Drilling data-calibrated shale compaction models for pore pressure evaluation from geophysical well logs in the North Alpine Foreland Basin, SE Germany

The study area is located in the SE German part of the NAFB, which is the peripheral foreland basin of the Alps (Fig. 1a). The NAFB is filled with Cenozoic sediments and extends from Lake Geneva in the west to Upper Austria in the east over a distance of 700 km (Bachmann et al. 1987). The basin is bordered by the Danube River in the north and by the Bohemian Massif in an ENE direction. The German NAFB widens significantly to the east, extending to a maximum present-day width of about 150 km at the longitude of Munich (Lemcke 1973; Jin et al. 1995), while deepening from north to south, where it reaches thickness of up to 5000 m in front of the Alps (Bachmann et al. 1987) (Fig. 1b).

The NAFB is underlain by widespread and locally 500–1000 m-thick Mesozoic sediments (Fig. 1b, c), and a Variscan crystalline basement. Permo-Carboniferous sediments are only preserved within basement troughs (Bachmann et al. 1987). Fractured and karstified carbonates of the Upper Jurassic crop out at the northern rim of the NAFB along the Danube River and dive southwards beneath the Cenozoic basin fill, reaching a depth of c. 5 km in front of the Alps. Upper Jurassic carbonates display excellent hydraulic properties and are one of the most prolific hydrothermal reservoirs in Germany (Agemar et al. 2014b; Flechtner and Aubele 2019). They are typically subhydrostatically pressured, following the hydraulic head of the Danube River in the north (Lemcke 1976). Only the Landshut–Neuötting High, a basement high in the eastern part of the study area (Fig. 2), acts at least partly as a hydraulic barrier, dividing the hydraulic system of the Upper Jurassic into western and eastern parts (Lemcke 1976; Birner 2013). Upper Jurassic carbonates therefore act as the regional drainage system of the NAFB and thus far the presence of significant overpressure has not been reported below Upper Jurassic carbonates. Cretaceous sediments are only preserved in the central and eastern parts of the NAFB in SE Germany and their thickness increases from NW to SE (Bachmann et al. 1987). While the carbonates of the Lower Cretaceous share the subhydrostatic pressure regime with their Upper Jurassic counterparts, Upper Cretaceous sediments comprise predominantly shales and marls that can be significantly overpressured (Drews et al. 2018) (Fig. 1c). Upper Cretaceous shales and marls possibly act as a hydraulic barrier between the subhydrostatically pressured Lower Cretaceous and Upper Jurassic carbonates and the Cenozoic basin fill, and therefore are most likely to control the presence of overpressure in the Cenozoic basin fill (Drews et al. 2018).

The Cenozoic basin fill comprises shales, marls, carbonates, sandstones and coarser-grained clastics of Late Eocene–Late Miocene age (Kuhlemann and Kempf 2002; Doppler et al. 2005) (Fig. 1c). Sedimentation is generally sourced from the calcareous Alps in the south, the carbonates of the Franconian Platform in the NW, and the granitoid magmatic and metamorphic rocks of the Bohemian Massif in the NE. Eocene sediments consist of limestones and sandstones, and due to erosion are also missing in the NW part of the study area (Bachmann et al. 1987) (Fig. 1c). They typically share the pore pressure regime of the underlying formation and can be significantly overpressured, although hydrocarbon production-related pressure depletion cannot be ruled out (Shatyrbayeva et al. 2023). Oligocene and Early Miocene (Aquitanian) sediments reflect two westward-orientated transgressions, leading to widespread shales and marls of early Oligocene (Rupelian) age and very late Oligocene (upper part of Chattian) age, and an eastward transition of terrestrial coarser-grained sediments into fine-grained marine sediments during the earlier Chattian and Aquitanian (Fig. 1c). Significant overpressure has been observed in Chattian sandstones, in particular the so-called Baustein Beds (Fig. 1c), and in the Rupelian sequences (Drews et al. 2018, 2020; Drews and Duschl 2022; Shatyrbayeva et al. 2023). In the Rupelian, in particular, the so-called Bändermergel Subformation (Fig. 1c) and Schöneck Formation can be significantly overpressured (Drews et al. 2018; Shatyrbayeva et al. 2023) and have caused severe drilling problems in the past, such as kicks in encased sandstones and wellbore instability in shales (cf. Lackner et al. 2018; Dorsch et al. 2021).

Despite its compressional nature, uplift in the NAFB is restricted to only a few hundred metres and is rather evenly distributed across the study area (Baran et al. 2014). The formation of overpressure is most likely to be due to disequilibrium compaction with peak overpressures roughly following sedimentation and burial rates, all of which are highest in the Lake Chiemsee area (Fig. 2) (cf. Zweigel 1998; Sachsenhofer 2001; Drews et al. 2018; Shatyrbayeva et al. 2023). However, horizontal loading due to horizontal shortening might increase the formation of overpressure towards the Alps (cf. Müller et al. 1988; Drews and Duschl 2022). In addition, the role of clay diagenesis and fluid expansion due to hydrocarbon generation and oil-to-gas cracking have been suggested (Drews et al. 2020) but dedicated studies are not yet available. Nevertheless, studies from the Upper Austrian part of the NAFB have observed clay diagenesis (smectite to illite transformation) (Gier et al. 1998) and the Rupelian Schöneck Formation in particular displays high organic carbon contents (Bachmann et al. 1987; Gier 2000; Sachsenhofer et al. 2010).

The available dataset consists of 310 wells drilled between 1953 and 2018 in the NAFB in SE Germany (Fig. 2). Oil and gas wells comprise 284 of the total, and the remaining 26 were drilled for deep geothermal exploration. Sonic and/or resistivity log data from 215 wells were used in compaction-based pore pressure prediction; both data types were present in 191 wells. Overview of oil and gas well data availability is summarized in Großmann et al. 2024.

Pore pressure measurements and pore pressure indicators investigated in our previous study (Shatyrbayeva et al. 2023) have been used to calibrate the compaction trends. Apart from measured pressure data, gas readings, drilling mud weights and collected drilling issues, salinity and temperature data were also gathered as input parameters for the study. Hydrochemical properties of the Jurassic carbonate aquifer were excluded in the salinity data as it is a different hydraulic system influenced by major freshwater infiltration (Lemcke 1976; Heidinger et al. 2019). Temperature data was derived from the Geothermal Information System GeotIS (Agemar et al. 2012, 2014a, b. All of the well data were referenced to true vertical depth (TVD). Furthermore, all drilling data used in this study were presented and discussed (also in terms of uncertainty) in great detail in Shatyrbayeva et al. (2023). Table 1 gives an overview of the data and data sources. The data availability of each investigated wellbore is outlined in Supplementary Table 1.

A regionally best-fitting NCT was constrained for sonic velocity and electrical resistivity of clay-rich sediments (shales and marls). High gamma rays with low-velocity and low-resistivity readings were principally considered for the differentiation of shales, along with geological well reports where shales/marls are stated as the primary lithology in their cutting descriptions.

The Waxman–Smits equation (Waxman and Smits 1968) was used to relate shale porosity to electrical resistivity. Unlike straight-line compaction trends that are often employed as pore pressure monitoring techniques, the Waxman–Smits method results in a curved NCT, offering a decent basis for a geologically and petrophysically reasonable investigation (see Bowers 2002 and Haugland and Tichelaar 2008 for a more comprehensive discussion). At the same time, the method is highly sensitive to lithological variations, providing valuable insights into subregional transitions of shale composition because it considers a number of petrophysical parameters, such as formation salinity, temperature, clay content and cation-exchange capacity (CEC).

In a final step, both the sonic and resistivity NCTs using equations (4–11) were calibrated to actual data pairs of vertical effective stress and shale sonic velocity or the shale/water resistivity ratio R_shale/R_T, respectively. We used R_shale/R_T to establish the temperature dependency of electrical resistivity and to obtain a monotonic relationship between vertical effective stress and shale resistivity. It is important to note that the input parameters were calibrated to get the best fit on a regional basis rather than on a well-by-well basis.

Vertical effective stress was obtained from a vertical stress estimate (equation 3) and actual pore pressure measurements from drill stem tests (DSTs), wireline formation tests (WLFTs) and reported kicks, along with increased drilling fluid densities adjusted to counterbalance high gas shows. In addition, maximum drilling mud weights, MW_max, have been applied in the analysis. Sonic velocity and resistivity values were further picked from shale intervals nearest to the pressure measurement. As the well tests were mainly carried out in the non-shaly reservoir rocks, it was assumed that the adjacent shales represented a similar pressure regime. It should be highlighted that the vast majority of these pressure indicators are subject to significant uncertainties (Shatyrbayeva et al. 2023).

In general, both sonic velocity and electrical resistivity (normalized to porewater resistivity) values of clay-rich intervals show very consistent relationships with vertical effective stress estimates from adjacent pore pressure measurements and indicators throughout the study area, which can be fitted with single regional trends for both data types (Fig. 3a, b). Thereby, the parameters applied for the sonic velocity-based NCT are in concordance with those in the previous study by Drews et al. (2018), who mainly used seismic velocities from check shots and vertical seismic profiles, with only slight modifications to the n exponent (equation 4), which we adapted to 2.1 according to Issler (1992) (Table 2). For the resistivity-based NCT we used the regional average of salinities recorded in Cenozoic reservoirs and shale-typical values for Archie's m exponent (Toumelin et al. 2006), tortuosity factor (Asquith et al. 2004; Glover 2016) and shale grain densities (Drews et al. 2019) (Table 2).

However, in the NE part of the study area (area shaded orange in Fig. 3c), both shale sonic velocities and resistivities were significantly lower in shallower intervals (predominantly above 2500 m TVD) and follow a different relationship (Fig. 3a, b). With the established regional trends, both sonic and resistivity would yield very high overpressure estimates, which, however, have not been observed by drilling in the area: the first oil and gas production in the NAFB started in the area in the early 1950s. Hundreds of wells have been drilled since then with a MW_max of around 1.3 g cm⁻³ with no major pore pressure-related drilling issues (Shatyrbayeva et al. 2023). Furthermore, the maximum recorded DST pressure was 1.15 g cm⁻³ in the area. Earlier studies on pore pressure magnitudes (Müller et al. 1988; Drews et al. 2018; Shatyrbayeva et al. 2023) emphasized that the area is showing minor overpressure, relating to a maximum EMW of 1.2 g cm⁻³. The reduced sonic velocity and electrical resistivity are therefore most likely not related to the presence of overpressure. Instead, we propose the following three scenarios as alternatives for the differing relationships between sonic velocities, electrical resistivities and vertical effective stress in clay-rich sediments in the NE part of the study area:

• (1) Sediment source (provenance): shales in the NE part of the study area are most likely to have been sourced from the Bohemian Massive (Kuhlemann and Kempf 2002), which comprises magmatic and metamorphic rocks that might yield a higher smectite content as a weathering product or at least a less carbonate content. In contrast, the western and southern parts of the study area were sourced from the carbonate-rich Franconian Platform and Northern Alps (Kuhlemann and Kempf 2002), respectively. The transition in provenance could therefore result in a NNE to SSW transition from more smectite-rich (lower velocity and resistivity) towards more carbonate-rich (higher velocity and resistivity) shales.

• (2) Clay diagenesis: the NAFB deepens from north to south. Sediments of the same age were therefore exposed to higher temperatures in the south compared to the north. Below c. 2500 m, temperatures were likely to exceed the threshold where clay diagenesis was initiated (smectite to illite transformation), as has been reported for the Austrian part of the NAFB (Gier 1998, 2000; Gier et al. 1998). A lower illite content in the overpressured shales of Oligocene and Late Cretaceous ages would result in lower velocities and resistivities (cf. Hoesni 2004; Katahara 2017) in the northern part of the study area.

• (3) Horizontal loading: horizontal shortening increases towards the Alps and with it most probably horizontal loading-driven compaction (cf. Lohr 1969; Schrader 1988; Drews and Duschl 2022). In porous low-permeability formations this effect might act as an additional overpressure mechanism in the southern part of the study area (Müller et al. 1988; Drews and Duschl 2022). In the context of vertical effective stress, the additional lateral compaction would result in relatively higher velocities and resistivities in the south compared to the north.

A subset of 215 of the 310 wells was studied in more detail according to the derived compaction trends. To compare the results between resistivity and sonic-based estimations based on the established regional compaction trends, we show three example wells in the west–east direction of the NAFB (indicated as west–east section in Fig. 4; the well locations are shown as square symbols in Fig. 5c).

Analyses revealed that pore pressure gradients predicted by the constrained regional NCTs on the basis of sonic velocity and electrical resistivity are in agreement, and overpressure starts building up below 2500 m depth in the Oligocene section towards the central part of the NAFB (Fig. 4a).

Example well 1 – Kinsau 1 (on the left-hand side of Fig. 4 and represented in the western part of the west–east cross-section in Fig. 5c) – is an exploration well drilled in 1983 targeting oil and gas in Upper Jurassic carbonates and Middle Jurassic sandstones in the SW of the NAFB. The well penetrated the entire Cenozoic, Lower Cretaceous and Jurassic sedimentary sections, and reached total depth in the crystalline basement. The well location corresponds to the western border of overpressure as introduced by Müller et al. (1988) and Drews et al. (2018). The estimated pore pressures indicate mostly hydrostatic pressure over the entire well section (Fig. 4a). In addition, the major part of the well was drilled with a MW_max of 1.1 g cm⁻³ with no pore pressure-related drilling issues. Drilling mud density was increased to a MW_max of 1.21 g cm⁻³ after running the third casing, most probably due to a rising total mud gas (<5%), which appeared in the Lower Oligocene Schöneck Formation and Lower Cretaceous Purbeck limestones (Fig. 4c). The drilling fluid density had to be reduced later to 1.1 g cm⁻³ to overcome significant mud losses, which occurred in the Upper Jurassic carbonates, where well tests confirmed subhydrostatic pore pressure that essentially follows the hydraulic head of the Danube River in the north (cf. Lemcke 1976).

Example well 2 – Holzkirchen 2 (middle plot in Fig. 4 located in the centre of the west–east cross-section in Fig. 5c) – is a hydrocarbon well drilled in 1969 and is located south of Munich in the southernmost extent of the NAFB. The Holzkirchen 2 well targeted Upper Eocene sandstones and was proved dry due to insufficient production. Holzkirchen 2 intersected the entire Cenozoic section and reached total depth at the top of Turonian sediments (Upper Cretaceous). The well has experienced high gas influxes in sandstones of the so-called Baustein Beds (Lower Chattian) (middle plot in Fig. 4c), which correspond to pore pressure magnitudes in an EMW of c. 1.5 g cm⁻³ estimated from sonic velocity and electrical resistivity of underlying shales. Shale sonic velocity and electrical resistivity suggest a further increase in pore pressure in EMWs up to c. 2.0 g cm⁻³ in the Rupelian Bändermergel Subformation (Lower Oligocene), which corresponds to high gas shows of 100% at the base of the Rupelian section. In addition, similar amounts of total gas were recorded in adjacent wells and a gas kick in the same formation had to be controlled with similar mud weights in the nearby Holzkirchen Th1 geothermal well (Lackner et al. 2018; Dorsch et al. 2021), providing further evidence of very high overpressures in the area.

Example well 3 – Walchenberg 1 (on the right-hand side of Fig. 4 and shown in the eastern part of the west–east cross-section in Fig. 5c) – is a nearly vertical well located in the SE corner of the study area some 20 km from the Austrian border that completed at the top of the Upper Cretaceous in 1984. The well is located in an area that was previously described as exhibiting high (Drews et al. 2018) to very high (Müller et al. 1988; Shatyrbayeva et al. 2023) overpressure. The Walchenberg 1 well encountered various pore pressure-related drilling problems, including fluid influxes, kicks, stuck pipes and multiple fishing operations, all of which caused major delays in the drilling process. The aforementioned complexities were also reflected in the actual mud weights that were continuously adjusted to maintain well control (bottom plot in Fig. 4a). Pressure measurements within the Upper Chattian sands and above confirmed that pore pressure is hydrostatic above 2000 m. Shale pore pressure estimations from sonic velocities and electrical resistivities, and the constant increase of drilling mud weights, as well as rising total gas recordings, indicate that overpressure builds up quickly below depths of 3000 m. As in the Holzkirchen 2 well, the shale sonic velocity and electrical resistivity indicated that pore pressure magnitudes of up to 2.0 g cm⁻³ are possible in the Lower Rupelian section, which is in line with a kill mud weight to control a kick at the same depth.

In addition to the west–east well section, we also showed a north–south well section in the eastern part of the study area to demonstrate the southward overpressure development and employment of the northeastern, eastern and regional NCTs (Fig. 5). Again, three example wells were chosen (well locations are shown as stars in Fig. 5c).

All compaction trends suggest only minor or no sign of overpressure above a depth of 2000 m. Meanwhile, shale pore pressures estimated from sonic velocity and electrical resistivity indicate overpressure magnitudes in excess of 1.4 g cm⁻³ below depths of 2500 m; the highest pressure peaks being observed mainly in the Bändermergel shales of the Lower Rupelian formation (Fig. 5). Overpressure becomes particularly prominent in wells towards the central part where the eastern NCT has been applied. Overpressure keeps on increasing in the southern part clearly adjacent to the NATF. Similar to the Holzkirchen 2 and Walchenberg 1 wells (Fig. 4), the highest estimated pore pressures exceeded 2.0 g cm⁻³ in the Lower Rupelian formation in the area of Lake Chiemsee, which have also been confirmed by a good-quality DST (Fig. 5a).

Figures 6 and 7 compare the lateral distribution of pore pressure estimated from shale sonic velocity and electrical resistivity (compaction-based pore pressure estimation) for the overpressured units of Rupelian (Fig. 6) and Upper Cretaceous (Fig. 7) formations. The pore pressure distributions in Figures 6a, b and 7a, b were derived from quality-controlled pore pressure measurements and indicators (Shatyrbayeva et al. 2023). Figures 6c and 7c have been generated by taking the arithmetic average between the sonic velocity-based and the resistivity-based pore pressure estimations at each well location. Possible recording or digitizing errors in geophysical logs, discontinuous spikes in thin log intervals (c. 10 m) and consequent high peaks were excluded when picking the estimated pore pressures. Similar to Drews et al. (2018), an uncertainty span of ±0.15 g cm⁻³ should be considered. Compaction-based pore pressure estimations are, for the most part, in agreement with the distributions that originated from pressure measurements and MW_max integrated with wellbore instabilities and pore pressure-related problems (Shatyrbayeva et al. 2023).

In line with the drilling data-derived estimations from Shatyrbayeva et al. (2023) (Fig. 6a, b) and the predictions by Müller et al. (1988) and Drews et al. (2018), the compaction-based estimations for the Rupelian formation (Fig. 6c) suggest very high overpressure in the SE of the NAFB and bordering on the North Alpine Thrust Front towards the SW. Compaction-based pore pressure estimation anticipates that high overpressure remains present c. 20 km parallel to the North Alpine Thrust Front, while pressure measurements point to intermediate overpressures in the area. It should be stressed that compaction-based pore pressures are largely influenced by the high pressure peaks in the Bändermergel shales of the Rupelian formation, where estimated pore pressures occasionally exceed 2 g cm⁻³ in EMW representation. In contrast, well tests mostly represent the less overpressured Rupelian sands above the Bändermergel deposits, where a few kick pressures were collected in the SE and in the vicinity of the North Alpine Thrust Front. Mild to intermediate overpressure highlighted by MW_max, on the other hand, could largely reflect underbalanced drilling given the severe wellbore instabilities and high gas shows (Fig. 6b) that the wells experienced in the area (cf. Shatyrbayeva et al. 2023). Higher overpressures towards the central part of the NAFB as suggested by the compaction-based estimations are therefore not unlikely. The study by Shatyrbayeva et al. (2023) on the basis of drilling data has introduced an overpressure extent beyond the northern border, as suggested by Müller et al. (1988). Our current study also predicts that the area beyond the 1.2 g cm⁻³ EMW isoline of Müller et al. (1988) southeastwards of Munich is still subject to mild to minor overpressures (Fig. 6c), which corresponds to the overpressure extent suggested by Drews et al. (2018). Comparable to the previous studies on pore pressure magnitudes (Müller et al. 1988; Drews et al. 2018; Shatyrbayeva et al. 2023), no sign of overpressure was observed in the western and northernmost parts of the study area

Regarding the overpressure magnitudes in the Upper Cretaceous, the compaction-based pore pressure map generated using the geophysical logs of 77 wells indicated high to very high overpressures (Fig. 7c) in the area of Lake Chiemsee and towards the SE corner of the NAFB. A comparable scenario is also represented by the drilling data-derived maps that originated from pressure measurements (Fig. 7a) and indicators (Fig. 7b) (Shatyrbayeva et al. 2023), and which correspond to pore pressure isolines presumed by Müller et al. (1988) and Drews et al. (2018), especially in the southeasternmost part of the study area. Similar to the Rupelian formation, compaction-based pressure estimations were predominantly influenced by the overpressured shales at the top of the Upper Cretaceous sediments, whereas limited pressure measurements from DST tests were available from the normally pressured sandstone layers beneath the shales. This is particularly evident in the central part of the NAFB above the 1.4 g cm⁻³ EMW isoline of Müller et al. (1988) (Fig. 7a), where compaction-based pore pressure estimations suggest that intermediate to high overpressure remains possible. A MW_max-based pore pressure map coupled with high gas readings and wellbore instabilities (Fig. 7b) (cf. Shatyrbayeva et al. 2023) illustrates that overpressure extends southeastwards of Munich towards the Landshut–Neuötting High and beyond the overpressure limit of Müller et al. (1988) and roughly bordering on the 1.6 g cm⁻³ boundary of Drews et al. (2018). Likewise, the compaction-based estimations exhibit a likelihood of mild to intermediate overpressures in the area (Fig. 7c), which in turn suggests an underestimation and overestimation in overpressure magnitudes by Müller et al. (1988) and Drews et al. (2018), respectively. Compaction trends further introduce minor and mild overpressure to hydrostatic pressure SE and east of Munich.

In our study, the extent of overpressure in both Oligocene and Upper Cretaceous sediments was constrained by a much improved database, both in terms of actual data and the spatial extent, compared to the previous study by Drews et al. (2018). The expanded database indicates that the extent of overpressure in Oligocene strata appears to be dependent on the presence of Upper Cretaceous shales (compare the distribution of overpressured locations in Fig. 6c with shale compaction-derived pore pressure in Fig. 7c), which decrease in thickness due to erosion towards the north and west (Bachmann et al. 1987). Drews et al. (2018) also noted this dependency and concluded that shales of Late Cretaceous age act as a hydraulic barrier between Oligocene sediments and the subhydrostatically pressured Lower Cretaceous and Upper Jurassic carbonates. The improved spatial coverage presented in our present study supports this hypothesis: compared to the extent of overpressure in Oligocene strata, the extent of overpressure in Upper Cretaceous strata decreases according to its diminishing thickness towards the north and west. A lesser thickness is likely to promote faster dewatering into the underlying subhydrostatically pressured carbonates of Early Cretaceous and Late Jurassic age.

This paper developed drilling data-calibrated shale compaction trends based on all sources of available pore pressure measurements and indicators using sonic and electrical resistivity logs of 310 hydrocarbon and deep geothermal wells in the North Alpine Foreland Basin (NAFB) in SE Germany. The established compaction trends were applied to estimate shale pore pressure magnitudes and were compared to previous regional pore pressure studies to improve the understanding of the overpressure distribution in the basin. Our study shows that both sonic velocities and electrical resistivities of clay-rich units can be used to assess and estimate pore pressure and overpressure on a regional scale if calibrated to vertical effective stress estimates from pore pressure measurements and indicators. However, as a key finding and in contrast to previous studies, our results highlight that more than a single shale normal compaction trend is required to characterize the lateral distribution of overpressure: two additional trends are necessary to estimate pore pressure from sonic velocity and electrical resistivity at shallower depth intervals in the northeastern part of the NAFB in SE Germany. The apparent change in compaction behaviour of clay-rich sediments is most likely to reflect NE–SW-orientated gradual changes in the mineralogical composition of clay-rich sediments in the area. An increase in horizontal shortening and/or diagenesis, which might intensify compaction in addition to vertical loading towards the Alps, also offers a possible explanation but fails to explain why the effect is restricted to the widest and coolest part of the NAFB. Finally, our compaction-based pore pressure distributions are in good agreement with previously investigated drilling data-based pore pressure evaluations, and offer an additional tool for pre-drill pore pressure prediction in the study area.

We would like to thank particularly the Bavarian Environment Agency (LfU Bayern), Bavarian deep geothermal operators and the Geothermal-Alliance Bavaria (GAB) for providing the data used in this study. We want to express our gratitude to Johannes Großmann (LfU Bayern) and Hans-Jürgen Brauner (LBEG) for their valuable support during the data acquisition. We thank Gary Couples and two anonymous reviewers for their thorough reviews, which greatly helped to improve the quality and readability of the manuscript.

IS: conceptualization (lead), data curation (lead), formal analysis (lead), investigation (lead), methodology (equal), writing – original draft (lead), writing – review & editing (lead); FD: investigation (equal), methodology (supporting), writing – review & editing (equal); MCD: investigation (supporting), methodology (equal), project administration (lead), writing – review & editing (equal).

This work was funded by the Bavarian State Ministry of Science and the Arts in the framework of the ‘Geothermal-Alliance Bavaria (GAB)’, by the Bavarian Environment Agency (LfU Bayern) through the research project ‘KompakT’ and by the Bavarian Ministry of Economic Affairs, Regional Development and Energy within the research project ‘BoostGeotherm.Bayern’.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The data used in this study were provided by the Bavarian Environment Agency (LfU Bayern) through the research project ‘KompakT’ and by the Geothermal-Alliance Bavaria (GAB), and are available from the authors upon request and with permission of the LfU Bayern and the GAB.