3.1 Data processing

Steeply dipping reflections are already visible in the raw data (Fig. 2a). To extract these reflections, the direct wave is removed via an alpha-trimmed 2D spatial filter after applying a static correction to flatten out the first arrivals. Subsequently, this static correction is reversed to place the reflections back into their original position (Fig. 2b). Since, the dataset was acquired with omnidirectional antennae, we can only determine the relative dip of the reflectors with respect to the borehole trajectory. It is not possible to constrain the azimuthal orientation of the reflectors. However, the OTV data indicate that the azimuths of most brittle and ductile structural features are constrained to one quadrant (Fig. 2c). Hence, it is justified to treat the reflections as up- and down-going wavefields originating at the same reflectors. Correspondingly, these up- and down-going wavefields are separated by f-k quadrant filters, then migrated using pre-stack Kirchhoff time-migration and converted to distance using a constant average velocity. Since the prevailing geological structure is near-vertical, the velocity is varying laterally, which was at least partially accounted for in the pre-stack time-migration process by a laterally varying velocity model derived from the first arrivals. Pertinent details of the processing and imaging flow applied to the BHR reflection data are given in Table 2.

Figure 2(a) Raw BHR reflection data and (b) after removal of the direct wave and reversed static corrections. (c) Relative dips and azimuths of fractures identified in the OTV data.

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Table 2Processing and imaging of BHR reflection data

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3.2 Estimation of fracture dip

Figure 3a shows the final migrated and distance-converted BHR reflection image, which consists of the up- and down-going wavefields, plotted in positive distance orthogonally from the borehole trajectory. We observe an abundance of reflections, most of which intercept the borehole wall. It is straightforward to calculate the relative dip of these events. In zones of low attenuation, which correspond to large first-cycle amplitudes of the direct wave in Fig. 3b, some of these events can be traced to distances of up to 10 m from the borehole. These zones are representative of more intact rock. Conversely, high signal attenuation, characterized by low first-cycle amplitudes in Fig. 3c, occurs in zones of intense brittle deformation, such as, for example, in the fault core and its vicinity.

Figure 3(a) Migrated BHR image consisting of the up- and down-going reflection data plotted in positive distance from the borehole trajectory. Red lines denote selected reflection events used for estimating the dips and locations of the associated fractures. (b) Maximum first-cycle amplitude of BHR first arrivals (black line), relative dip of fractures from OTV data (turquoise dots), and relative dips picked from the depth-converted BHR reflection image (red dots and squares). For the OTV data, the size of the dots is a relative measure of fracture aperture. The dips of events denoted by red lines in (a) are identified by red dots encircled in blue.

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From the image shown in Fig. 3a, we manually pick the dips of the brightest reflections as well as some of the weaker cross-cutting events to capture the variety of dips encountered. A representative selection of the picked events is superimposed on the image as straight red lines, and their locations with regard to the borehole track and their dips are illustrated in Fig. 3b by red dots encircled in blue. All picked events are plotted in Fig. 3b, and their values are compared to the fracture dips inferred from the OTV data, which are shown as turquoise dots whose diameter is indicative of the fracture aperture (Egli et al., 2018). Following Egli et al. (2018), fractures with very large apertures are classified as cataclastic zones; aperture refers here to the thickness of the fractures and not to the mean open space. Most of the fractures with a large aperture contain some infill. Overall, the range of dip angles picked from the imaged BHR reflection data is consistent with those inferred from the OTV data, although it is difficult to match individual reflection events with specific fractures in the OTV images. The reason for this is 2-fold. (1) Both datasets contain the signatures of an abundance of fractures, which, in turn, necessitates an inherently subjective selection; and (2) the depth locations and dips assigned to BHR reflectors might differ slightly with regard to those of the OTV data.

Nevertheless, the comparison of the two datasets confirms that in such an environment fluid-filled fractures and cataclastic zones are the most likely cause of BHR reflections. The BHR reflection image allows one to trace the associated brittle deformation structures several meters from the borehole into the adjacent formation. The BHR reflection image and the OTV data provide clear and consistent evidence for a dense and complex network of fluid-filled intersecting fractures and cataclastic zones above and below the main fault core. Such a network of fractures provides effective fluid pathways through the otherwise tight granitic host rock (e.g., Berkowitz, 2002).

4.1 Full-waveform sonic data: identification of brittle deformation zones

As illustrated by Fig. 3b, the first-cycle amplitude of the BHR first arrivals is a good proxy for the degree of brittle deformation. Similarly, FWS data are expected to be sensitive to brittle deformation as the associated wave propagation is governed by the underlying elastic and hydraulic properties of the medium. Here, we utilize the 2 kHz low-gain FWS data, which are mainly sensitive to low-frequency Stoneley waves. This wave type is an interface wave traveling along the borehole wall. Its velocity depends predominately on the shear modulus of the formation and bulk modulus of the fluid. Its amplitude decreases across compliant and hydraulically transmissive features, such as fractures and cataclastic zones, due to transmission losses, reflections, and pressure diffusion processes (e.g., Paillet, 1994). Following Paillet (1983), the local Stoneley wave energy deficit can be used as an indicator of the hydraulic transmissivity of a system. For the considered data, a quantitative analysis is, however, not possible, since the data quality due to the roughness of the borehole wall caused by enlargements as well as the recording time are not sufficient, and the data recorded at receiver 1 is clipped even for the lowest possible gain of the tool. Nevertheless, we can still estimate the local energy deficit of the recorded waveforms, which are dominated by Stoneley waves, and use this measure as a qualitative proxy. To account for borehole enlargements, we compare the FWS data with the caliper and the neutron–neutron log data. While the neutron–neutron log is also affected by the borehole enlargements, it is primarily sensitive to the water content and thus to the porosity, which in the considered environment is dominated by fracture porosity (Egli et al., 2018).

Figure 4(a) Low-gain FWS data acquired with a nominal central frequency of 2 kHz overlain by the caliper log; (b) corresponding power spectrum overlain by the neutron–neutron log; (c) relative energy deficit for two different frequency bands, one capturing the Stoneley wave and the other the complete spectrum, in conjunction with the first-cycle amplitude of the BHR direct wave and the brittle deformation data from the OTV; (d–g) examples of brittle deformation based on a comparison of OTV data and corresponding drill core sequences.

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Figure 5Summary of the brittle deformation based on the OTV data (Egli et al., 2018) (a) fracture aperture, (b) relative dip, and (c) relative azimuth. All identified fractures are displayed in histographic form along the borehole. Fractures with measurable aperture (greater than 0.8 mm) are displayed as red dots. In (a) additionally cataclastic zones, the cementation zone, and main fault core are plotted.

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In Fig. 4, we compare the aforementioned log data to the OTV-based brittle deformation data of Egli et al. (2018). Figure 4a shows the low-gain FWS log data recorded at receiver 2 for a nominal center frequency of 2 kHz and Fig. 4b the corresponding power spectrum. The former is overlain by the caliper log and the latter by the neutron–neutron log. The color scale in Fig. 4a is chosen such that the primarily visible signal is the Stoneley wave. The first arrival P- and S-waves are much lower in amplitude. The local energy deficit is shown in Fig. 4c for two frequency bands and overlain with the OTV-based brittle deformation data of Egli et al. (2018). Figure 4c also depicts the BHR first-cycle amplitude. From the FWS data, we can clearly distinguish five characteristic zones denoted as A through E, which also find their expressions in the first-cycle BHR amplitudes. In the following, we compare these zones to the brittle deformation data of Egli et al. (2018), which is summarized in Fig. 5, comprising the apertures as well as the relative dip and azimuth of the fractures with respect to the horizontal of the borehole trajectory. Apertures below 0.8 mm were deemed not to be reliably measurable for the recorded resolution of the OTV data.

• Zone A consists of three cataclastic zones. The OTV image and the core material of two cataclastic zones are shown in Fig. 4d and e. These cataclastic zones are characterized by time-delayed, low-amplitude Stoneley waves with an energy reduction of 15 % as well as low BHR amplitudes. Moreover, they find their expression as prominent anomalies in the caliper and neutron–neutron logs. As such, zone A is likely to represent a hydraulically transmissive interval of low shear strength and high porosity.

• Compared to zone A, zone B is characterized by a smaller energy deficit and an overriding high-frequency wave corresponding to the pseudo-Rayleigh wave, which only exists in fast formations and thus suggests a zone of higher shear strength and less brittle deformation. The latter is consistent with the high BHR amplitudes. Nevertheless, even in this section, fractures are still present (Fig. 5), albeit with apertures below 0.8 mm.

• Conversely, the FWS signal in zone C is dominated by low frequencies in the power spectrum with a decrease in high frequencies towards zone D and the vanishing of the pseudo-Rayleigh wave, which is indicative of a decrease in shear strength. The BHR amplitudes decrease towards zone D as well, in which the borehole collapsed and had to be cemented and redrilled. The BHR amplitudes already show a strong decrease at 70 m depth, whereas the other logs (caliper, neutron–neutron, energy deficit) only show a pronounced changes around 75 m. Due to their small penetration depths, the latter are affected by the cemented section of the borehole, whereas the BHR measurements have a deeper penetration depth and are averaged over a larger support volume. Thus, the BHR measurements are likely to reflect the “true” formation properties better in this section. The core material in zone C (e.g., Fig. 4f) is partly noncohesive due to intense brittle deformation, which explains the observed characteristics of the BHR amplitude and FWS data. Local vanishing of the FWS amplitudes in conjunction with anomalies in the caliper and neutron–neutron logs at 65 to 65.3 and 66.74 m are due to a cataclastic zone and an individual large-aperture fracture of 3.71 mm, respectively.

• Zone D comprises the wider zone of the main fault core where most of the FWS signal is lost. One reason is the large borehole enlargements and the associated rugosity of the borehole wall, which prevents the propagation of Stoneley waves. In the upper part of this zone, a weak signal is recorded between a borehole depth of 82 and 86 m with a shift towards higher frequencies. This section corresponds to the GBF core consisting of fault gouge (Egli et al., 2018).

• Finally, zone E is characterized by an alternating sequence of regions with pronounced low and high energy deficits, which is indicative of an overall rather compact rock volume with prominent isolated fractures (e.g., Fig. 4g). This interpretation is consistent with a correspondingly alternating sequence in the BHR amplitudes.

4.2 Cluster analysis

To refine the zonation identified in Fig. 4 and infer the associated petrophysical properties, we consider a pertinent selection of the logging data acquired in 2015 under open-hole conditions and in 2016 through a screened PVC casing. These are shown in Fig. 6 and include from left to right the caliper and natural gamma log, the sonic P- and S-wave velocities, the gamma–gamma and neutron–neutron logs, the BHR direct-wave velocity and amplitude, and electrical resistivity measurements. All logs are superimposed onto the brittle deformation data mapped from the OTV. The larger-scale trends of most of the logs are consistent with the previously inferred zonation A through E, which is depicted on the left-hand side of Fig. 6. The GBF fault core, which is located between 82 and 86 m borehole depth, is marked by borehole enlargements and clearly defined across the entire suite of logs. Most of the remaining anomalies observed in the borehole log data correlate with caliper anomalies, which, in turn, are associated with enlargements and can be linked to zones of the brittle deformation identified in the OTV data. In the following, we analyze the relationship between the various borehole logs and address the question whether their response can be linked to the degree of brittle deformation. To this end, we perform a cluster analysis on a selection of the log data.

Figure 6Representative selection of borehole log data comprising from left to right caliper, natural gamma, sonic velocity, neutron–neutron and gamma–gamma, BHR direct-wave velocity, and amplitude as well as normal resistivity logs with a separation of 8 in. (0.2 m), 16 in. (0.4 m), 32 in. (0.8 m), and 64 in. (1.6 m). The brittle deformation features interpreted from the OTV data (Egli et al., 2018) are superimposed on the log data. The sizes of the circles are indicative of the relative fracture apertures. Zones A through E refer to zonation shown in Fig. 4.

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In a first step, we perform a correlation analysis of the log data shown in Fig. 6. Before doing so, the datasets are normalized to account for the different unit scales. We obtain an overall good correlation between the BHR velocity and amplitude and the neutron–neutron, the P-wave velocity, and the normal resistivity logs. In the following, these datasets will be subjected to a cluster analysis. Although the S-wave velocity log shows a good correlation with other log data in the more intact parts of the borehole, it is not considered due to its unreliability around the main fault core. The gamma–gamma log is strongly affected by large borehole enlargements and shows otherwise little variation. The poor correlation of the natural gamma log with the other datasets is probably due to the fact that, in the crystalline environment, it is primarily sensitive to mineralogical alterations, which, compared to the brittle deformation structures, have a secondary effect on the other borehole logs. The BHR velocities and amplitudes are primarily sensitive to the fluid-filled porosity and the bulk electrical conductivity, respectively. The neutron–neutron log is sensitive to the total amount of hydrogen present in the formation, while the P-wave velocity log is sensitive to the mechanical properties, and the normal resistivity is sensitive to the bulk resistivity.

The upper triangular region in Fig. 7 shows crossplots of the selected log data, which confirm the overall good correlation. The somewhat spurious nature of these crossplots is due to the fact that the various geophysical logs average the petrophysical properties over significantly differing support volumes. This is problematic when dealing with small-scale, high-contrast features, such as fractures, embedded in an otherwise relatively homogeneous matrix. An effective way to display such datasets is in histograms, as shown in the triangular region below the diagonal in Fig. 7, which clearly illustrate the overall strong correlation trends between the various datasets. The largest spread of values is observed for crossplots containing either the P-wave velocities or the BHR amplitudes, whereas the other properties show generally well-defined correlation trends.

Figure 7Lower triangle with regard to diagonal: histogram crossplots of selected borehole logs – BHR amplitude, neutron–neutron (NN), BHR velocity, P-wave velocity (Vp), and normal resistivity 16 in. (0.4 m) (Norm16 res.). Upper triangle with regard to diagonal: color-coded crossplots of groups identified based on cluster analysis. The diagonal shows the corresponding cluster boxplots for each property.

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To analyze these trends in more detail, we perform a cluster analysis using the k-means algorithm of the MATLAB Statistics Toolbox with a squared Euclidian distance criterion (Arthur and Vassilvitskii, 2007). The analysis is performed on the normalized data in two subsequent steps. First, we test for the optimal number of clusters to group the data into. To do this, we use the so-called silhouette and gap criteria (Tibshirani et al., 2001), which both suggest an optimum of four clusters. Then, we apply the k-means algorithm to group the data into four clusters. The median, the 25th percentile, and the outliers of each cluster and each petrophysical property are shown in the form of boxplots along the diagonal of Fig. 7. Across all petrophysical properties, the identified clusters show a good separation with regard to each other.

Figure 8 shows the borehole log data used for the above cluster analysis color-coded according to the four cluster groups identified in Fig. 7 and overlain by OTV-based brittle deformation data. Also shown is the sequence of clusters along the borehole track together with the fracture density inferred from OTV data as well as the caliper log. Comparing these various datasets allows the characterization of the clusters as follows: (1) GBF fault core, (2) zones of high fracture density or cataclastic deformation, (3) zones of moderate fracture density or large-aperture fractures, and (4) zones of low fracture density. There is a mismatch at the bottom of the borehole between the cluster-based interpretation of the borehole log data and fracture density estimated from the OTV data. The reason is that partially and fully closed fractures are accounted for in the OTV-based fracture density, while the logs are largely insensitive to these types of fractures. This problem only manifests itself at the bottom of the borehole, since the occurrence of closed fractures compared to open fractures is larger in this region than elsewhere along the borehole. An essential result of the cluster analysis is that the signatures of the selected borehole logs as well as their interrelations are predominantly governed by brittle deformation in general and that the individual clusters seem to be clearly linked to the degree of deformation in particular. In this context, it is interesting to note that the sequence of clusters along the borehole displayed on the righthand side of Fig. 8 is fully consistent with the more generic zonation A through E inferred from the Stoneley wave analysis (Fig. 4).

Figure 8Borehole log data used for cluster analysis, color-coded according to the four cluster groups identified in Fig. 7 and overlain by brittle deformation inferred from the OTV data. The righthand column shows the sequence of clusters along the borehole together with the fracture density inferred from the OTV data, the ductile deformation intensity log (Egli et al., 2018), the caliper data, and the zonation A through E inferred from the Stoneley wave analysis (Fig. 4).

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Interestingly, the P-wave velocities and normal resistivity data exhibit a larger variability in cluster 4 than in the other petrophysical properties. This becomes especially apparent in zone B, which exhibits a comparatively low fracture density and variable degrees of ductile deformation (Fig. 8). In this partially intact zone, the P-wave velocity assumes maximum and minimum values of 5600 and 4600 m s⁻¹, respectively. The former is close to P-wave velocities of non-fractured granitic rocks, which typically range between 5700 and 6200 m s⁻¹ (e.g., Holbrook et al., 1992; Salisbury et al., 2003). The variability in the P-wave in these more intact zones might thus be an indication of variations in the ductile rock fabric. We also observe strong fluctuations in electrical resistivity and relatively low resistivity values on average for a granitic environment. The latter may point towards the influence of surface conductivity, most likely due to the abundance of mica notably in the gneissic and mylonitic parts of the formation, which, in turn, may result in regions of elevated conductivity compared to the unaltered granites (Keys and Sullivan, 1979). A recent study of electrical properties of mylonites from the Alpine Fault project in New Zealand found resistivity values ranging from 675 to 75 Ω m (Kluge et al., 2017). This is significantly lower than literature values of granite, which range from 10³ to 10⁶ Ω m. The variability in the P-wave velocity and resistivity is also reflected in the natural gamma log, which, in turn, points to the potential influence of mineralogical changes associated with ductile deformation.

5.1 Porosity estimation

The porosity ϕ is obtained from the BHR velocity v using the so-called complex refractive index method (CRIM)

where c is the speed of light and v the velocity of the formation; ϵ_r, ϵ_w, and ϵ_s are the relative dielectric permittivities of the formation, the pore water, and the solid material, respectively (e.g., Greaves et al., 1996). For low porosities, the method is quite sensitive to the dielectric permittivity of the solid material ϵ_s. To find a representative value for ϵ_s, we constrain the possible range by laboratory-based density measurements. Archimedes-type density measurements have been performed along the entire core recovered from the GDP1 borehole. These measurements were taken at 20 to 30 cm intervals (Jörg Renner, personal communication, 2016). The inferred densities are compared to densities calculated from BHR porosities for different values of ϵ_s (Fig. 9a) using an average grain density of 2653 kg m⁻³ determined from corresponding laboratory analysis of eight samples measured. Subsequently, an upper and lower bound for ϵ_s is chosen so that the laboratory-measured densities from competent samples fall between the resulting calculated density values from the BHR velocities. This provides well-constrained bounds for low and intermediate porosities. However, the estimation of high porosities is less reliable due to core loss and poor quality of the retrieved core material from the heavily fractured zones. The results are shown in Fig. 9b together with the porosity curve for the median of the best-fitting dielectric permittivity. For the latter, we only consider the zones without borehole enlargements.

Figure 9(a) Porosity estimates from BHR velocities for different dielectric permittivities of the solid material ϵ_s and from neutron–neutron (NN) data compared with laboratory-based measurements for selected core samples (Jörg Renner, personal communication, 2016). (b) Inferred density from BHR porosities compared to Archimedes-type density measurements on the core samples (Jörg Renner, personal communication, 2016).

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The resulting porosity logs obtained from the BHR velocity measurements are, as expected, smooth due to the large support volume of the method, and, hence, the strong fluctuations in response to the intense fracturing observed in other borehole logs are averaged out. To capture the variability in the porosity on a smaller scale, the neutron–neutron measurements are utilized to downscale the BHR porosity. Details are given in Appendix A. The resulting downscaled porosity log is compared to laboratory-measured porosities for selected core samples (Fig. 9) and to a multiscale porosity analysis of Egli et al. (2018), which includes OTV data, thin sections, and He-pycnometry (Fig. 10a). Across all these different methods, the corresponding porosity estimates agree remarkably well. Figure 10b shows the sequence of brittle deformation groups inferred from the cluster analysis for comparison along the borehole. The largest porosities prevail, as expected, in the main fault core with a decreasing trend away from this zone. Other high-porosity zones are associated with cataclastic zones and large aperture fractures. Even in the most intact zones, the porosity is, however, still higher than common values of the matrix porosity in crystalline rocks of ∼1 % or less (Schmitt et al., 2003).

Figure 10(a) Comparison of log-based porosity estimates with corresponding values from thin section image analysis and He-pycnometry (Egli et al., 2018) and (b) brittle deformation groups inferred from cluster analysis (Figs. 7 and 8) with the caliper log and OTV-based fracture density log superimposed.

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5.2 Fluid flow characteristics

The prevailing fracture network and high-porosity zones associated with brittle deformation are the main flow pathways of the GBF system in its present state. To shed more light on the hydraulic characteristics of this system, we analyze a combination of SP logs from 2016 and 2017 in conjunction with temperature and fluid resistivity logs. The first part of this subsection describes the processing and interpretation of the SP data, while the second part focuses on the combined interpretation of the various log data with respect to the fluid flow characteristics.

Self-potential data

The SP logs were acquired in the same logging run as the normal resistivity and single-point resistance logs. In this setup, the reference electrode for the SP measurements is the steel cable along which the logging tool is suspended. This causes a very strong drift in the measurements until ∼30 m of the exposed steel cable is below the water level; afterwards the measurements start to stabilize. For this reason, we only show measurements from 60 m borehole depth onwards for the 2016 and 2017 SP logs, as the water table was at 33 m borehole depth at the time of the measurements. To compensate for the remaining drift of the data, we removed a linear background trend (Appendix B). The resulting logs are shown in Fig. 11 and compared to the open-hole measurements at the bottom of the section acquired in 2017. There are some differences in the absolute values between the open- and cased-hole measurements, however, the main features of the data, especially the position and the character of the anomalies are the same. Overall, the anomalies in the SP logs along the entire considered depth range are pronounced and well defined and show remarkable repeatability between the data acquired in 2016 and 2017.

Figure 11Comparison of the trend-corrected SP data with complementary borehole logs. From left to right: electrical resistivity and zones of in- and outflow inferred from an analysis of natural hydraulic heads (Cheng and Renner, 2017) as well as passive flow meter tests (2015), results of cluster analysis (Figs. 7 and 8) overlain with the detrended SP data, the fluid resistivity log measured in 2016, the temperature logs, and the OTV-based brittle deformation logs (Egli et al., 2018) overlain by the SP data. The fluid resistivity measurements are shown at ambient conditions and corrected to a constant temperature of 25 ^∘C. The detrended temperature logs of the polyprobe tool (2016, 2017) and the STS tool (2016) as well as the not trend-corrected temperature profile (black line) acquired with the STS (2016) tool are displayed.

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SP anomalies can be of electrokinetic, electrochemical, and thermoelectric origin (e.g., Jackson, 2015). In the studied fractured hydrothermal environment, SP anomalies are most likely of electrokinetic origin. This assessment is supported by an analysis of flow meter data by Cheng and Renner (2017), which identified zones of in- and outflow into the borehole associated with hydraulically open fractures. For SP signals of electrokinetic origin, the corresponding streaming potential φ can be linked, to the first order, to the hydraulic pressure gradient Δp (e.g., Jackson, 2015)

$$\begin{array}{}\text{(2)}& \mathrm{\Delta }\mathit{\phi }=C\mathrm{\Delta }p,\end{array}$$

where C<0 is the electrokinetic coupling coefficient. The magnitude of C depends on several factors. Notably, it scales with the electrical conductivity of the pore water over several orders of magnitude, thus justifying a simple empirical relation derived from laboratory data for estimating the coupling coefficient for field observations (Revil et al., 2003). Given that, at ambient conditions, the average fluid resistivity along the GDP1 borehole is ∼320 Ω m (Fig. 11), which is high compared to common groundwater, this results in a large coupling coefficient of $\sim -\mathrm{6600}$ mV MPa⁻¹. This, in turn, can explain the large magnitudes of the observed SP anomalies, even in the presence of moderate to weak hydraulic pressure gradients. The high resistivity of the water in the borehole is not unusual for the area. The adjacent lake water, which has a direct glacial inflow and mostly consists of melt water, has a resistivity of ∼500 Ω m.

Figure 11 shows that the observed SP anomalies are abundant and reach values of up to 400 mV, which is indeed very large for signals of electrokinetic origin. Using the above estimate for the coupling coefficient of C ≈ −6600 mV MPa⁻¹, the largest SP anomalies in our data, imply hydraulic pressure gradients on the order of 0.06 MPa. This is approximately one order of magnitude lower than the pressure gradients estimated by Suski et al. (2008) in a saline artesian fractured hydrothermal system for maximum SP anomalies of ∼50 mV. Despite their unusually large magnitudes for SP signals of electrokinetic origin, the anomalies observed along the GDP1 borehole thus seem to be realistic for the specific setting. Indeed, SP anomalies of similar magnitude were recorded in the Grimsel Test Site (Himmelsbach et al., 2003), which is situated in the same granitic formation ∼400 m below the Grimsel Pass. In this case, the anomalies could be attributed to electrokinetic responses of distinct fractures. An additional contribution to the measured SP signals along the GDP1 borehole could arise from variations in the bulk resistivity. This might come into play between 95 and 120 m borehole depth, where we observe relatively strong variations in resistivity, which are linked to the variable degree of fracturing, as illustrated by the results of the cluster analysis (Fig. 8).

Considering the described uncertainties and the abundance of SP anomalies due to the intensely fractured nature of the formation, associating a single anomaly deterministically with in- or outflow is impossible. To overcome this problem, we apply a probability tomography based on Di Maio and Patella (1994). This approach reconstructs an image of the most probable locations of SP sources, which explain the observed data by assuming that an anomaly measured at location $\overrightarrow{r}$ can be represented by a linear superposition of partial SP effects due to elementary electric source elements located at $\overrightarrow{r_q}$. For the considered borehole measurements, we scan a region which cuts the borehole along its trajectory for such source elements with the scanning function

$$\begin{array}{}\text{(3)}& S_c(\overrightarrow{r},\overrightarrow{r_q})={\displaystyle \frac{\overrightarrow{r_q(x,z)}-\overrightarrow{r(x,z)}}{\mid \overrightarrow{r_q(x,z)}-\overrightarrow{r(x,z)}{\mid }^{\mathrm{3}}}}.\end{array}$$

The result of this procedure is an electric charge occurrence probability (ECOP) map given by the cross-correlation between the scanning function and the electrical field associated with the SP measurements. For SP signals caused by a distribution of dipole sources, corresponding dipole occurrence probability (DOP) maps can be calculated for the horizontal and vertical component of the dipoles. A more detailed description of the method is given by Hämmann et al. (1997), Mauriello and Patella (1999), Iuliano et al. (2002), and Saracco et al. (2004).

Figure 12(a) Electric charge occurrence probability (ECOP) and (b) dipole occurrence probability (DOP) maps along the borehole track overlain by the SP log and fractures from OTV data, and DOP vectors with an absolute probability larger than 0.15, respectively. (c) Most probable DOP vectors in each 1.2 m interval mapped onto the borehole track together with a projection of fracture planes and their color-coded apertures.

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Figure 12a and b show the resulting ECOP and DOP for the largest of the two dipole components at each location along the borehole track. The DOP map is overlain by DOP vectors constructed from the horizontal and vertical dipole components. These vectors are indicative of the direction of fluid flow at a specific location. For display purposes, a threshold has been chosen, and only vectors with an absolute probability larger than 0.15 are shown. Also shown are the most probable vectors, which are selected in subsequent 1.2 m intervals and mapped onto the borehole trajectory together with the orientation and aperture of the fractures identified from the OTV data in Fig. 12c. Positive and negative values in the ECOP map indicate regions that gain and loose water, respectively; as such they are possible locations of in- and outflow along the borehole. The selected DOP vectors in Fig. 12c are color-coded correspondingly and indicate possible in- and outflow scenarios. For the interpretation of the hydraulic behavior, we focus on these scenarios.

5.3 Hydraulic zonation

The observed SP anomalies can be associated with fractures and cataclastic zones identified in the OTV data (Fig. 11). The representative DOP vectors and corresponding ECOP values indicate that above 95 m borehole depth inflow is dominating. Inflow into the borehole can be caused by flow from fractures and downflow along the borehole. Both scenarios are likely to occur. The former is supported by DOP vectors coinciding with the direction of the fracture dip suggesting flow along fractures and the latter by flow meter measurements conducted in 2015 indicating a generic downflow regime along the entire borehole (Fig. 11). Below ∼95 m borehole depth, the character of the SP data and the associated DOP vectors and ECOP values are more variable, including both inflow and outflow with an increase in the number of outflow regions towards the bottom of the borehole and a dominant outflow around 120 m borehole depth. These observations are generally consistent with results from flow meter measurements and an analysis of natural hydraulic heads by Cheng and Renner (2017). The study identified inflow between 81 and 119 m and a zone of prominent outflow below 119 m borehole depth, as indicated by the blue and green rectangles in Fig. 11.

With regard to the zonation derived from the analysis of Stoneley waves (Fig. 4), the relevant zones in the given context are C, D, and E (Fig. 11). Zone C consists of partially noncohesive core material and contains nine fractures with apertures above 3 mm, the largest one being 6.4 mm; zone D is the wider zone of the main fault core, which is largely brecciated, and zone E is represented by more compact rock with prominent individual fractures (16 fractures with apertures above 3 mm, the largest one being 16.4 mm). The largest SP anomalies are observed in zone E and some distinct signals in zone C, whereas the zone around the main fault core shows much less variability and smaller anomalies. This suggests that zones of in- and outflow are likely to be dominated by individual fractures or localized fracture clusters. Furthermore, the fluid resistivity shows a very distinct layering along the borehole track (Fig. 11). Although, the corresponding variations are not large in magnitude, they clearly imply distinct variations in salinity, which, in turn, point to differing origins and flow paths of the water in the borehole. Potential sources of water in the steeply dipping, fracture-dominated geological structure around the GBF may comprise direct infiltration of meteoric water through the outcropping parts of the GBF, shallow groundwater flow, and upflow from greater depth along the GBF zone. There is a hydraulic connection between the Transitgas AG tunnel and the GDP1 borehole, as evidenced by polymers from the drilling operation found in the tunnel. Two zones with relatively low fluid resistivities prevail around the main fault core (cluster 1) and below ∼95 m borehole depth, whereas above the main fault core and in the intensely fractured interval between 85 and ∼95 m borehole depth relatively high fluid resistivities are observed. The latter coincide with a small low-temperature anomaly in the detrended temperature data. These observations suggest infiltration of meteoric water along the fracture network in the more resistive zones, whereas in the other zones inflow of more mineralized water, possibly from greater depth, occurs. One explanation might be the presence of two distinctively different reservoirs: a shallow, less saline one, above 95 m, where meteoric water penetrates into the formation through the fracture network exposed at the Earth's surface; and a deeper more saline one below 95 m depth alimented by hydrothermal water rising up from depth (e.g., Wanner et al., 2019). However, there is no clear evidence of a hydraulic barrier between the two zones.