We would like to thank the reviewer for their careful evaluation of the manuscript and for the constructive comments provided. In the following text, we present a draft on how we propose to address the comments of the reviewer individually in the revised manuscript.

Answer to Comment 1:

In our geomechanical numerical models, the initial stress state is established by applying gravitational loading (producing the vertical stress, S_v) together with the lateral boundary conditions representing the regional tectonic stresses (producing additional horizontal stresses, S_Hmax and S_hmin). In the initial conditions, we do not make any assumption that S_v is the maximum principal stress (S₁). Instead, the three principal stresses (S₁, S₂, S₃) develop naturally from the applied loading and the lateral boundary conditions.

To further clarify, we provide a plot (attached below) showing the depth profiles of the S₁, S₂, S₃ together with Sᵥ along the Trüllikon borehole. The left panel displays the magnitudes of S₁, S₂, S₃ and Sᵥ as a function of depth, showing that Sᵥ is not always identical to the S₁. Sᵥ more closely corresponds to one of the principal stresses depending on the local stress regime, plotted as Regime Stress Ratio in the right panel [Simpson, 1997]. While not clearly visible in the plot, there is a very minute difference in between the magnitudes of the principal stresses and the vertical stress. We did not originally include vertical stress curves in Figure 5 because the differences between the model scenarios were small and only noticeable in the shallowest ~100 m. However, we agree that including them will improve clarity, and we will add the vertical stress profiles to the revised figure. We also clarify that all stresses presented in the manuscript refer to total stresses, as pore pressure effects were not considered in this study. We will state this explicitly in the revised manuscript.

Answer to Comment 2: 

The Mesozoic sedimentary units in the Northern Switzerland can be regarded as tectonically stable with low strain rates and are mechanically intact. This makes linear elastic constitutive relationship an appropriate first-order approximation for modeling the present-day stress state. Several geological factors, specific to the region and the siting area, support this assumption:

• No significant tectonic deformation since Miocene with extremely low strain rates of ~1-3 m/Myr/Km,
• Lack of active faulting at repository depths and no evidence of any quaternary faults’ reactivation, and
• The differential stresses; S1-S3 of the units range between 0.5 MPa and 13 MPa), far below their measured uniaxial compressive strength limits (33-180 MPa) [Nagra, 2024]. Therefore, the units are far below their peak strength so they are safely within an elastic domain.

Due to these reasons, plastic yielding or damage is not expected under current stresses. Since the primary objective in this paper was to assess the far-field, first-order effects of fault-related stress perturbations at a safe distance (> one km) from faults, the assumption of linear elasticity is appropriate. We briefly mentioned about these region-specific details in the Section 5.4: ‘Limitations of the study’s results and future outlook’. However, the reviewer is correct that we could have explained this better and explicitly, and we will address this in the modified draft.

Answer to Comment 3: 

We agree that horizontal (depth) slices would offer a complementary perspective on the lateral spatial variability of the stress magnitudes and orientation. Therefore, we will include atleast one or two Figures from each model realization containing horizontal depth slices along the target storage zone, and a stiffer and mechanically contrasting unit above or below it.

While enlarging the regions near the faults from Figures 6–9 is technically possible, we found that such close-up views do not result in providing additional interpretive value to the reader. As discussed in Section 4.2: “2D results along a cross-section”, the high localized stress concentrations adjacent to the faults are primarily numerical artefacts arising from element resolution limitations in particular near the fault tips. To show this, we provide a zoomed example of the area between Rheinau and D2 faults (below figure) from the top inset of Figure 7, originally showing Δ (S_Hmax-S_hmin) between the REF-NF and REF model. The enlarged view does not reveal information beyond what is already visible in the full image. For this reason, we propose to retain the original cross-section figures while adding the additional horizontal slices.

Answer to Comment 4: 

The Neuhausen Fault is the only known active fault in our study area and is a tertiary-origin fault. In our numerical models, minor amounts of slip in the order of a few 10s of cm occur on this fault after the application of the lateral displacement boundary conditions (shortening of 4.1 m in the N–S direction and 0.82 m in the E–W direction to achieve the best-fit w.r.t. the stress magnitude data). This slip produces shear stress decrease along the fault that is small compared to the much larger background in situ stresses and the differential stress S1-S3. We will add a brief discussion to clarify that minor slip occurs but does not influence the overall stress field analysis.

Answer to Comment 5: 

For low strain intraplate regions, we think that our findings are general and independent of the stress regime, but we cannot prove this with our model as it resembles a specific geological setting. Nevertheless, the differential stress S1-S3 is generally increasing with depth in the upper brittle crust (regardless of the stress regime) whereas the slip on the intraplate faults does not. Assuming that the slip-rate and thus, the stress changes along the faults are in the same order for different faulting styles, their impact on the in-situ stress is local and confined to the near-field of the fault. We will add our interpretation to the discussion in more detail.

In the end, we would like to thank the reviewer once again, as well as all others involved in the discussion phase, for taking the time to provide their valuable comments and suggestions. We are sincerely grateful.

References:

Simpson, R. W.: Quantifying Anderson's fault types, Journal of Geophysical Research: Solid Earth, 102, 17909-17919, https://doi.org/10.1029/97JB01274, 1997.

Nagra: In-Situ Stress Field in the Siting Regions Jura Ost, Nördlich Lägern and Zürich Nordost, NAGRA, Wettingen, Switzerland, NAGRA Arbeitbericht NAB 24-19, 131 pp., 2024.

Citation of our article: 

 Velagala, L. S. A. R., Heidbach, O., Ziegler, M., Reiter, K., Rajabi, M., Henk, A., Giger, S. B., and Hergert, T.: Spatial Influence of Fault-Related Stress Perturbations in Northern Switzerland, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2025-4559, 2025. 

We would like to thank the reviewer for his careful evaluation of the manuscript and for the scientific comments provided. In the following text, we describe how we propose to address the comments of the reviewer individually in the revised manuscript.

Comment 1: First of all, I would moderate the “universality” of the results of the study. For example, stress and structural data gathered in the vicinity of the San Andreas fault (Zoback et al., 1987) demonstrate that stress perturbations can be far more significant than what is advanced in the present Ms. The latter conclusion from Zoback et al. (1987) finds support in e.g. the paleostress reconstructions of Homberg et al. (1997), which evidence stress rotations of up to 20° near the Morez Fault Zone in the French Jura, the numerical modelling of Pascal and Gabrielsen (2001), later on benchmarked by the in-situ stress measurements of Roberts and Myrvang (2004), and the field observations and geomechanical modelling of Maerten et al. (2016). In brief, the results advanced in the present Ms are representative of the modelled area and cannot be safely extrapolated to other regions.

Answer 1: We agree with the reviewer that the results of our study apply in the strict sense only to Northern Switzerland and probably to similar geological settings in Foreland Basins. We will strengthen this perspective in Section 5.4 (Limitations of the study’s results and future outlook), where we already addressed this point to some extent. We will rephrase the text accordingly in our revised manuscript to avoid any implication of universality. Before doing so, however, we would like to clarify how the results of our work relate to the studies cited in the comment, as this helps to contextualize the significance of our findings within the broader literature.

We acknowledge the significance of the studies cited by the reviewer and will integrate these in the discussion section of our manuscript. However, the fault systems discussed in these studies i.e the Morez Fault Zone (Homberg et al., 1997), the Møre-Trøndelag Fault Complex (Pascal and Gabrielsen, 2001; Roberts and Myrvang, 2004), and the San Andreas Fault (Zoback et al., 1987) differ significantly from the Alpine Foreland Basin in terms of their governing tectonic processes and fault/fault-system structure complexity. In particular, the San Andreas Fault is a major plate boundary structure, while the Møre-Trøndelag Fault Complex is a complex and large crustal fault system in crystalline rock. Both show 100s of meters to kilometers of relative displacement whereas the maximum observed fault displacement in our model is less than 50 meters.

Furthermore, the applied friction coefficients of μ = 0 in the DEM model of Pascal and Gabrielsen (2001) to reproduce the ‘shield effect’ of the Møre-Trøndelag Fault Complex, and the friction values of μ < 0.2 derived for the San Andreas fault from heat flow measurements and numerical models (D'alessio et al., 2006), are not comparable with those in the Northern Switzerland (Kastrup, 2002). Also, the low differential stresses reported in Pascal and Gabrielsen (2001), which facilitates larger and large-scale rotations of S_Hmax due to local and regional stress perturbations (Ziegler et al., 2017), are not observed in the Zürich Nordost region.

In summary, the studies cited by the reviewer address settings at plate-boundary and major crustal fault systems characterized by high-strain, low-friction faults, and low differential stresses. Our work is in intraplate setting in the Alpine Foreland Basin and focuses on the impact of relatively small faults on an otherwise undisturbed rock volume, which are based on the 3D seismic interpretations from the region. We will strengthen the manuscript wording to reflect this, as suggested by the reviewer.

Comment 2: The origin of the data used to calibrate the models and summarised in Table 1 is enigmatic. Please add the apparently missing references and explain briefly how these data were obtained. Also, important information is missing in the text about the model set-up (e.g. dimensions, type of elements used to mesh the models).

Answer 2: We will add the missing reference for the dataset summarized in Table 1. While we had stated the general procedure used to measure the datasets in the manuscript, we agree that the readers would benefit from a brief description of the procedures used to obtain these datasets and the model set-up, and will add this information in the revised manuscript. We will edit Section 2.2 to make this information more readily visible to the readers.

Comment 3: The modelling considers faults as contacts, whereas natural faults are complex zones of deformation, where rock rheology can be drastically different from that of the “intact” host rock and, thus, fault zones may promote pronounced stress perturbations. A thorough discussion on the latter is crucially missing in the paper. Also, the models do not involve fault tips, whereas it is well-known that they host the most dramatic stress perturbations (e.g. Homberg et al. 1997). Once again, the latter point should be addressed in the discussion section.

Answer 3: We agree that simplifying the faults to a contact surface in our models does not capture the real nature and complexity of faults on the 1-10 m scale. This is acknowledged in the original manuscript in Section 5.3 (Dependence of the modeling results on fault implementation) and Section 5.4 (Limitations of the study). However, we justify our approach in the following and will add these arguments in the model set-up section.

Given that our models have lateral dimensions of 14.7 × 14.8 km² the width of the fault core with a few 10s of meters is small compared to our model dimensions and the numerical resolution. Thus, we cannot resolve the internal fault structures. Furthermore, the semi-generic study of Reiter et al. (2024), which uses a model of similar dimension, assumptions, data and geometrical setting shows that different technical implementations of faults do not have an impact on the modelled stress tensor components in the far-field, i.e. at distances larger than a few hundred meters. This is also supported by other works (Caine et al., 1996; Treffeisen and Henk, 2020) and was briefly mentioned in our Section 5.3 (Dependence of the modeling results on fault implementation). However, we agree that this information must be better expressed in our manuscript, and we will do this in our revised manuscript.

Regarding the work of Homberg et al. (1997) and Nicol et al. (2020), we acknowledge their findings that there are large stress rotation at fault tips, but they note that these rotations are localized and rarely extends beyond a few hundred meters from the fault tip, which is in general agreement with our work. Furthermore, we also have fault tips in our model where the contact surfaces end within the Mesozoic sediments (and they actually show stress concentrations as well as larger stress rotations at the tips). However, an analysis of the stress state at the actual physical fault tips of these faults falls outside the scope of our study and would need a much higher numerical resolution around the fault tips. To give a more complete picture about the fault tips stresses, we will expand the text in the revised manuscript.

Other major and minor comments:

Regarding use of suggested terminology

L24: “Coulomb friction”. The term does not apply to contact surfaces as Coulomb friction (i.e. internal friction) is a property of the continuous medium that controls rupture (i.e. creation of shear fracture not sliding along a pre-existing one). I recommend to use “Byerlee friction” or “Amontons friction”.

Answer: We thank the reviewer for the careful attention to the used terminology. However, we respectfully disagree with the statement that the term ‘Coulomb friction’ does not apply to contact surfaces. Coulomb’s law of friction describes the frictional resistance between two dry solid surfaces, where the frictional force is proportional to the normal force and independent of the apparent contact area (described by Amontons-Coulomb law). In fault mechanics, this directly applied to frictional sliding along pre-existing discontinuities.

It is true that in the Mohr–Coulomb constitutive framework, the friction coefficient is combined with a cohesion term to describe the strength of intact material, described as continuous by the reviewer. However, the same is also commonly used to describe the damaged or frictional sliding regime, in which the friction coefficient represents resistance to sliding along contact surfaces rather than internal friction of an intact medium. This usage is standard in rock mechanics. By contrast, Byerlee friction refers to an empirical relationship derived from the laboratory experiments on intact rock samples. Therefore, it represents a specific observed constraint on the friction coefficients for certain lithologies and at certain conditions, rather than a general definition of the frictional behavior. As the result, very low friction coefficients cannot be justified by the Byerlee’s law alone. The term Coulomb friction has also been used to describe sliding along a pre-existing fracture by Zoback (2007) and Jaeger et al. (2007).

To avoid this confusion and to improve clarity for the readers, we will refer to μ as contact surfaces with a coefficient of friction, without using the term ‘Coulomb’, in the abstract and throughout the revised manuscript, as we will cite Zoback (2007) to explain the reasoning behind the proposed referencing of μ.

L194: “flexures”. The term “flexure” is traditionally used to indicate a mechanical process and not a geological structure. Please explain what do you mean by “flexure” (fold hinge? Drape fold?). Also, it is unclear to me how the “flexures” impact the stress field (e.g. if they are open folds I do not expect much of it). Please, justify their inclusion into the model.

Answer: The Marthalen-Rafz Flexur and Wildensbuch Flexur are monoclines (Nagra, 2024). These Flexures dominate the overlying Mesozoic strata in the siting area by a step-like bending rather than a discrete break in otherwise gently dipping strata. During the interpretation of 3D Seismic sections, several hundred fault patches were identified and for the model combined to seven individual faults and implemented as contact surfaces. Although, except for the Neuhausen fault which shows a distinctive displacement, the other faults do not show a measurable displacement in the footwall and the hanging wall, they are included in the model because they represent first-order geological structures (discontinuities in the otherwise reasonably continuous lithology) observed within the siting region. They also help in quantifying the maximum possible stress perturbations that such observed structures could impose on the far-field stress state (Seen in Fig. 10). We will add brief clarifying information about these distinctions in the revised manuscript.

(L340): “stiffness”. The word “stiffness” has a precise meaning in continuum mechanics and involves typical dimensions of the object under consideration. Obviously, the term is erroneously used in the Ms. I presume that one has to read “Young’s modulus” instead. Please correct.

Answer: The term stiffness contrast has been used in multiple earlier works by different authors to describe the contrast of the Young’s modulus from one lithology to another. We would prefer to stay with this wording given that earlier publications and models of similar setting use the same terminology. However, we will introduce this choice in the beginning of the revised manuscript that stiffness contrast is similar to Young’s modulus contrast.

Regarding providing additional clarification

(Section 3.1):Model discretization Strategies”. Please, explain briefly in introduction the rationale of the modelling and why different models are tested. As it is now, the text is rather confusing and does not allow the reader to grasp right away the adopted modelling strategy and its goals.

Answer: We agree that the text can be a little confusing to the readers. We would make the sentence clearer. While we had already mentioned in the manuscript that different models were tested with different element property assignment strategies to see if a simpler and faster python-based method would still provide the same results as the reference model, we will make this information better accessible in the revised manuscript.

(Section 5.2): Impact of varying fault friction coefficient of the implemented faults”. This section reads like a presentation of some of the results and not like a discussion. Please consider moving it to section 4.

Answer: In the section 5.2 ‘Impact of varying fault coefficient of the implemented faults’, we artificially lower the friction coefficient of the Reference model upto 0.2. This was not a part of the results section as we had to tweak the realistic parameters to extremely low values to explore the effect of friction coefficient on the predicted far-field stress state. Therefore, we propose that the subsection is better placed in the Discussion section than the Results section.

(L518): “possible values of friction coefficient in Switzerland”. Is there a particular reason to believe that physics operate otherwise in Switzerland compared to the rest of the universe? I presume that friction coefficients are there similar to the ones measured elsewhere on the planet. Please, rephrase.

Answer: We agree and will change the text accordingly.

(Fig 4):please add scale.

Answer: This conceptual figure is well served and scale-independent. It represents a visual comparison of the two strategies used in our work for model discretization and mechanical property assignment to the geomechanical units, and the scale is immaterial for the comparison.

(Table 2): what is the reason for (slightly) changing boundary conditions from one model to the other?

Answer: The slight changes in the values of the boundary conditions between the different model realizations are explained by the Reference model having contact surfaces. The contact surfaces allow dissipation of elastic energy by means of displacement which is not possible in the fault agnostic models. It is important to note that each model used in our study are calibrated to the same dataset to get the best fit. We will explain this in the revised manuscript.

Other minor comments

We will address all the other minor comments in the revised draft as they pertain to use of English grammar and including additional references. For this, we will make use of a scientifically accepted tool ‘Grammarly’ to assist us with making grammatical changes in the revised manuscript.

References:

Caine, J. S., Evans, J. P., and Forster, C. B.: Fault zone architecture and permeability structure, Geology, 24, 1025–1028, https://doi.org/10.1130/0091-7613(1996)024%3C1025:FZAAPS%3E2.3.CO;2, 1996.

d'Alessio, M. A., Williams, C. F., and Bürgmann, R.: Frictional strength heterogeneity and surface heat flow: Implications for the strength of the creeping San Andreas fault, Journal of Geophysical Research: Solid Earth, 111, https://doi.org/10.1029/2005JB003780, 2006.

Homberg, C., Hu, J. C., Angelier, J., Bergerat, F., and Lacombe, O.: Characterization of stress perturbations near major fault zones: insights from 2-D distinct-element numerical modelling and field studies (Jura mountains), Journal of Structural Geology, 19, 703–718, https://doi.org/10.1016/S0191-8141(96)00104-6, 1997.

Jaeger, J. C., Cook, N. G. W., and Zimmerman, R. W.: Fundamentals of Rock Mechanics, 4, Blackwell Publishing, 2007.

Kastrup, U.: Seismotectonics and Stress Field Variations in Switzerland, Dissertation, Swiss Federal Institute of Technology Zurich (ETH Zurich), Zurich, 162 pp., https://doi.org/10.3929/ethz-a-004423062, 2002.

Maerten, L., Maerten, F., Lejri, M., and Gillespie, P.: Geomechanical paleostress inversion using fracture data, Journal of Structural Geology, 89, 197–213, https://doi.org/10.1016/j.jsg.2016.06.007, 2016.

Nagra: Geosynthesis of Northern Switzerland, NAGRA, Wettingen, Switzerland, NAGRA Technischer Bericht NTB 24-17, 604 pp., 2024.

Nicol, A., Walsh, J., Childs, C., and Manzocchi, T.: Chapter 6 - The growth of faults, in: Understanding Faults, edited by: Tanner, D., and Brandes, C., Elsevier, 221–255, https://doi.org/10.1016/B978-0-12-815985-9.00006-0, 2020.

Pascal, C. and Gabrielsen, R. H.: Numerical modeling of Cenozoic stress patterns in the mid-Norwegian margin and the northern North Sea, Tectonics, 20, 585–599, https://doi.org/10.1029/2001TC900007, 2001.

Reiter, K., O. Heidbach, and M. O. Ziegler (2024), Impact of faults on the remote stress state, Solid Earth, 15(2), 305–327, doi:10.5194/se-15-305-2024.

Roberts, D. and Myrvang, A.: Contemporary stress orientation features and horizontal stress in bedrock, Trøndelag, central Norway, NGU Bull., 442, 53–63, 2004.

Treffeisen, T. and Henk, A.: Representation of faults in reservoir-scale geomechanical finite element models – A comparison of different modelling approaches, Journal of Structural Geology, 131, 103931, https://doi.org/10.1016/j.jsg.2019.103931, 2020.

Ziegler, M. O., O. Heidbach, A. Zang, P. Martínez-Garzón, and M. Bohnhoff (2017), Estimation of the differential stress from the stress rotation angle in low permeable rock, Geophysical Research Letters, 44(13), 6761–6770, doi:10.1002/2017GL073598.Zoback, M. D.: Reservoir Geomechanics, Cambridge University Press, Cambridge, https://doi.org/10.1017/CBO9780511586477, 2007.

Zoback, M. D., Zoback, M. L., Mount, V. S., Suppe, J., Eaton, J. P., Healy, J. H., Oppenheimer, D., Reasenberg, P., Jones, L., Raleigh, C. B., Wong, I. G., Scotti, O., and Wentworth, C.: New Evidence on the State of Stress of the San Andreas Fault System, Science, 238, 1105–1111, https://doi.org/10.1126/science.238.4830.1105, 1987.