The approach used in this study is based on outcrop observations of discontinuities, namely opening-mode fractures, small-scale faults, fracture arrays and stylolites, that are genetically associated with a certain stress field (Fig. ). Discontinuity sets are defined on the basis of both orientation and discontinuity type e.g.. A theoretically complete discontinuity association (DA) consists of four sets of discontinuities: one opening-mode set, oriented perpendicular to σ3; a conjugated pair of small-scale faults, with a 60 to 30° angle respectively, bisected by σ1; and a stylolite forming perpendicular to σ1. Relative timing based on cross-cutting and abutment relationships between individual sets within a discontinuity association is not considered in this study, as they do not reveal additional information on the orientation of the paleo principal stresses. In the study area, many fractures contain mineral deposits, and are then termed as veins. They are mainly found in arrays, belonging to semi-ductile shear zones that may form conjugate pairs similar to faults . As the aperture and infill of fractures in the outcrop do not necessarily coincide with subsurface see e.g., we use veins in the same way as other fractures to define DAs in the field. The consequences of this approach will be later discussed.

DAs are documented in the field per station with a size of around ten squared meters. Discontinuities that are compatible in a single stress field are thus observed in close vicinity of each other. In each station, we document the discontinuities that can be placed into a DA. The orientation of the DAs are used to map the related paleostress directions. To ensure the robustness of the reconstructed paleostress directions, we consider a minimum of two discontinuity sets that are associated together to define a DA. For example, a stylolite together with a conjugate pair of small-scale faults is considered a very reliable indicator. On the contrary, we discard features which provide ambiguous stress information, such as isolated opening fractures.

This method inherently means that not all discontinuities observed are documented. To quantify how representative the defined associations are for the total network, we measured augmented circular scanlines on seven pavements on the Parmelan . Per pavement, a total of four to twelve scanlines with a radius of one meter are collected. The orientation and type of discontinuities that intersect the circular scanlines are documented. The qualitatively defined associations from the nearest by station are used to separate the loose features that cannot be understood in the framework of an association from those that do. This gives an indication of the portion of discontinuities that fit within the framework of associations with respect to the total network.

The mapped paleo principals stress axes per station are used to determine the stress regime in which the DA was formed (i.e. normal, reverse, or strike-slip). We assume that all DAs are formed in Andersonian stress fields , i.e. two of the principal stresses were positioned horizontally at the timing of discontinuity formation. This is used to reconstruct the relative timing between the formation of a DA and the tilting of the strata (Fig. ). If two of the three principle paleostresses are oriented parallel to the bedding, and the bedding is tilted, we infer that the DA formed prior to the tilting of the strata. Multiple DAs can be observed in a single station (in this study, we document a maximum of three). If the difference between the stress fields of two different DAs is only a permutation of the principle stresses, the simplest cause is a change in overburden or by intermediate stress regimes , rather than a different tectonic event. Therefore, these DAs are grouped into single events.

We use two criteria to define regional, background network forming events. Firstly, the relative timing of the DAs that make up the event must be prior to tilting of the strata. Secondly, the orientation of the principle stresses of the DA must be similar in all analogue outcrops that surround the target reservoir, i.e. constant on a regional scale. If the two criteria are fulfilled, we predict that the target reservoir that is located between the analogue outcrops, also is affected by these regional events. We use this prediction to separate the background-related discontinuities observed on BHI of the two wells that penetrate the target reservoir, namely GEo-01 and GEo-02.

Veins, stylolites and small-scale faults are common on the Parmelan and can be arranged in discontinuity associations. The oldest association (PA1) is expressed by a conjugate pair of small-scale faults and tectonic stylolites, observed on meter-scale. The faults strike ∼ 045–225° with a low dip angle with respect to the bedding (∼ 15–30°). Dissolution on the shear planes makes them clearly visible on bed-perpendicular exposures (Fig. A). In some instances, slickensides are preserved on the shear planes, indicating reverse kinematics. The tectonic stylolites have a similar strike as the small-scale faults, but are bed-perpendicular. The angular relationship between the faults, stylolites and bedding are observed everywhere, even in the steeply dipping limbs of the box fold that shapes the Parmelan (e.g. station 18). Therefore, they are formed prior to the tilting of the strata. This association formed in a reverse stress regime with σ1 oriented NW-SE.

The second association (PA2) comprises both small and large discontinuities, ranging from meter to kilometer in length. The smaller discontinuities are made up of two sets of sub-vertical vein arrays with opposing sense of shear (Fig. B) and tectonic stylolites. The latter similarly oriented as those of PA1. Sinistral arrays have an average strike of 150–330°, whereas dextral arrays strike 120–300° on average. The cement of the veins is yellow-white and have a blocky texture.

On a large scale, the plateau is dissected by two sets of fractures with similar orientation as the vein arrays (Fig. ). They range in length from 100 to 3000 m. In the field, they appear as narrow bundles (< 1 m) of smaller sub-vertical fractures. Dissolution along these fractures has created a karst system that is connected to an extensive cave system below the plateau . On the plateau, there are no offset markers that indicate horizontal displacement along these structures and no kinematic indicators are observed. At the northern edge of the plateau however, in front of the entrance to the Diau cave (see Fig.  for location), these fractures intersect a vertical cliff, and here bed-parallel slickensides on the fracture planes are preserved. The faults form a conjugate pair, so their structural attitude is similar to the vein arrays on top of the plateau, and are thus grouped into PA2. The associated stress regime of PA2 is a strike-slip regime, with σ1 oriented NW-SE. This is similar to PA1, with the only change being a permutation of σ2 and σ3. Therefore, PA1 and PA2 together are considered as part of one event.

The third association (PA3) is also made up of a conjugated pair of sub-vertical vein arrays and tectonic stylolites, but with different orientations than those of PA2 (Fig. C). The dextral vein arrays strike ∼ 080–260° and the sinistral arrays strike ∼ 120–300°, with the cement of the veins being grey-coloured. The length of the discontinuities range from cm to 10s of meters. The stylolites are bed-perpendicular and strike ∼ 170–350°. The veins that form the arrays occasionally cross-cut and displace those of PA2 (Fig. D), and are therefore interpreted as being younger in age. The paleostress regime related to this association is strike-slip, with σ1 oriented ∼ W-E.

To investigate how representative the above described associations are for the total network present on the Parmelan, we measured augmented circular scanlines on 7 different pavements on the Parmelan (see Fig.  for location). Up to 75 % of the total discontinuities observed can be understood within the framework of the predefined associations, and the majority belong to PA3 Fig. . The percentages vary per pavement investigated, illustrating the spatial variability of the background network.

Four different associations have been documented in the Jura and Vuache. In all cases, they formed prior to tilting of the strata. The first association (JA1) comprises a conjugate pair of small-scale faults with a low-angle with respect to the bedding and bed-perpendicular, tectonic stylolites (Fig. A). The strike of the small-scale faults and stylolites is ∼ 035–215°. Slickensides on the shear planes indicate reverse kinematics. The reconstructed σ1 of JA1 is oriented NW-SE.

The second association (JA2) is made up of a conjugated pair of bed-perpendicular small-scale faults (Fig. B), together with tectonic stylolites. Sinistral fractures strike ∼ 170–350°, dextral fractures strike ∼ 110–290°. Slickensides on the shear planes are always parallel the bedding. Tectonic stylolites strike of ∼ 035–215°, similarly as those of JA1. The stress regime of JA2 is strike-slip, with σ1 oriented NW-SE. The difference between JA1 and JA2 is a premutation of σ2 and σ3. Therefore, they are grouped into a single event.

The third association (JA3) is composed of ∼ 000–180° striking reverse faults with a low angle with respect to the bedding (Fig. C), and bed-perpendicular tectonic stylolites. They formed in a reverse stress regime with σ1 oriented W-E.

The fourth association (JA4)is expressed by bed-perpendicular ∼ 140–320° striking sinistral faults and ∼ 075–255° striking dextral faults (Fig. D), together with ∼ 010–100° striking bed-perpendicular stylolites. This association is indicative of a strike-slip regime with σ1 oriented W-E. This orientation is the same as JA3, and therefore they are part of the same event.

In the Salève, only one (SA1) is documented. Small-scale faults that strike ∼ 030–210° and have a low angle with respect to the bedding (Fig. ) are associated together with ∼ 035–215° striking bed-perpendicular stylolites. The related stress field is a reverse regime with σ1 oriented NW-SE.

Based on the orientation of σ1 of the associations in the different studied areas, we can define two regional discontinuity formation events (Fig. ). The first event (E1) is characterized by a NW-SE trending, sub-horizontal σ1. This orientation of σ1 is both recorded by the reverse associations (PA1, JA1 & SA1) as well as by strike-slip associations (PA2 & JA2). In all outcrops, the reverse regime is similarly expressed by low-angle conjugate pairs of small-scale faults. Bed-perpendicular vein arrays of the strike-slip association are also observed in the Parmelan, Jura and Vuache. On top of this, in the Jura and Vuache, the strike-slip association is also expressed by conjugated brittle, sub-vertical faults.

The second event (E2) is also made up of a reverse and strike-slip association, but with a sub-horizontal σ1 oriented ∼ W-E (Fig. ). In the Parmelan, only the strike-slip association is documented in the form of vein arrays and bed-perpendicular stylolites (PA3). In the Jura and Vuache, there is also a reverse association documented (JA3) with similar σ1 as a strike-slip association (JA4). The latter is mainly depicted by bed-perpendicular faults, and less so by vein arrays, in contrast to the Parmelan.

A pre-tilting relative timing for E1 and E2 is observed in all studied areas. This implies that E1 and E2 were formed prior to Alpine fold-and-thrusting, and thus form the background network. As these events are consistently observed on all sides of the Geneva Basin where the target reservoir is located, we predict the presence of this background network in the subsurface as well.

We use the prediction of the background network in the subsurface of the Geneva Basin based on the analogue outcrops for the interpretation of BHI of two geothermal wells drilled in the basin (GEo-01 and GEo-02, for location see Fig. ). The discontinuities of which the orientation fits within the predicted background network are identified in the dataset and subsequently considered as part of the background network. Then, we evaluate the proportion of the background network with respect to all discontinuities observed in the well.

The two investigated wells both penetrate the Lower Cretaceous carbonates, and as there are no cores of the wells, all features are interpreted on the BHI only. In GEo-01, the Lower Cretaceous is observed between 411 and 533 m (MD). In this well, two types of image logs are acquired for fracture analysis: optical borehole imaging (OBI) and acoustic borehole imaging (ABI). GEo-02 is located 7 km south-southeast of GEo-01 and here the Lower Cretaceous is found at a depth between 770 to 996 m (MD). For this well, only ABI-logs are available. Feature picking on these logs was carried out with WellCAD (ALT) program software.

The feature picks are divided over 5 different categories; bedding, veins, open fractures, induced fractures and unclassified fractures. Bedding planes are defined by their repetitive character and the fact that they cannot cross-cut any other feature. Veins are highly reflective in OBI, whereas open fractures are transmissive. Veins were not observed on the ABI logs, either because they are not present, or due to the limited contrast between the host rock and fracture infill. As GEo-02 only has an ABI-log, no veins are interpreted in this borehole. If features are transmissive in OBI, have an irregular surface and the dip angle is high (> 85°) they are classified as induced fractures, although it should be noted that separating induced fractures from natural fractures remains a challenge . Features that are both transmissive in OBI and have a low amplitude on the ABI are interpreted as open fractures. Distinguishing mode-I from mode-II is not possible on the image logs, so they are not differentiated during the picking of fractures. If a fracture pick did not meet any of the above criteria, it was not classified.

Firstly, the bedding planes are separated from the other interpreted features. In GEo-01, a total of 195 bedding surfaces are identified (Fig. ). When plotted against depth, the dip direction of these planes exhibit a clockwise rotation with depth, from north-dipping at the top, gradually transitioning into south-dipping at the bottom. Also, the dip angle varies with depth, with a low angle at the top and bottom, but a gradual increase between 440–480 m (MD) up to 60°, giving an overall bell-shaped curve. In GEo-02, a total of 176 bedding planes are picked (Fig. ). In contrast to GEo-01, the dip direction remains constant with a dip towards the ESE and a dip angle between 10–20°.

For the implementation of the prediction based on outcrop work, we only considered the natural fractures (open fractures and veins), and discarded the induced and unclassified picks from the datasets. Then, the total amount of natural fractures observed in GEo-01 is 820, and for GEo-02 is 211. To compare these discontinuities with the outcrop prediction, they were backtilted with respect to the closest bedding measurement on the BHI (Fig. ). The backtilted discontinuities are subsequently compared with the predicted background network as defined in the outcrops.

The orientations of the regional events in the outcrop are used to predict the geometry of individual discontinuity sets that make the background network in the subsurface. We consider the average orientation of the principal stresses of the regional events, and define orientations of discontinuity sets related to this orientation. For E1, the orientation of σ1 is 135–315° and for E2 it is 097–277° (Fig. ). For the low angle small-scale faults, we assumed a strike perpendicular to σ1 with a dip angle of 30°. For the stylolites, the strike is also perpendicular to σ1, but with a dip angle of 90° (perpendicular to the bedding). As in the outcrop, the majority of the discontinuities that make up the strike-slip associations are bed-perpendicular vein arrays, we considered a 15° angle between σ1 and the strike of the vein arrays for the prediction in the well. Lastly, the opening fractures are bed-perpendicular with a strike parallel to σ1. The combination of these sets are used to identify the fractures in the well that fit within this predicted assoications. If a fracture pick on the BHI deviates less than 30° (azimuth + dip) from the predicted orientation of a set, these fractures are considered as part of that discontinuity set (Fig. ). This maximum deviation is considered reasonable, as there is some variability in the observed DAs in the outcrop. On top of that, there is a margin of error in the BHI interpretation as well.

For the well GEo-01, 350 discontinuities (44 % of total) fit in the associations of E1 and E2, of which 236 are open fractures, and 114 veins. In GEo-02, the total number of discontinuities that fit the predicted associations is 104 (50 % of total). As there is only ABI for Geo-02, all the fractures that are identified are open. The contribution of E1 and E2 is about equal. The majority of the discontinuities in the two wells are low-angle small-scale faults (175 and 86 for Geo-01 and Geo-02 respectively).

The regional events captured by the method of DAs reveal similar paleostress orientations as previous studies focusing on the deformation history of the Parmelan and the Jura and Vuache ranges . In the Parmelan, define two pre-folding events with a reverse and strike-slip component with an ∼NW-SE orientation of σ1, similar to E1. These authors also document a strike-slip event with an ∼ E-W oriented σ1 identical to E2 but interpret this event to be post-folding . In the Jura and Vuache ranges, the reverse and strike-slip regimes of E1 are also observed by . However, the inferred timing of these regimes is different; only the strike-slip component is interpreted as pre-tilting of the strata, whereas the reverse regime is considered syntectonic, because the majority of the observed reverse slip vectors were not pre-folding . This is in contrast to our observations of clearly pre-folding small-scale faults related to the reverse regime (Fig. A).

The main difference between the DA method and previous studies is the interpreted timing of discontinuity-forming events, which reflects the specific aim of the methodology proposed in this study. The goal of the DA method is to use the outcrop as an analogue of the subsurface to better predict the geometry of the background discontinuity network present at depth that is not directly observable. This is in contrast to the studies of and that focus on the deformation history of the outcrop itself, aiming at retracing the chronological succession of events that created the discontinuities in the outcrop. The consequences of these different approaches are best illustrated with the reverse regime of E1. If this event is linked to folding, it may be expected to produce localized deformations, opposed to the distribution of a background network . However, this event, producing reverse small-scale faults, could also be interpreted as having formed during the layer-parallel-shortening (LPS) phase before the onset of regional folding. dated the sequence of events shaping a series of folds observed in the Apennines, Pyrenees and in the Rocky Mountains. They found that the LPS-phase largely predates the onset of localized deformations occurring during fold growth and late stage fold tightening. Therefore, the LPS deformation phase is likely to produce the same diffuse fractures observed in the Vuache and the Jura. On the other hand, previous work in the Jura belt, northeast of the area of interest of this study, has shown that stress perturbations impacted the orientation of deformation structures around major left-lateral strike-slip faults Pontarlier and Morez faults;. These faults are similarly oriented as the Vuache fault that bounds the Geneva Basin on the southwestern side. We document two stations in the vicinity of this fault (station 32 and 39, see Fig. ), where the orientation of E1 is rotated 10° counterclockwise with respect to the average orientation of E1. It is possible that this small rotation is related to a perturbation of the stress field around the Vuache fault. However, the relationship of E1 with the bedding indicates that it was formed prior to tilting of the strata, and therefore we consider it to be part of the background network. Considering the discontinuities related to E1 as localized and restricted to fold and/or fault structures dramatically changes the prediction of these features in the subsurface. In the absence of folds in the subsurface, these fractures will be overlooked, although they are present in the investigated well in the Geneva basin where no folds or faults are observed (i.e. GEo-02, see Fig. ).

A key aspect of the DA-method is that it targets to capture regional events to enhance the predictability for the subsurface. The interpretation of E2 demonstrates this capability of the DA-method. On the Parmelan itself, there is no direct evidence for the relative timing of E2 with respect to the folding. In the Jura however, small-scale faults of E2 are consistently tilted with the bedding (e.g., Fig. C) and thus formed prior to tilting. Therefore, we consider that the simplest interpretation is that E2 is also part of the background network, and consequently predict its presence in the subsurface. Absolute dating of the calcite veins that are part of the background network could potentially constrain the timing even further, but so far, geochronology studies in the region have only focused on dating fault activity .

The DA-method can be used to predict the geometry of the background network in the target reservoir, but is limited in extrapolating the aperture and mineral infill of fractures. The geometry is useful when considering stimulating the reservoir, as even the sealed discontinuities may create a strength anisotropy that will control the orientation and propagation of hydraulic fractures . However, for predicting flow behaviour in the reservoir caused by natural discontinuities, modeling the aperture and mineral infill of discontinuities is crucial, as only (partially) open discontinuities might contribute to the flow. At the same time, outcrops should be treated with care when extrapolating these properties to the subsurface e.g., also when the link between outcrop and subsurface is established with the DA-method. The timing of fracturing, emplacement of the infill and potential dissolution are important factors to consider when extrapolating these characteristics to the subsurface. On the Parmelan, for example, many small-scale (< 10 m) fractures of E1 and E2 are calcite filled (e.g. see Fig. ). The diagenetic evolution can be used to constrain the timing of calcite cement formation in the outcrop e.g., and subsequently provide insights how the aperture of these discontinuities can be modeled in the subsurface . On the other hand, the large-scale fractures (> 100 m) of E1 on the plateau are currently conductive due to dissolution and karstification (see Fig. ). It depends on the timing of fracturing and subsequent dissolution if the conductivity of these fractures can be used as an analogue for the paleokarst network that is observed on top of the Lower Cretaceous in the subsurface of the Geneva Basin . If E1 was formed prior to sub-aerial exposure of the Lower Cretaceous during the Paleogene, it is likely that they partially controlled the orientation of karst development. On the contrary, if the karstification on the Parmelan only occurred after the exhumation in the Pliocene, similarly dissolved fractures cannot be expected in the subsurface. So, in order to predict the aperture and if discontinuities are sealed in the reservoir, solely based on outcrops, the timing of fracturing and the diagenetic evolution of the formation are both essential to predict which discontinuity sets in the subsurface are likely to be conductive. Another possibility is to use borehole data to assess which discontinuities are conductive, and the DA-method can be part of the workflow to improve the interpretation.

Borehole images are a practical, widely used, and relatively inexpensive way to sample and characterize the sub-seismic scale discontinuity network in the subsurface. However, there are two main drawbacks to this type of data. Firstly, core-to-log correlations have shown that image logs only are not suitable for characterizing the type of fracture e.g.. Secondly, image log interpretations are prone to subjective bias of the interpreter , similarly as has been demonstrated for fault interpretation in seismic data and fracture data collection in outcrops .

DAs can complement BHI interpretation by providing the discontinuity type of identified background features. Typically, discontinuity sets defined on BHI (in particular when cores are not available) are all considered as opening-mode fractures. Based on this assumption, a classical workflow consists of defining fracture sets, extracting statistical distributions for these sets, and stochastically extrapolating these distributions at the reservoir scale in a discrete fracture network model e.g.. However, the type of discontinuity will impact the evaluation of the flow behaviour of the network in multiple ways. Several studies have demonstrated that stylolites can be either flow conductive or form flow barriers and could potentially induce compartmentalization in subsurface reservoirs . and showed that opening fractures are good flow conductors if cement bridges create a natural propping mechanism in the fracture. Finally, the roughness of a discontinuity, which is related to the type, has an impact on its capacity to be reactivated under present-day stress field, which in turn influences its hydraulic aperture under reservoir conditions . These authors also add that typically, shear fractures have a higher roughness than opening fractures, therefore highlighting the importance of being able to constrain fracture type in the reservoir.

The DA-methodology provides a prediction of the discontinuity type of up to 50 % of the observed discontinuities in the two boreholes in the Geneva Basin, even though the resolution of the BHI is too low to determine discontinuity type, and there is no core available to correlate the BHI with. The percentage of background-related discontinuities is similar in the two wells, whereas the total number of features is higher in GEo-01. A possible explanation is that there is only ABI-log available for GEo-02, and no OBI. It might be that not all discontinuities present in GEo-02 are visible on the ABI log, due to a lack of contrast in acoustic properties between host rock and discontinuity, resulting in a lower number of features picked. Another possibility is that the difference in number of background-related features is caused by the spatial variability within the background network. GEo-01 might have penetrated a denser part of the background network compared to GEo-02. After the emplacement of the background network, GEo-01 is affected by localized deformation (i.e. a fold, see Fig. ), producing more discontinuities in this well. At present-day, the percentage of background-related discontinuities is then the same as in GEo-02.

To reduce biases in fracture interpretation in general, propose to develop a clear sampling strategy before the actual interpretation. The DA-methodology provides a guideline for such a strategy. For example, in the Geneva Basin, the two events that shape the predicted background network are composed of discontinuity sets with a known range of orientations, based on outcrop work. An adequate fracture picking strategy in the BHI could be to initially discard all features that fall significantly outside this predefined range. This strategy will isolate the background network from more recent discontinuities produced by local drivers. This separation can subsequently be considered during fracture modeling on the reservoir scale. After this, the impact of the background network on the flow behaviour of the reservoir can be assessed with flow simulations.

The tectonic driver of the background network is fundamentally different from the rest of the network, and therefore isolating the background network in the reservoir will improve fracture modeling on reservoir scale. developed a method that links discontinuities observed in the well with seismic-scale faults. A given number of random far-field stress states are simulated around the faults, and the perturbation of the stress directions around the faults is calculated. For each simulated stress state, the number of small-scale discontinuities whose orientation fits within the modeled stress field is counted (goodness of fit). The stress state with the highest number of fitting discontinuities is considered the best stress regime, and the discontinuities falling outside this model are discarded from the dataset. The input data for these models are generally all the fractures interpreted from wells, or, in other words, it is assumed that all subsurface fractures are fault-related. Instead, we propose to first isolate the background network, as these discontinuities should be extrapolated to the entire reservoir. Only after this separation, the goodness of fit of fault-related discontinuities should be considered. In this way, the geological understanding of discontinuity formation is better incorporated in the fracture modeling in the reservoir.

Another way how the DA method can improve fracture modeling in the reservoir is in the up-scaling strategy. advocated for mixing explicit and implicit representation of fractures in the model as an effective up-scaling method, as it balances the accuracy of the process, whilst preserving the geometrical complexity of the network. Typically, the selection criterion between implicit and explicit representation is the length of the fractures . As an alternative to this method, we propose to use the genetic origin of the fracture as a second criterion. Due to its regional character, the background network is very suitable for up-scaling strategies. By assessing the impact of the background network on the effective permeability on reservoir scale, either by analyzing the topology of the network e.g., or by numerically simulating flow through stochastically generated DFNs e.g., the decision can be made to either represent the background explicitly or implicitly in reservoir scale models. After the significance of the background network is defined, the next step is to include the discontinuities observed in the well that could not be placed in the framework of the background network. These discontinuities are thus likely created by local drivers and scale differently on the reservoir scale than the background network. For example, if there are seismic-scale faults present in the subsurface, the above mentioned method of is a suitable approach to extrapolate these discontinuities to the reservoir scale.

This dynamic workflow will de-risk future geothermal drilling projects in different ways. The separate modeling of the permeability of the background network can be used to assess whether the background only can already produce economically viable fluid volumes, or if seismic-scale discontinuities are essential for production. Also, the well-placing strategy can be adjusted to the heterogeneity of the background permeability field. For example, in the Geneva Basin, most of the background discontinuities are striking NE-SW, and thus, a higher permeability in that direction is expected. A deviation of the well perpendicular to this strike will therefore likely optimize the well screen and thus the fluid inflow.