A significant aspect of reservoir characterization in carbonates is the fact that it is much more complicated than in sandstones. Carbonates are more complex due to diagenetic overprints, karstification, fracturing and the formation of reef buildups (Fig. 14a–k). Thus, the carbonate rocks are typically heterogeneous regarding porosity and permeability distribution (Ehrenberg and Nadeau 2005; Lucia 2007; Ghafoori et al. 2009). In the following section the diagenetic processes that have influenced carbonate reservoir porosity in the greater Munich area will be examined, the porosity distribution trends and the reservoir quality will be discussed and the methodological approach will be inspected.
Diagenetic processes
The most important diagenetic processes affecting the porosity in carbonates are cementation, compaction, dolomitization, and dissolution (Ghafoori et al. 2009). Cementation is a main reason for porosity reduction in carbonates. With increasing burial depths and temperatures the solubility of CaCO\(_{3}\) declines, leading to the precipitation of, e.g., calcite that can clog or seal both primary and secondary porosity. This can be observed in outcrop analogues from the Franconian Alb, where the Jurassic carbonates crop out (Fig. 14g) and has been proven by laboratory investigations of rock probes from the Jurassic carbonates (Wolfgramm et al. 2011; Homuth 2014). Another porosity reducing process is compaction due to increasing burial depths. For depths of around 2 km, limestone and dolomitic limestone are presumed to be more porous than dolomites, and at greater depths dolomites are more porous and permeable than limestones according to a study carried out in Florida (Schmoker and Halley 1982). In the Munich area, the reservoir is located deeper than 2 km depth, but the highest porosities are still found in the dolomitic limestone and the dolomites show the lowest porosities (Fig. 13). This shows that no generalized statement about the porosity–depth relationship with regard to the different lithology types can be made for our study area. During dolomitization calcite is replaced by dolomite leading to a reduction of the rock volume and, therefore, an increase of the total porosity by creating secondary porosity (Sajed and Glover 2020). Furthermore, early dolomitization can preserve primary porosity by creating a stable framework which hampers compaction (Lucia 2007). This often results in a more heterogeneous distribution of petrophysical properties (Ehrenberg and Nadeau 2005; Ehrenberg 2006) and it can lead to a redistribution of the pore space, e.g., in the Leduc reef carbonates in Alberta (Mountjoy and Marquez 1997). The percolation of unsaturated water can lead to the dissolution of calcite or aragonite, and the formation of secondary porosity and even large cavities, sinkholes and sagging structures (Kendall and Schlager 1981; Xu et al. 2017), as it is observed in the Franconian Alb (Fig. 14f–i) and in the Malm carbonates of the Munich area. This is the most important process that increases reservoir potential. Due to these many and complex processes affecting the porosity of carbonate rocks, the final porosity may not be related to the original depositional environment at all.
With respect to the German Molasse Basin and the associated carbonate platforms, the petrophysical and hydraulic properties of the Malm aquifer are very heterogeneous due to the variability of depositional and diagenetic features, karstification, fractures, and faults (Koch 2000; Mraz 2019; Bohnsack et al. 2020). In our study area, these features led to the formation of a dual porosity reservoir mainly affected by karst and fractures (Fig. 14). Both are important controlling factors of the reservoir quality and they also have an influence on permeability which varies according to, e.g., fracture type, -intensity, -orientation and -distribution, and karstification intensity (Konrad et al. 2019; Bohnsack et al. 2020; Sajed and Glover 2020). For example, the fracture orientation in relation to the maximum horizontal stress field (SHmax) may have an influence on whether the fractures are open or closed (Cacace et al. 2013). The strong variability of porosity and permeability, due the irregular distribution of karstified and fractured zones, pose a problem for geothermal reservoir characterization, e.g., prediction of hydraulically active zones.
Porosity distribution
In general porosity of carbonates can vary from almost 0% in tightly cemented rocks to about 35% in unconsolidated sediments (Lucia 2007). Log analysis from Moosburg and Dingolfing in the GMB revealed porosity ranges of 1.0 to 24.0% for the Malm (Bohnsack et al. 2020); a similar range of 0.0 to 20.0% is also observed in our study area in Munich (Fig. 13). At Moosburg and Dingolfing high porosities correlate with karstified zones, vuggy layers or bioturbation based on image log interpretations. In addition, gamma ray logs show very heterogeneous deposits in the upper part of the reservoir and more uniform sediments in the lower part based on a study by Bohnsack et al. (2020). Furthermore, they showed that the Upper Jurassic formation can be subdivided into the three porosity units, Malm \(\zeta\) (0.3 to 19.2% – median 4.8%), Malm \(\epsilon\)–\(\delta\) (0.5 to 12.2% – median 2.9%), and Malm \(\gamma\)–\(\alpha\) (0.3 to 3.5% – median 1.7%) (Bohnsack et al. 2020). This porosity distribution corresponds with the results of this study in which the lowest porosity values are found in the lower most part of the Malm carbonates. Therefore, we interpret it as a zone of poor potential for geothermal exploitation due to unsuitable porosity conditions. In the middle depth range, the carbonates below Munich have mostly low porosities except for zones affected by, e.g., dolomitization (as observed in the SLS boreholes), karstification (visible in the SLS boreholes and the GRAME 3D seismic) and reef buildups (identified by the seismic inversion), thus improving hydraulic connectivity. The highest porosity values are located in the upper part of the carbonate succession, which is consistent with the results of Böhm (2012) and Böhm et al. (2013).
The spatial variability of porosity in the Munich area results from the heterogeneity of the lithology types, the different diagenetic processes described above, and varying karstification intensity. The spatial porosity distribution seems to follow a trend as observed in the inversion results with higher porosities and more intense karstification to the north of Munich compared to the south (Fig. 15). This is indicated by the presence of numerous sinkholes identified in the reflection seismic data and by circular structures with low impedance and, therefore, high porosity as indicated by the inversion results. The low impedance values within the sinkholes are supported by the modelling results from Sell et al. (2019) for the GRAME area, who showed that seismic velocities decrease in the sinkhole center compared to the surrounding or overlying material. Furthermore, we show that the sinkholes form local clusters within the footwall of the Munich Fault and along the faults. Carbonate dissolution can also occur along bedding planes, without forming sinkholes, which can lead to increased secondary porosities that can stretch across large areas. The dissolution within the massive facies and along bedding planes in the bedded facies can form disrupted and vuggy layers which are observable as discontinuous reflectors and/or undulating reflectors in the 3D seismic. In these areas the top of the carbonate reservoir formation is often characterized by low seismic amplitudes, because the leaching of the carbonates significantly reduces the original high impedance contrast with the overlying rocks. Furthermore, the generation of many small-scale features such as cavities created by dissolution or fractures induced by local stress redistribution due to collapsing cavities, can lead to increased scattering of the seismic waves which results in a loss of reflected energy and, therefore, reduced seismic amplitudes. The more intense karstification of massive, but also bedded carbonate facies north of Munich and the resulting higher transmissivity was also observed by Birner et al. (2012), who investigated the hydraulic parameters of the Upper Jurassic aquifer with respect to it’s potential for geothermal exploitation. We assume the reason for the intense karstification to the north are the more widespread higher (secondary) porosities combined with a higher permeability due to fractures and a better connected porosity. The higher permeability allowed intensified circulation of unsaturated waters which dissolved large rock volumes, removed the dissolved material and formed new secondary pore space and cavities. Over time new fractures can form in the surrounding areas of cavities due to collaps and local stress redistribution. These fractures can serve as additional fluid pathways for unsaturated water leading to self-reinforced carbonate dissolution. The typically strong fracturing around faults and, therefore, often enhanced permeability is also the presumed reason for the accumulation of sinkholes along the Munich- and the Ottobrunn Fault. Similar observations for enhanced dissolution of soluble rocks close to faults were made by Abelson et al. (2003); Closson and Abou Karaki (2009); Wadas et al. (2017) and Wadas et al. (2018).
Besides karst structures, we also identified carbonate reef buildups in our study area, which are associated with massive facies, e.g., microbial–sponge buildups, and they often pass laterally into the surrounding bedded facies (Słonka and Krzywiec 2020). They are favoured targets for reservoir exploitation, but commonly they are very complex regarding the distribution of petrophysical parameters and facies. Often the reef core is described as a good exploitation target, but this is not always the case as demonstrated by Słonka and Krzywiec (2020) and this study. We show that the reef caps and reef slopes have increased porosities with around 7 to 14% and the reef cores have low porosities of mostly < 3%. We assume that this is the result of intense karstification and gravitational mass flows on the slopes. The reef slopes show a characteristic interfingering of the reef facies with the surrounding strata, in the form of rounded pine tree shaped edges, which indicates a syn-sedimentary reef development with slightly varying build up growth rates. The same was observed by Słonka and Krzywiec (2020) for the Miechów Trough in Poland using well data and 2D seismic lines. Buildups can appear as either continuous elongate bodies oriented parallel to the shelf edge or isolated structures, where the reef geometries are affected by sea level changes and the accommodation space produced by regional subsidence (Moore 2001). In the Munich area, it seems that the reefs are roughly oriented parallel to the former passive Tethys margin and, therefore, the Franconian Alb striking W–E to SW–NE at this location. Furthermore, the reefs seem to be larger and better pronounced south of Munich compared to the north (Fig. 15). However, this interpretation mirrors only the results for the GRAME 3D seismic area and on a larger scale there might not necessarily be a preferred orientation of the reef structures. This preferential reef orientation can only be proven by analysing other 3D seismic data sets of the GMB. In addition to the typical large-scale (\(\sim\) > 1 km diameter) buildups we also identified small notch-like reefs on top of a larger complex, which we interpreted as pinnacle reefs. Pinnacles are formed by so called frame builders, while normal reef build ups consist of accumulated lime silt, mud, sponges, algae and crinoids. In the case of a very fast rising sea level, pinnacles can be formed locally in areas, where the carbonate production can keep pace. Both pinnacle reefs and reef buildups are formed on local highs due to the presence of karst topography or other surface irregularities, and seaward build ups contain more porous grainstones (grain-supported carbonate rocks that contain less than 1% mud-grade material) than shelfward buildups. Cementation is also greater seaward causing a decrease in porosity (Moore 2001). The Munich area was located in a shallow marine environment with probably less porous grainstones and less cementation, but still displays a complex porosity distribution throughout the carbonate reservoir.
Reservoir quality
In general, the cut-off porosity for most carbonate reservoirs is 3%, compared to 8% for sandstones (e.g., Tiab and Donaldson 2015; Mehrabi et al. 2019). Based on this assumption and the observed porosity ranges, we define porosity evaluation levels for estimation of reservoir quality as follows: 0 to 3% are negligible, 3 to 6% is poor reservoir quality, 6 to 9% is moderate, 9 to 12% is defined as a good reservoir, and > 12% is a very good reservoir quality. As described above, the porosity values show a strong difference between the upper part and the lower part of the carbonate reservoir. Therefore, we subdivided the Malm reservoir into three units similar to Bohnsack et al. (2020), based on the sequence stratigraphic interpretation for the geothermal site SLS by Wolpert et al. (2020), and created average porosity maps for each unit to define areas with high and low reservoir quality (Fig. 16). Note that the values at the far edge of the model are influenced by edge effects during modelling and should be neglected. For the first unit, Berriasian to Malm \(\zeta\)4, almost all areas have a moderate to good reservoir quality, especially the northern and northeastern parts of the footwall of the Munich Fault and the southwestern part of the hanging wall due to increased secondary porosity as a result of intensified karstification as shown by several large sinkholes, sinkhole clusters and widespread dissolution along bedding planes. Further areas with good reservoir quality are found on the intermediate block of the Munich Fault and along the deformation zones of the Munich Fault and the Ottobrunn Fault. For the second unit, Malm \(\zeta\)3 to Malm \(\zeta\)1, the only large areas with moderate reservoir quality are found on the footwall block, except for the most western area, and on the hanging wall block west of the Munich Fault. The east of the hanging wall and the area around the Ottobrunn Fault show a mixture between poor and moderate quality. A larger area with negligible reservoir porosity is located in the central part of the hanging wall, where larger reef buildups with low porosities in the reef core are situated. For the third unit, Malm \(\epsilon\) to Malm \(\alpha\), the entire study area has a negligible to poor reservoir quality, except for some smaller zones in the northeast of the footwall block, and along the Munich Fault with moderate quality.
It has to be noted that this reservoir quality estimation is just based on a porosity evaluation and no permeability values are included. Normally, rock (matrix) permeability is linked to (primary) porosity, for example in sandstones (Albrecht and Reitenbach 2014; Al Saadi et al. 2017; Ganat 2020). However, in our study, area primary porosity is of minor importance and secondary porosity, as described above, is the controlling porosity factor. In addition, regarding permeability, other studies carried out in the GMB, using, e.g., laboratory analysis, hydraulic tests in wells, and numerical modelling, have shown that especially fracture permeability and to a certain part also karst permeability can have a more dominant influence on the hydraulic properties of the reservoir compared to matrix permeability resulting in a mainly fracture- and karst-controlled reservoir (Ehrenberg and Nadeau 2005; Birner et al. 2012; Cacace et al. 2013; Homuth et al. 2015; Moeck et al. 2020; Balcewicz et al. 2021; Bauer et al. 2021). As a result, no general trends describing the porosity–permeability relationship based on stratigraphic units or lithology can be established. This circumstance has already been described for the Molasse Basin, e.g., by Homuth (2014); Bohnsack et al. (2020) and Moeck et al. (2020). Therefore, we cannot directly convert the porosity model into a permeability model and so far, no seismic method exists that is able to derive permeability values from seismic amplitudes or seismic inversion (Pride et al. 2003). However, the improved identification of karst areas and reefs through the inversion can help to determine zones that might have higher permeability.
Methodical approach
We have shown the applicability of stochastic seismic amplitude inversion and demonstrated its benefits for porosity estimation and characterization of a carbonate reservoir in the GMB. Nevertheless, there are some things to consider regarding the used workflow and the chosen inversion method, from which recommendations for future inversion studies in the GMB can be derived.
The first element that has a big influence on the later inversion result and which partly also influences the choice of the inversion method is the available input data. The 3D seismic data set should always be examined in terms of data quality, especially with regard to the signal-to-noise ratio, the frequency spectrum and the recovery of the true amplitudes. In most cases some preconditioning of the seismic data must be performed to meet these requirements (Veeken and Da Silva 2004). For the GRAME data set most of these objectives have already been taken into account by the contractor during data processing by application of, e.g., filtering, surface-wave noise attenuation and amplitude corrections, such as surface consistent amplitude correction, spherical divergence correction, and predictive deconvolution (Scholze and Wolf 2016a, b). Therefore, the post-stack data set used already had a good data quality for the inversion, except for the frequency spectrum which should be as broadband as possible, but which normally drops off sharply towards the higher frequencies (Zeng 2012). We have partially compensated for this by application of spectral balancing, also called spectral whitening. However, this should only be used with great caution as it can also amplify the high frequency noise, so the results should be checked with spectral analysis and visual inspection before and after whitening like it was done for the GRAME data set. The correct application of frequency spectrum enhancement also leads to an improvement in resolution (Zeng 2012). Other seismic preconditioning methods that might give good results for a different data set could be, e.g., frequency-wavenumber filtering and radon transform or Tau-P processing (Veeken and Da Silva 2004). If an inversion should be carried out, e.g., for other already existing 3D data sets in the GMB, e.g., for Unterhaching or Geretsried, it should be noted that reprocessing may be necessary, to meet the above mentioned requirements.
Another important input data is logging data from wells, in case of availability. Ideally, the number of available wells should correspond to the heterogeneity of the reservoir. Therefore, the more heterogeneous the reservoir, the more boreholes should be implemented into the inversion, to ensure that all possible lithologies and facies types are represented in the well logs (Pendrel 2001). With regard to the carbonate reservoir of the GRAME area, for example, one or two wells might not be sufficient enough to obtain a representative image of the heterogeneously distributed carbonate types as it can be observed in Fig. 5, e.g., Th5 contains mostly dolomitic limestone, Th2a contains mostly dolomite, and Th6 contains mostly limestone. Therefore, implementation of all six available wells and the corresponding well logs delivered a more comprehensive overview of the reservoir. Nonetheless, it should be kept in mind that the wells cover only a limited area of the study site.
Important logs, e.g., for the generation of synthetic seismic traces for the seismic-well tie and the implementation of frequencies outside the seismic bandwidth into the inversion should be measured directly in all wells if possible. At the ‘Schäftlarnstraße’ geothermal site sonic logs were measured in all six wells for the reservoir section, but in the upper part, sonic logs were only measured in some sections, which is why measurements from several ‘Schäftlarnstraße’ wells had to be combined to create a continuous log that is required for the seismic-well tie. In the filled up sonic log sections, there will most likely be some uncertainties that will affect the correlation of the reflectors from the seismic data and the reflectors in the synthetic traces. For example, the neighbouring wells might not have drilled the same lithologies in the same depths and the resulting discrepancies can, therefore, influence the quality of the seismic-well tie in these zones. However, this is not the case in the reservoir section, which is our target formation, because direct sonic measurements are available for the reservoir section in all six wells. The direct sonic measurements enable an accurate well-seismic tie for the reservoir formation. The combination of sonic logs and density logs is used to create the synthetic seismic traces on which the seismic-well tie is based and the impedance logs that are used as broadband input parameters for the starting model of the inversion. In our study, like in many others, unfortunately, no density logs were measured, which is why they were determined from the sonic logs based on the Gardner equation, which can lead to uncertainties. For future geothermal drilling projects in the GMB, we recommend that the boreholes are fully surveyed, not only with sonic logs, but also with, e.g., density measurements, if possible.
Reliable high-quality sonic log data is also crucial for the creation of the starting or trend model which enables the calculation of a broad-band impedance model through the inversion process. The stochastic impedance volume derives its lateral resolution from the seismic data, and its vertical resolution from the sonic log data. Therefore, a typical stochastic inversion delivers a vertical resolution of approximately 1 to 2 m (Robinson 2001). In our study the vertical resolution of the impedance model is around 6 m. This limitation is due to the height of the model grid cells that we have specified. In principle, we could have further refined the cell height by implementing even more pseudo-layers. However, this would have resulted in the model consisting of even more grid cells, which would have significantly increased the computing time. The same goes for the number of calculated model realizations. The more realizations are calculated and then combined into an averaged model, the better the model fits to the real geological conditions. In other words, the problem of non-uniqueness is reduced. In our study we calculated 100 realizations of the impedance model and from these 100 models, an averaged model was calculated, which was than used for the interpretation of the acoustic impedance. However, each additional realization also increases the calculation time. To at least reduce this problem, we would, therefore, recommend using larger computing clusters for performing such inversion processes.
There is a also a general trade-off between the quality of the inversion results and the chosen inversion method and the invested time and costs for data acquisition and analysis. In this study, we have shown that full-stack stochastic seismic inversion delivers good results, but newer inversion methods using, e.g., partial stack seismic data offer an even more sophisticated reservoir characterization. Some examples are AVO inversion, simultaneous inversion or time-lapse inversion (Pendrel 2001; Veeken and Da Silva 2004; Filippova et al. 2011; Maleki et al. 2019). In case of amplitude variations with offset (AVO) the inversion should not be performed on fully stacked data. Instead during data processing the traces reflected at a common midpoint should be gathered and sorted by offset, which is related to the incidence angle. For example, the far-offset, the mid-offset, and the near-offset traces can be used to create three different data sets of which each can be inverted separately (Veeken and Da Silva 2004; Barclay et al. 2008). Since seismic amplitude variations with offset contain not only information on the P-impedance, but also on S-impedance and density, AVO inversion delivers more elastic properties describing the reservoir than classical full-stack inversion which delivers only one property. The AVO inversion of the different partial stacks can also be carried out simultaneously, which also enables time-lapse inversion if there are several seismic data sets of the same area measured at different times. This allows to quantify changes in elastic properties due to, e.g., hydrocarbon production (Oldenziel 2003; Barclay et al. 2008; Maleki et al. 2019).
Converting the resulting impedance model into a porosity model strongly relies on a parameter relationship between AI and porosity, which is mostly derived from logging data. Ideally, directly measured porosity logs should be used for this, but if these are not available like in our study, a derived porosity log can be obtained from the sonic logs using Archie’s law and the Wyllie time-average equation. However, this procedure can lead to uncertainties in the porosity values. In our study, the derived porosity logs are consistent with results from laboratory analyses of sidewall cores taken from the wells Th4 and Th2 (Pfrang 2020). Thus, verifying the results of the calculated porosity logs. A crossplot of the AI logs and the porosity logs from the six wells was generated and it showed a clear relationship from which a linear function could be derived similar to other studies, e.g., Pendrel and Van Riel (1997); Dohlberg et al. (2000); Zeng (2012). By incorporating the data of all six wells we were able to better represent the heterogeneity of the reservoir in terms of, e.g., lithology and facies distribution, and thus porosity distribution, because even from one well to another the drilled lithologies vary significantly in our study area. If a function would have been used just based on, e.g., Th5 the results would have delivered an AI/porosity relationship that fits for dolomitic limestone, but this function would not have sufficiently taken into account the other carbonate lithology types occurring in the study area, which would have led to inaccuracies. As a consequence, when estimating an AI/porosity relationship in such a heterogeneous reservoir as many data as possible should be incorporated to take all the different lithology and facies types into account to get reliable results. The good representation of the AI/porosity relationship by the linear function is also reflected in the correlation coefficient of 0.75. Based on the linear function, in which low AI correlates with high porosity and high AI with low porosity, the AI volume was converted into a porosity volume to describe the geothermal potential of the reservoir. The calculated porosity model using the linear function was then compared along the drilling paths of the six wells with the corresponding porosity logs to investigate the amount of uncertainty. The comparison shows that the inversion results match the porosity logs by ± 1% of porosity. Therefore, if we show that the highest porosity in the reefs is 14%, then it could actually also be 13% or 15% because of the uncertainty. This uncertainty is quite small and has, therefore, no significant influence on the classification of the porosity-related reservoir quality, which confirmed our approach.
Taking all this into account, we suggest for future geothermal exploration projects that the possibility of a later inversion should be taken into account when processing the seismic data (preconditioning of the data set). In addition, care should be taken to ensure that well logging data sets are as complete as possible. Then, as a first approach, a stochastic full-stack inversion should be carried out and if this shows promising results, an extended simultaneous AVO inversion can be carried out if necessary. The additionally determined elastic properties, such as the shear impedance and the V\(_{P}\)/V\(_{S}\) ratio could also be used, e.g., in geomechanical modelling and simulations of possible seismicity.