig. 1 for location; modified after Mazur et al., 2005). Note the uplifted position of the southern basin margin including the Lower Saxony Basin with respect to the North German Basin. The fault-slip data for the present study are derived from rocks cropping out along this and other uplifted parts of the south-western inverted margin of the CEBS. Vertical scale (seconds, two-way travel time) is twofold depth exaggerated. AL: Aller Lineament. low-misfit angles and that of high shear-to-normal-stress ratios. We apply this integrated technique to fault-slip data from the southwestern margin of the CEBS, demonstrating its main advantages and discussing the paleostress states detected in the area. 2. Major structural elements of the study area Our study area covers outcrops in the western parts of the Elbe Fault System (EFS, Fig. 1) — an area of polyphase deformation since Late Carboniferous times which was most intensely deformed in the course of the Late Cretaceous–Early Tertiary inversion (Scheck et al., 2002a). The EFS consists of several major NW–SE- to WNW–ESEstriking faults which controlled the structural evolution of associated sub-basins of the North German basin (Fig. 3). The Osning Lineament (OL) roots in the pre-Permian basement of the Lower Saxony Basin (LSB) separating the Rhenish Massif below the Münsterland Basin in the South from the Lower Saxony block in the North (Fiedler, 1984; Drozdzewski, 1988). The outcropping prolongation of the lineament is a zone of inversion-related thrust faults along which Mesozoic to Lower Cretaceous sediments of the LSB mainly were thrust southwards over the stable Münsterland platform and its thick cover of Upper Cretaceous rocks. Likewise, the Northern Harz Boundary Fault (NHBF) separates the Harz block in the South — comprising Devonian to Lower Carboniferous sediments deformed during the Variscan orogeny — from the Mesozoic sediments of the Subhercynian Basin in the North. During Late Cretaceous and Early Tertiary times the basin fill of the Subhercynian Basin was tilted and partly overthrust by the Variscan basement due to the relative uplift of the Harz block along the NHBF (with a displacement of at least 5 km according to Thomson et al., 1997). During the same period also the block of the Flechtingen High (FH) experienced uplift, its transition to the north thereby evolving as a flexure rather than a fault (Scheck et al., 2002a). The south-central part of the study area is occupied by a N–S trending depression which is structured by major N–S striking normal fault systems. At the eastern side of this depression, the marginal faults of the Leine Graben (LG) offset a central block of Upper Triassic (Keuper) to Lower Jurassic rocks against Lower to Middle Triassic rocks (Buntsandstein, Muschelkalk) of the eastern and western graben flanks. The displacement amounts up to 1000 m, the average being much smaller in the West than in the East (Tanner, 2007). Though the initiation of this structure is assumed to date back to Late Jurassic/ Early Cretaceous times (Ritzkowski, 1999), the main tectonic pulses preserved by faults on outcrop scale can be related to the Late Cretaceous–Early Tertiary inversion of the CEBS (Tanner, 2007). The recurrent deformation along the EFS might be related to a rheologically weaker lower crust which supports strain localisation (Scheck et al., 2002a). In fact, the kinematic interpretation of its structural inventory still remains a matter of debate. Some authors Fig. 3. Geology and important tectonic elements of the south-western margin of the CEBS with locations of the investigated outcrops. AL — Aller Lineament, FH — Flechtingen High, LG — Leine Graben, NHBF — Northern Harz Boundary Fault, OL — Osning Lineament, 1 — Dörenthe, 2 — Lienen, 3 — Halle, 4 — Künsebeck, 5 — Steinbergen, 6 — Sonneborn, 7 — Upstedt, 8 — Emmenhausen, 9 — Elvese, 10 — Papenberg, 11 — Flechtingen, 12 — Bodendorf, 13 — Dönstedt, 14 — Mammendorf. 132 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 Liesa and Lisle, 2004; Zalohar and Vrabec, 2007). At best, kinematically inconsistent structures are identified directly in the field, either by crosscutting relations between individual faults or by superimposition of striae on the same fault plane (Fig. 4). If such information is missing, additional separation techniques must be applied. The Multiple Inverse Method (MIM; Yamaji, 2000) and the PBT-Method (PBT; Sperner et al., 1993) are two completely different approaches, especially developed for the separation of fault-slip data. We shortly describe both techniques by exemplarily applying each to the heterogeneous fault-slip data from Bodendorf quarry (Flechtingen High area). 3.1. Multiple Inverse Method (MIM; Yamaji, 2000) Fig. 4. Steeply SSW-dipping fault surface (198/77) covered by two superimposed sets of striae (Bodendorf quarry). Note the configuration of striae framed by the circle: assuming that late-stage coatings usually conceal the initial striae, i.e. that younger slickensides lie above older slickensides (Meschede, 1994; Doblas, 1998), we conclude that a sinistral displacement (x: sub-horizontal frictional grooves covered with hematite) took place before the fault plane shown here was reactivated with a normal sense (y: sub-vertical calcite fibres). The fact that the differently oriented striae differ also in terms of mineralisation confirms that the two fault/striae pairs belong to different subsets each related to a specific paleostress state (i.e. subsets bod1 and bod3; Fig. 7). favour pure compressional, respective pure extensional, regimes for different periods (for the OL: Kockel, 2003; for the NHBF: Franzke et al., 2007) whereas others postulate recurring phases of wrench tectonics (for the OL: Drozdzewski, 1988). 3. Paleostress inversion in the case of heterogeneous fault populations According to Wallace (1951) and Bott (1959), one can predict the slip direction along any plane of known orientation (with unit normal Y n) under a given stress tensor σ, assuming that slip takes place parallel to the direction of maximum resolved shear stress Y s : hYT i Y s=r·Y n−n ·r·Y n Y n ð1Þ where the superscript T means the transpose of the matrix. At the same time, a newly formed fracture plane shows an orientation that allows the relative magnitudes of the shear stress τ and the normal-stress σn in this plane to meet with the Mohr– Coulomb yield criterion, s = C + Arn ð2Þ where C is the cohesion and µ is the coefficient of friction (Coulomb,1776; Mohr,1900). According to these mechanical laws, two types of techniques have been established, either based on slip criteria or frictional criteria, to solve the inverse problem, i.e. to derive the reduced stress tensor from measured fault-slip data (for comprehensive reviews on various stress inversion techniques we refer to Angelier, 1994, and Ramsay and Lisle, 2000). To allow for solutions as realistic as possible some techniques even combine both approaches (Reches, 1987; Celerier, 1988; Angelier, 1990; Zalohar and Vrabec, 2007). Being aware of the critical assumptions and limitations of fault-slip analysis (already discussed by Pollard et al., 1993; Dupin et al.,1993, Twiss and Unruh,1998; Marrett and Peacock,1999), we apply selected techniques to our fault-slip data. We consider the results as states of stress assuming a direct cause-and-effect relationship between the observed strain and the responsible stress. Relating fault kinematics to stress states implies that all faults under consideration have slipped in response to the same deviatoric stress state. One of the great challenges of paleostress analysis is to separate stress tensors from heterogeneous fault-slip data documenting changes of the paleostress field through time (Etchecopar et al., 1981; Huang, 1988; Nemcok and Lisle, 1995; Nemcok et al., 1999; Yamaji, 2000; Shan et al., 2003, 2004; MIM is a modification of the Direct Inverse Method (Angelier, 1984) assuming that slip is parallel to the maximum resolved shear stress. It determines the best-fitting stress tensor for a group of faults by minimizing the sum of associated misfit angles with the misfit angle β being defined as the angle between the calculated maximum shear stress and the measured slip direction for an individual fault plane (Fig. 5a). Being developed particularly for the separation of heterogeneous data sets, MIM comprises the following steps: first, subsets of kelements are created from the whole data set (Fig. 5b; Yamaji et al., 2005a). For k = 4, each possible group of 4 faults is created so that each fault is related to any possible combination of three other faults. To all of these artificial k-fault-subsets Angelier's (1984) inverse technique is applied. Finally, all calculated reduced stress tensors, i.e. one for each 4fault-subset in our case, are plotted in a pair of lower-hemisphere plots (Yamaji and Sato, 2005; Fig. 5c): the left part of the obtained MIM plot shows the calculated directions of σ1-axes and the right part displays the directions of the corresponding σ3-axes. The symbols for stress axes are colour-coded according to the respective values of the stress ratio R. With this technique, all significant stress states inherent in a heterogeneous data set can be detected, as they are indicated by clusters of symbols that agree in terms of σ1- and σ3-directions as well as colours. MIM uses a computational grid of 60,000 evenly distributed points for the search of best-fitting stress states in the parameter space of σ1, σ2, σ3, and R. The optimal stress for a single k-fault-subset is approximated by the nearest grid point. Thus, several stress states derived from a data set may be tied to a single grid point. Grid points with a large number of stress states correspond to more significant solutions for the entire fault population. The enhance factor e (with 0 ≤e ≤ 99) defines a minimum number of solutions at a grid point which is required for this particular stress state to appear in the MIM stereograms (Yamaji et al., 2005b). When selecting e = 0, all solutions for a data set are plotted. Larger values of e, on the other hand, correspond to a reduced number of plotted solutions and are chosen to thin out erroneous stress states and enhance the most relevant clusters. To further test the significance of different stress states, the MIM software provides a tool for the simulation of stresses (MIM Post Processor). Based on the Wallace–Bott hypothesis (Eq. (1)), this application calculates the theoretical slip directions on evenly distributed theoretical fault planes for a selected reduced stress tensor. The theoretical slip directions can be compared to the slip directions of the measured fault-slip data by visual inspection and calculated misfit angles (see below). 3.2. PBT-Method (PBT; Turner, 1953, after a solution of Sperner et al., 1993) PBT is a kinematic analysis that constructs a triple of theoretical strain axes for each individual fault-slip datum, i.e. a contraction axis P, a neutral axis B, and an extension axis T (Fig. 6a). The method is incorporated in the software programme TectonicsFP 1.6.5 (by Reiter and Acs, 1996–2003). According to the Mohr–Coulomb fracture criterion, it adopts a defined fracture angle θ between P and the fracture plane (the angle being measured in the plane containing the fault plane normal and the slip line). Neglecting its dependence from potentially varying material properties, PBT applies a uniform angle θ to all faults. As J. Sippel et al. / Tectonophysics 470 (2009) 129–146 133 Fig. 5. (a) The misfit angle β is the angular distance between the observed and predicted slip direction (Wallace–Bott hypothesis). Considering the known sense of slip, β is always in the range of 0°≤β ≤180°. (b) Fault-slip data from Bodendorf quarry in a tangent-lineation plot (after Twiss and Gefell, 1990): each arrow in this lower-hemisphere, equal-area projection represents one fault-slip datum; the centre of each arrow indicates the pole to the respective fault plane while the arrowhead indicates the slip direction of the footwall block. (c) Stress states calculated according to MIM for the number of n = 45 striated faults from Bodendorf quarry presented in b. The calculation was performed by the MIM Software Package (Yamaji et al., 2005a,b; Yamaji and Sato, 2005). A number of n = 45 fault-slip data produces a number of X =n!/(k!·(n −k)!) k-fault-subsets (for k = 4 we obtain a number of 148,985 solutions). The σ1-axis of each stress state is plotted in the left stereonet, the σ3-axis in the right stereonet (lower-hemisphere, equal-area projections). The diamonds represent the directions (azimuth and plunge) of stress axes. The tail of a σ1 symbol indicates the direction and plunge angle of the corresponding σ3-axis. The tail of a σ3 symbol indicates the direction and plunge angle of the corresponding σ1-axis. The stress ratio R is colour-coded. Violet (R =0.0) represents axial compressive deviatoric stress (σ1 ≫σ2 =σ3), green (R = 0.5) expresses plane deviatoric stress (where σ2 is the arithmetic mean between σ1 and σ3) and red (R = 1.0) stands for axial tensile deviatoric stress (σ1 =σ2 ≫σ3). recommended by Sperner et al. (1993), we apply a fracture angle of θ = 30° — a value (i) derived from laboratory studies on brittle deformation (Hubbert, 1951; Byerlee, 1968; Jaeger and Cook, 1979), (ii) associated with high shear-to-normal-stress ratios on the fracture planes (Twiss and Moores,1992, p.172) and (iii) which also has proved to be appropriate for natural fault-slip data (Sperner, 1996; Reicherter and Peters, 2005). By regarding all faults as neoformed, i.e. as fractured and moved by the same stress state, this concept assumes the orientation of each fault plane to depend on the causative stress field. Accordingly, the B-axis is constructed to lie in the plane of a fault. The application of PBT to the entire fault population of an outcrop results in a comprehensive pattern of kinematic axes (Fig. 6b); such a cumulative plot facilitates kinematic consistencies to be detected as clusters of P-, B-, and T-axes, on the basis of which kinematically consistent subsets of faults can be separated from a heterogeneous fault population. 4. Our strategy: Combine the results of PBT and MIM In the case of Bodendorf quarry, both the results of MIM (Fig. 5) and the results of PBT (Fig. 6) reflect the heterogeneity of the fault-slip data as indicated by clusters of differently oriented stress and kinematic axes, respectively. To find the most relevant stress states that explain the kinematics of this fault population as complete as possible, we introduce the following stepwise procedure. Step 1: Preliminary separation by clusters of P-, B-, and T-axes. For this step, we use the construction of kinematic axes with θ = 30° (Fig. 5). Clusters of kinematic axes indicate subsets of faults with the same kinematic trend and can be isolated. Thus, we can separate three kinematically homogeneous subsets for the Bodendorf site: bod1, bod2, and bod3 (Fig. 7a). For each subset, we calculate the mean vectors for P-, B-, and T-axes, respectively. Any of the three axes of a fault-slip datum should not deviate by more than 40° from the respective mean vector. To accentuate the clusters of stress axes we additionally plot the associated cones of confidence (with a significance of 99%). A part of the data cannot be assigned to any consistent subset (“remnants” in Fig. 7a). Considering the clusters of sub-horizontal and sub-vertical strain axes derived from the fault population and following Anderson's law of horizontal and vertical strain axes (Anderson, 1951), the obliquity of these remaining faults implies 134 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 Fig. 6. (a) Construction of the kinematic axes P, B, and T for a normal fault following the rules of the PBT-Method with a fracture angle of θ = 30° (lower-hemisphere, equal-area projection). The neutral axis B lies in the fault plane (090/60). The contraction axis P and the extension axis T lie in a plane given by the shear plane normal and the slip line. The centre of the slip line arrow indicates the attitudes of the striae (090/60) and the arrow points the slip direction of the hanging wall block (normal sense of movement). P is constructed with an angular distance of θ = 30° from the slip line in a direction opposite to the one indicated by the slip line arrow. P, B, and T are mutually perpendicular. (b) Results of PBT for the entire fault-slip data from Bodendorf quarry (Fig. 5b) adopting a fracture angle of θ = 30° to each fault-slip datum. The wide scattering of P-, B-, and T-axes, respectively, reflects the heterogeneity of the data set. that they may represent pre-existing/reactivated planes of weakness. We ignore this group of faults for the next step but reconsider them at the end of our stress inversion procedure. As PBT processes each fault-slip datum separately, the separation is very rapid and straightforward. We conclude that the subsets bod1 and bod2 represent strike-slip regimes with horizontal contraction and extension axes and a vertical B-axis each. In the case of subset bod1, the average sub-horizontal contraction axis strikes approximately NE–SW and the extension axis NW–SE, whereas for bod2 it is vice versa. On the contrary, subset bod3 corresponds to an extensional regime with a vertical contraction axis and an extension axis striking horizontally NNE–SSW. Step 2: Application of MIM to the PBT-derived subsets. As PBT regards all faults as neoformed and uncertainties concerning the value of θ are accepted by the method, we complementarily apply MIM to each of the kinematically homogeneous subsets bod1, bod2, and bod3 (Fig. 7b). As its dynamic conception considers also slip along pre-existing planes, MIM yields for each subset the complete number of stress states determined on the basis of the low-misfitangle criterion. Each couple of corresponding σ1- and σ3-axes in the plots represents the reduced stress tensor calculated for a single 4fault-subset. As these stress axes form large and diffuse clusters for bod1, bod2, and bod3, it is not unambiguous which stress state is the most relevant for the respective subset. However, if we transfer the mean vectors of the strain axes P, B, and T as well as their cones of confidence from the PBT plots (Fig. 7a) to the MIM plots (Fig. 7b), considerable consistencies between the results of PBT and MIM become obvious. As exemplarily shown for subset bod1, we would achieve almost the same consistency when adopting slightly different fracture angles for PBT, such as θ = 20° and θ = 40° (Fig. 7b). The associated cones of confidence would indicate the same clusters of horizontal NE–SW-directed σ1-axes and horizontal NW–SE-directed σ3-axes in the MIM plot. Step 3: Find preliminary stress states by means of an interactive stress simulation. To find the most relevant stress state for a homogeneous subset we perform two series of stress state simulations (using the MIM Software Package), the first of which shall yield a preliminary solution. A single simulation run implies the designation of the parameters σ1, σ3 and R and the calculation of the associated misfit angle β for each fault-slip datum. We start with a stress state of which the principal axes are derived from the mean vectors of the associated PBT-axes. As these mean vectors are calculated separately for P-, B-, and T-axes, they do not necessarily have to be mutually perpendicular. For this reason, we take the precise attributes of the P-mean vector for σ1, whereas for σ2 and σ3 we slightly modify the azimuths and plunges of B and T, respectively, to achieve the required perpendicularity. At last, we select an R value which is indicated by the colours of those MIM solutions that are consistent with the PBT mean vectors of the same subset. For the fully designated stress state, we obtain a list of misfit angles for the complete data set which is directly linked to both a fluctuation histogram and a tangent-lineation plot (Fig. 7c). The latter displays the Fig. 7. Our strategy: data separation and stress inversion for the fault-slip data from Bodendorf. (a) PBT separation. The separation by clusters of P-, B-, and T-axes yields three homogeneous subsets (bod1, bod2, and bod3) of kinematically consistent faults and a group of faults with non-uniform kinematics mainly comprising oblique-slip faults (“remnants”). The PBT plots are complemented by the mean vectors calculated for P-, B-, and T-clusters (larger PBT symbols) and their associated cones of confidence for 99% significance. (b) Complete number of reduced stress tensors calculated by MIM for bod1, bod2, and bod3 (plot properties as in Fig. 5c, e = 1). σ1- and σ3-plots are complemented by the mean vectors and the cones of confidence derived from the respective P- and T-clusters in a). For the plot of subset bod1, also the cones of confidence (99% significance) for the mean vectors of P- and T-clusters constructed with θ = 20° and θ = 40° are plotted. (c) Results of the first stress simulation: The stress states BOD1′, BOD2′, and BOD3′ are the “preliminary” solutions for the subsets bod1, bod2, and bod3, respectively. Tangent-lineation plots, left: The theoretical slip patterns (light grey arrows) of the stress states BOD1–3′ coincide very well with the measured slip patterns of bod1, bod2, bod3 (arrows coloured according to R). Fluctuation histograms, right: The low degree of misfits of BOD1′, BOD2′, and BOD3′ are expressed by a large number of faults with low-misfit angles (mainly β ≤ 30°). Mohr-circles diagrams: Each striated fault is indicated by a dot, the centre of which indicates the shearto-normal-stress ratio (τ/σn) calculated for the associated stress state. (d) Results of the second stress simulation: Each of the stress states BOD1, BOD2, and BOD3, is set in relation to the complete fault population from Bodendorf. Tangent-lineation plots: Given the theoretical slip pattern of BOD1, BOD2, and BOD3 (thin grey arrows), faults with misfit angles β ≤ 30° (coloured arrows) can be separated from faults of low slip potentials indicated by β N 30° (dark grey arrows). Mohr-circles diagrams: Coloured dots indicate faults with misfit angles β ≤ 30°, grey dots represent faults with β N 30°. Most faults with low-misfit angles reveal a high τ/σn, reflecting a high slip tendency. (e) Symbols for the reduced stress tensors: Nearly horizontal principal stress axes are projected to the horizontal and plotted as arrows (in black, grey, and white for σ1, σ2, and σ3, respectively). Nearly vertical principal stress axes are projected to the vertical and plotted as solid circles (also black, grey, and white for σ1, σ2, and σ3). To illustrate the value of R we plot the σ2-symbol with variable sizes (e.g. equally sized to σ1 if σ1 = σ2 and equally sized to σ3 if σ2 = σ3) and the background colour is plotted according to the MIM code for R. J. Sippel et al. / Tectonophysics 470 (2009) 129–146 135 136 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 stress state-specific theoretical slip pattern and the measured slip directions. Furthermore, we calculate the shear-to-normal-stress ratio (τ/σn) for each fault given the selected stress configuration (software FLUMO, Sperner, 1993). On the basis of these results we can successively compare the significance of different stress states. At this stage, we regard the stress axes derived from PBT clusters as sufficiently significant. Therefore, we only have to test different values for the free parameter R which may vary in a range indicated by the different colours of MIM clusters. Among the tested stress configurations, the stress states BOD1′, BOD2′, and BOD3′ are the ones with the lowest degree of misfit so that we consider them as preliminary solutions for the subsets bod1, bod2, and bod3, respectively (Fig. 7c). For estimating the slip potential of a single fault-slip datum under a certain stress field, the upper limit for misfit angles has been proposed to range between β = 20° (Etchecopar et al., 1981; Sperner et al., 1993) and β = 30° (Nemcok and Lisle, 1995). In the case of the estimated preliminary stress states the majority of the assigned fault-slip data are related to misfit angles of β ≤ 20°. Moreover, none of the few faults with 20° b β ≤ 30° would fit better to an alternative solution found by our stress inversion (neither in terms of β nor of τ/σn). Consequently, the PBT separation can be regarded as reasonable. Another common feature of the three preliminary stress states is that they would induce relatively high shear-to-normal-stress ratios on the respective faults. The presence of many points near the external envelopes of the Mohr-circles diagrams (i.e. near the Mohr–Coulomb fracture criterion which corresponds to a tangential to the σ1–σ3 circle) further indicates that many faults contain the σ2-axis in their plane which may imply a neoformed character. Step 4: Complete the separation and improve the solutions (second simulation). In a second simulation series, we assess the relevance of BOD1′, BOD2′, and BOD3′ by testing each preliminary stress state against the entire fault population. With this step, we check their potential to be responsible also for the slip on other faults from the outcrop, in particular, on those which so far have been ignored (“remnants”). To evaluate the slip potential for a single fault-slip datum we take a threshold of a maximum misfit angle of β = 30°. Having identified all fault-slip data that might have been slipped by the same stress state, we then try to improve our solutions by minimising their degree of misfit. We regard a stress configuration which is related to the majority of faults by β ≤ 20° as an ideal solution for a subset. As the MIM software interactively allows following any changes of the misfit angle distribution when changing the parameters of stress, it is very simple to identify the best-fitting stress state for a data set. For our example, this means, we start with BOD1′, BOD2′, and BOD3′, modify successively their parameters by selecting alternative values for σ1, σ3, and R to finally find the most appropriate solution for bod1, bod2, and bod3. The analysis of numerous data sets has shown that this interactive search via successive simulations can be restricted to a space which is indicated by the consistent solutions of MIM and PBT. Hence, we only test stress states covered by those MIM clusters which are surrounded by or even in the immediate vicinity of the PBTderived cones of confidence. Within only a few simulation runs we find a stress configuration of which the associated degree of misfit cannot be further decreased by modifying its parameters. Thus, we determine the stress states BOD1, BOD2, and BOD3 as optimal solutions for the subsets bod1, bod2, and bod3, respectively (Fig. 7d). As expected from the PBT results, the stress states BOD1 and BOD2 correspond to strike-slip regimes with a sub-vertical σ2-axis each. For stress state BOD1 the maximum principal stress axis strikes subhorizontally NE–SW, whereas for BOD2 it strikes NW–SE. These stress states differ also in the derived stress ratios: in the case of BOD1 the ratio tends towards an axially compressive state of stress (R = 0.2) and for BOD2 it represents a plane deviatoric stress state (R = 0.6). Finally, stress state BOD3 corresponds to an extensional regime (sub-vertical σ1) with a sub-horizontally NE–SW-directed σ3-axis. The various dip and slip directions of the associated normal faults in subset bod3 require a relatively low R value (R = 0.2). For our example, the integrated analysis yields three stress states which together almost completely explain the observed fault-slip pattern. Each solution is related to the assigned fault-slip data by a maximum number of misfit angles in the range of β ≤ 20° which is the primary criterion required for a reasonable solution. If a single faultslip datum fits to more than one stress state in terms of its misfit angles, we assign it to the solution with the larger τ/σn (given that field observations do not preclude this). For pre-existing planes of weakness even relatively low shear-to-normal-stress ratios may be sufficient to induce slip (Twiss and Moores, 1992). Of the total fault population, only the fraction of the “remnants” shows such low values of τ/σn confirming their reactivated character. To consider the affiliation of these data is essential because (i) as mainly being reactivated they often document age relations to other fault-slip data (thus providing constraints on the chronology of stress states) and (ii) as often being oblique and generally not containing a principal stress axis they constrain the stress ratio R (Angelier, 1989). Our example further proves the interactive stress simulation to be suitable for the isolation of outliers (e.g. erroneously measured faults) so that they do not influence the stress inversion (REST, Fig. 7e). In a similar way, incomplete data (e.g. fault-slip data with unknown sense of slip) could be incorporated in the interpretation by plotting them together with the theoretical slip pattern of a stress state. Finally, even in the case of a fault population only comprising reactivated faults, data separation and stress inversion are possible as the results of MIM may provide the starting points for the simulation and the reliability of different stress states can be tested by the complementary evaluation of τ/σn. Step 5: Presentation and chronology of stress states. We present the results of our analysis by means of stress symbols which represent the directions of principal stress axes and the stress ratio (Fig. 7e). As the complete Bodendorf data set is derived from a single volcanic unit, a separation based on the distribution of the data among differently-aged rocks is impossible (paleostress stratigraphy, Kleinspehn et al., 1989). However, having assigned each fault-slip datum to a specific stress state (or the “REST”), we can infer a relative chronology of stresses. From cross-cutting and overprinting relationships between individual fault-slip data (such as in Fig. 4) we conclude that both stress states BOD1 and BOD2 were active before stress state BOD3. Unfortunately, no such direct constraints could be found for the relative timing of BOD1 and BOD2. 4.1. Why not considering only the MIM results prior to a stress inversion via simulation? For a comparative test of the results, we additionally check the validity of those clusters which are the most relevant according to the original concept of MIM. As for MIM the most significant solutions for a data set are presented by the grid points with the largest number of solutions, we find these particular clusters by enlarging the enhance factor of the corresponding MIM plots. For our demonstration (Fig. 8) we exemplarily select a value of e = 50 to compare its implications to those of e = 1 (Fig. 7b). This is equivalent to filtering out a much larger number of solutions. By comparing the results of simulations for the small number of remaining solutions we can identify the stress states BODx, BODy, and BODz as the ones with the lowest degree of misfit (Fig. 8c). These stress states are different from the solutions BOD1, BOD2, and BOD3 (Fig. 7d). For subset bod1, the grid points with the maximum number of solutions indicate a reverse regime (BODx) instead of a strike-slip system (BOD1). BODy corresponds to an extensional regime whereas BOD2 is strike-slip in character. For bod3, the solutions BODz and BOD3 differ with regard to their directions of minimum horizontal stress (σ3). Considering only the misfit angles (fluctuation histograms), BODx, BODy, and BODz better explain the observed slip patterns of the subsets bod1, bod2, and bod3 than do our J. Sippel et al. / Tectonophysics 470 (2009) 129–146 Fig. 8. Simulation of the stress states BODx, BODy, and BODz which are the most relevant solutions provided by MIM. a) PBT separation (as in Fig. 7a). b) Reduced number of stress tensors calculated by MIM for the subsets bod1, bod2, and bod3. Note the large enhance factor, e = 50, compared to the plot of Fig. 7b. The stress state selected for the subsequent simulation is indicated by circles around the respective σ1 and σ3. c) The stress states BODx, BODy, and BODz in relation to the subsets bod1, bod2, and bod3, respectively. Note the difference of these stress states compared to BOD1, BOD2, and BOD3, respectively (Fig. 7d). Tangent-lineation plots: The measured fault-slip data (coloured arrows) fit well with the theoretical slip patterns of BODx, BODy, and BODz (grey arrows). Fluctuation histograms: A maximum number of fault-slip data is related to the simulated stress states by misfit angles of β ≤ 10°. Mohr-circles diagrams: Most faults reveal very a low τ/σn, reflecting a minor slip tendency. This illustrates that applying exclusively MIM does not necessarily yield the most realistic stress states inherent in a fault population. 137 138 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 139 Fig. 9. Compilation of measured data and results of PBT and MIM, both methods applied to the entire fault population of a single location. Stereograms are lower-hemisphere, equalarea projections. a) Fault-slip data shown in tangent-lineation plots (plot properties as in Fig. 5b). Asterisks mark data sets which are modified due to a back-tilting of the raw data. A back-tilting was performed where the activation of faults pre-dates folding. Parameters for the folding process are derived from the attitudes of the corresponding bedding planes. b) The kinematic P-, B-, and T-axes for each location (plot properties as in Fig. 6b); c) Optimal stress tensors calculated by MIM (plot properties as in Fig. 5c, e = 1). d) Bedding planes presented as great circles and poles to planes (not back-tilted even where a back-tilting of the fault-slip data is required). solutions BOD1, BOD2, and BOD3. However, as the fault-slip data mainly plot to the lower right in the Mohr-circles diagrams, they are associated with much lower shear-to-normal-stress ratios. As the slip tendency of a fault plane is larger for high values of τ/σn, the comparative test suggests BODx, BODy, and BODz not to be as relevant as the stress states BOD1, BOD2, and BOD3 for the Bodendorf data. To summarize, we use the results of PBT to identify the most relevant stress states for a given set of fault-slip data among the numerous solutions provided by MIM. As PBT is mainly used for a preseparation of data sets (later verified by simulations), the selected value of the fracture angle θ does not influence the results of stress inversion. By separating heterogeneous data sets before applying MIM we solve the problem of minor subsets not being indicated adequately by MIM when appearing together with much larger subsets (Liesa and Lisle, 2004). Especially in the case of girdle distributions of σ1- or σ3axes, the PBT-Method helps designating the most realistic direction of the unknown σ2-axis. As demonstrated (Fig. 8), the most relevant solutions produced by MIM might represent stress states associated with unrealistically low shear stresses on the respective faults. 5. Results The basis of our paleostress study is the structural inventory of 14 locations (active and abandoned quarries) storing Upper Carboniferous, Middle Triassic, Upper Jurassic and Upper Cretaceous rocks (Figs. 3, 9). Thus we intend to cover a wide range of rock ages to potentially derive differently-aged stress states from the preserved fault patterns. The investigations were restricted to limestones and volcanics because these lithologies offer the most favourable conservation conditions for kinematic indicators in the area. Each sampled fault-slip datum includes the fault plane orientation (dip direction, dip), the slip direction (azimuth, plunge), and the sense of slip (reverse, normal, dextral, or sinistral), the latter having been derived from kinematic indicators (mostly calcite or quartz slickensides, Fig. 4). Where possible, the faultslip data are complemented by information on their spatial and chronological relationships to other related structures as faults, bedding planes, folds, or dykes. Most of the fault populations from the south-western margin of the CEBS are heterogeneous which is indicated by differently oriented strain 140 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 Fig. 10. Results of separation and stress inversion for all investigated locations (except for Bodendorf). Tangent-lineation plots display the fault-slip data for both homogeneous subsets and non-assignable faults (REST, rightmost column). For each subset, the data are plotted together with the directions of σ1 (black dot), σ2 (grey rectangle), and σ3 (white triangle). The fault-slip data are related to the associated stress state by a specific distribution of misfit angle β (fluctuation histograms) and of shear-to-normal-stress ratios, τ/σn (Mohr-circles diagrams). J. Sippel et al. / Tectonophysics 470 (2009) 129–146 141 Fig. 10 (continued). axes produced by PBTas well as by diverse clusters of stress axes calculated by MIM (Fig. 9b, c). Correspondingly, we separate different subsets for these sites which are presented together with the derived stress states in Fig. 10. Each subset is related to the determined stress state by low-misfit angles (fluctuation histograms) and relatively high shear-to-normal-stress ratios (Mohr-circles diagrams). In some cases (e.g. LIE1), when the precise stress ratio is not fully constrained by the fault-slip pattern, the presented R covers a certain range instead of being a distinct number. For the correlation of local stress states, we first consider agreeing directions of σ1. As a second-order criteria we check the directions of the remaining stress axes and the stress ratios, as they might represent local variations instead of differences between successive regional stress fields (see below). Given a high consistency of stress states, we consider them as being related to the same regional stress field. The chronological order of different stress states for a single location, as shown in Figs. 11 and 12, is either derived directly from 142 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 Fig. 11. Paleostress map of the south-western margin of the CEBS (abbreviations as in Fig. 3). The reduced stress tensors are calculated according to the procedure exemplarily described for Bodendorf quarry (symbols of stress states as in Fig. 7e). The stress states at each location are shown in the derived chronological order with older stress states to the left and younger stresses to the right. field observations (rightmost column of Fig. 12) or indirectly from the findings at other locations. This cross-outcrop correlation is authorised by the fact that in terms of field observations there are no conflicting chronological relationships between the different sites. The total number of 33 stress states extracted from the different sites along the south-western margin of the CEBS can be classified into 4 groups of corresponding stress configurations (Fig. 12): (i) an early extensional regime with a horizontal WNW–ESE- to NW–SE-directed σ3-axis (stress A); (ii) strike-slip and reverse systems with a horizontal N–S- to NE–SW-directed σ1-axis (stress B); (iii) a strike-slip regime with a horizontal WNW–ESE- to NW–SE-directed σ1-axis (stress C); and (iv) a late extensional regime (stress D). 5.1. Stress A The early extensional regime is restricted to Middle Triassic rocks of the Leine Graben and its prolongation to the North (Elvese and Upstedt quarry). At both sites, normal faults of varying dip directions (requiring a vertical σ1-axis and low stress ratios of R ≤ 0.2) represent the oldest traces of deformation. The direction of maximum extension differs slightly between the sites as indicated by WNW–ESE- and NW– SE-directed σ3-axes, respectively. 5.2. Stress B The regime of N–S- to NE–SW-directed maximum compression is the most prominent in the area. This stress could be derived not only from the fault-slip data in the Upper Carboniferous andesites at Bodendorf (stress state BOD1), but also from sites of Middle Triassic, Upper Jurassic and Upper Cretaceous rocks. We correlate the individual stress states because of their accordance in terms σ1-axes as well as relatively low stress ratios (0.0 ≤ R ≤ 0.6). Depending on the prevalence of reverse or strike-slip faults, the vertical principal stress axis is either σ3 or σ2, respectively. At some sites, more than one stress state corresponds to stress B. For instance, two different generations of striae on fault planes at Lienen argue for an earlier activation of reverse faults (LIE1) and a later (re)activation of strike-slip faults (LIE2). The local exchange of the minimum and intermediate principal stress axes is accompanied by an increase of the relative stress differences (from 0.0 ≤ R ≤ 0.1 to R = 0.5), while the direction of σ1 remains almost constant. A similar development from a reverse to a strike-slip stress regime is found for Halle (HAL1 and HAL2). At Künsebeck, we find two strike-slip stress states, KÜN1 and KÜN2, which both can be assigned to stress B but differ with regard to their directions of σ1 (NE–SW and N–S). The bedding at this site (Fig. 9d) indicates a partly synsedimentary tilting of the strata around a NW–SE trending rotation axis which argues for a NE–SW-directed compression. As this direction of compression corresponds well with the NE– SW-directed σ1-axis of KÜN1, this stress state might have directly followed the process of folding while KÜN2 post-dated KÜN1. In a similar way, one can correlate the fold axes derived from bedding attitudes at Dörenthe, Lienen, Halle, and Steinbergen with the oldest phases of faulting at these sites (DÖR, LIE1, HAL1, and STE, respectively). At Flechtingen we infer the same development of the horizontal σ1-axis as at Künsebeck; at both sites σ1 changes from a NE– SW direction (FLE1/KÜN1) to a later N–S trend (KÜN2/FLE2). We attribute both respective stress states to the same stress field B, as their difference in σ1-directions is within the range that σ1 varies between all other stress states assigned to stress B. An oppositely directed rotation of σ1 is documented at Elvese, where this axis changes its direction from a NNE–SSW trend to an ENE–WSW trend (superimposed striae prove the stress state ELV3 to be older than ELV4). 5.3. Stress C Another group of stress states could be correlated on the basis of a horizontal E–W- to NNW–SSE-directed σ1-axis and a vertical σ2-axis (stress C). The associated stress ratios cover a wide range (0.2 ≤ R ≤ 0.9). As the previously described one, this group of stress states is documented by differently-aged rocks comprising Upper Carboniferous, Middle Triassic and Upper Cretaceous units. Field observations yield only weak constraints on the relative timing of stress fields B and C. At Künsebeck, for instance, a southward-dipping fault plane shows a J. Sippel et al. / Tectonophysics 470 (2009) 129–146 143 Fig. 12. Synthesis of results. Despite the different rock ages (indicated in the left column), our stress inversion technique yields very consistent results among the different investigated sites of the study area. The stress states for each outcrop are shown in chronological order with older stress states to the left and younger ones to the right (abbreviations of stress states as in Fig. 10). Stress states from different locations are primarily correlated according to agreeing directions of σ1 and agreeing values of the stress ratio R (colour-coded). Symbols for the reduced stress tensors are plotted as in Figs. 7 and 11. 144 J. Sippel et al. / Tectonophysics 470 (2009) 129–146 generation of reverse striae (KÜN2 with a N–S-directed σ1) covered by dextral striations (KÜN3 with a NW–SE-directed σ1). Secondly, at Sonneborn we find NE–SW-striking dextral faults (SON1 with a NE– SW-directed σ1) being offset by NNW-dipping reverse faults (SON2 with a NNW–SSE-directed σ1). According to these findings, stress C postdates stress B. 5.4. Stress D Locally, the described compressive and strike-slip stress fields are post-dated by an extensional stress regime (stress D). In this case, a vertical σ1-axis and the timing relative to other stress states are the only arguments for the correlation of stress states from different sites. Like in Bodendorf, where initial WNW–ESE-striking strike-slip faults are reactivated with a normal sense during this period (BOD3), we also find the normal faults at Künsebeck (KÜN4) and Elvese (ELV5) to be the youngest of the fault-slip data. In addition, the presence of young normal faults at some other places supports the activity of late tensional stresses (see “Rest” of Lienen, Sonneborn, and Flechtingen). However, the directions of the minimum principal stress axes (σ3) and the stress ratios are not consistent throughout the correlated outcrops. At Künsebeck, a NNW–SSE trending σ3-axis is associated with a high stress ratio (0.9 ≤ R ≤ 1.0), whereas at Elvese and Bodendorf we observe low stress ratios (0.2 ≤ R ≤ 0.3) and a NE–SW-directed σ3-axis. 6. Discussion in Wales and Belgium which are Late Cretaceous to Paleogene in age and mainly associated with a horizontal N–S-directed σ1 (Vandycke, 1997, 2002). The relation to the Alpine Orogeny is further confirmed by a Cenozoic paleostress analysis in the northern periphery of the Alpine chain where Bergerat (1987) finds a N–S-directed compression of late Eocene age. As previously stated, the constraints on the relative timing of stress fields B and C are weak in the studied area. Furthermore, we find only few paleostress configurations that would correspond to a strike-slip regime with a horizontal E–W- to NW–SE-directed σ1 (stress C) when considering adjacent subareas of Central Europe. Delvaux (1997), however, derived a state of horizontal E–W- to NW–SE-directed maximum compression from fault-slip data in western Belgium which he attributes to the Maastrichtian–Early Paleocene. On the other hand, this direction of compression coincides well with the NW–SE-directed maximum horizontal stress axis, SHmax, of the present-day stress field within the subsalt layers of the study area (Reinecker et al., 2005). In the same way, we can relate the late extensional stress field D (with SHmax = σ2) to recent stresses in North Central Europe. Hence, the paleostress fields C and D might have led over to the present-day stress configuration. Furthermore, stress field D with its varying directions of extension may be correlated to a N–S-directed extension found in SE Poland (Lamarche et al., 2002), to a NE–SW-directed extension in prominent N–S-striking structures of Central Europe (Reicherter et al., in press) or to differently oriented extensional regimes detected in S-Wales and NE-Belgium (Vandycke, 2002) for which the authors unanimously postulate Neogene ages. 6.1. Chronology 6.2. Mechanisms Stress A could only be derived from Triassic rocks within a subarea that covers the Leine Graben and its northern prolongation west of the Hartz Mountains. Some non-striated, N–S striking normal faults at the Eastern margin of the Leine Graben (Papenberg) may also correspond to stress A, as these faults likewise represent the oldest preserved deformation structures and they indicate an analogous trend of E–Wdirected extension. This extensional regime might be related to the same tectonic phase which was responsible for the formation of several large N–S-trending grabens in the central parts of the CEBS during the Late Triassic (e.g. Glückstadt Graben, Maystrenko et al., 2006). On the other hand, the low stress ratios (R ≤ 0.2) of the associated stress states reflect almost concentric patterns of normal faults which could alternatively be explained by uprising salt structures beneath these locations. Of course, the two mechanisms could have acted in concert as well. The youngest rocks which show the traces of the N–S- to NE–SWdirected compression (stress B) are the Upper Cretaceous (Cenomanian) limestones from Künsebeck. Considering (i) their consolidation age as the maximum age for this stress state and (ii) the consistent properties of the derived stress states across the study area, implies that even the deformation traces preserved in the Upper Carboniferous volcanics of the Flechtingen High area may be attributed to postCenomanian times. Hence, we can relate the stress field B clearly to the Late Cretaceous–Cenozoic intra-plate compressional deformation that affected the Alpine foreland as a result of the Alpine orogeny (Ziegler, 1987). This orogeny which induced the inversion of mainly NW–SE striking elements of the CEBS (Betz et al., 1987; Nalpas et al., 1995; Vejbaek, 1997; Krzywiec, 2002; Scheck et al., 2002a; de Lugt et al., 2003; Lamarche et al., 2003; Otto, 2003; Scheck-Wenderoth and Lamarche, 2005) comprises a succession of compressive phases, the culmination of which varies between the respective subareas. Accordingly, Lamarche et al. (2002) derive a paleostress pattern of NE–SW-oriented compression from fault-slip data in southeastern Poland. The authors attribute this stress field, which is an analogy to our stress B, to the Maastrichtian–Paleocene compression that causes the inversion of the Polish Trough. Further correspondences are provided by the strike-slip and reverse paleostress regimes from areas As demonstrated, the described consistencies between locally derived stress states may give implications on the regionally active paleostress fields. On the contrary, we find differences between single stress states related to the same overall stress field which argue for local perturbations of the latter. Along the Osning Lineament, for instance, the horizontal σ1 of stress B changes its direction gradually from the north-western to the south-eastern parts of this subarea (the azimuths of σ1 being 014 at Dörenthe, 021 at Lienen, 027 at Halle and 231 at Künsebeck). Though this issue requires further investigations of an enlarged data base, the stress state variations might be explained by different orientations of the nearby fault zone with respect to the regional stress field (Homberg et al., 1997). In the same way, the evolution of stress states at Elvese with a clockwise rotation of the horizontal principal stress axes (ELV2, 3, 4) might reflect the changing response of a structurally weaker zone in the crust to the same stress field B. On the other hand, the transition between the early extensional and the following strike-slip regime (from ELV1 to ELV2) and from the reverse to the late extensional regime (from ELV4 to ELV5) correspond to a permutation of a pair of principal stress axes indicating more distinct changes between the respective paleostress fields. Such a permutation of stress axes, which we also find at other sites of the study area, is a very common phenomenon in brittles tectonics and favoured by contrasts and anisotropy in rock properties that may result from earlier deformation phases (Hu and Angelier, 2004). 7. Conclusions Our complementary approach of integrating the Multiple Inverse Method and the PBT-Method facilitates (i) the separation of complex data sets into kinematically homogeneous subsets and (ii) the inversion of stress states that fulfil both the criteria of low-misfit angles and of high shear-to-normal-stress ratios. PBT allows a fast (pre-) separation of a heterogeneous fault population, whereas MIM yields the entire number of potential stress states for the same set of striated faults. The pivotal element of our stepwise technique, however, is an interactive stress simulation which provides direct J. Sippel et al. / Tectonophysics 470 (2009) 129–146 control on the relation of a single striated fault to a stress state in terms of its associated misfit angle. Thus, the main advantage of a stress inversion via simulation is that of not being a “black box”. The reliability of our technique is confirmed by the fact that irrespective of (i) the number of fault-slip data from an outcrop, (ii) the number of subsets they represent and (iii) the proportion of newly formed and reactivated faults, we obtain very consistent results in terms of reduced stress tensors from outcrops of variously aged rocks. The consistency between individual outcrops concerning the derived stress states as well as their evolution is impressively documented by two paleostress fields of regional relevance: (i) a strike-slip and reverse regime with a horizontal N–S- to NE–SW-directed σ1-axis and low stress ratios and (ii) a pure strike-slip regime of a horizontal E–W- to NW–SE-directed compression with intermediate stress ratios. Both these stress fields are post-Cenomanian in age and correspond to the Late Cretaceous–Tertiary phase of basin inversion in response to the Alpine collision. The dominance of the Late Cretaceous–Tertiary compressional and strike-slip stress fields may be related to the position of the study area in one of the most intensely inverted parts of the CEBS where the traces of older stress fields seem to be widely overprinted. Considering the prevalence of strike-slip movements which these stress fields are associated to, the investigated part of the Elbe Fault System is clearly dominated by wrench tectonics during these times. The only detected stress state which pre-dates the inversion of the CEBS corresponds to an extensional regime with an approximately NW–SE-directed σ3-axis and is restricted to a subarea within and north of the Leine Graben. The youngest tectonic imprints detected in the area also correspond to locally appearing extensional stress states with varying directions of σ3. At many sites, the youngest derived paleostress state coincides in terms of the direction of the maximum horizontal stress axis, SHmax, with the present-day stress field, thus maybe representing the direct precursor of the present stress conditions. Acknowledgements This study is supported by the Deutsche Forschungsgemeinschaft (DFG) under the SPP 1135. 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