The paper investigates, through numerical modelling, a range of parameters associated with faults that exert an influence on stress magnitude and tensor orientation. The discussion of the problem, methodology, and presentation of the results are good, and reasonable.  

We are taken through a series of experiments that depart from a reference model  (variable coefficient of friction, 10 thin layer, 3 weak elements; 30 m of 9 weak, elastic elements; staircase elements with elasto-plastic rheology;  4 staircase elements with elasto-plastic rheology; influence of fault dip angle on stress components; effect of strike angle on stress magnitude; Youngs modulus on stress perturbation; fault size; variable strain on stress components). 

This provides important information about the stress variations associated with changing a range of parameters around a single fault and provides support for conclusions from previous studies.  They conclude that stress magnitudes and stress tensor orientation is not significantly affected beyond distances in of c. 1,000-1,500 m (check line 408, I assume that the . should actually be a ,). Up to this point I would accept the manuscript as it stands. It is well written, the illustrations are sufficient, and the referencing is appropriate. 

It is the second half of the conclusions regarding fault controls on regional stress tensor rotation where I question whether the data in the study really supports such a strong conclusion. 

There is very little in the experiments that addresses stress tensor rotation. I maybe wrong, but I get the impression that it is assumed that variations in stress magnitude are proxies for stress tensor orientation (i.e. stress tensors will only deviate from regional in the narrow region where stress magnitudes are perturbed). There are no figures provided that show how the principal stress orientation are perturbed in the model by varying the fault strike and dip values. Figure 16, which is the only figure that address changing the strike angle of a fault, only plots variations in stress magnitude, it does not address orientation of the stress tensor. Consequently, I question why over half of the text in the conclusions focuses on stress tensor rotations, when none of the modelling data presented in the text directly addresses this topic. It is an important conclusion to address, since it affects our understanding of continental and basin-scale stress variations.

The experiments described in the paper focus on the effect of a single fault on stress variations. To take the results of this experiment and  conclude that stress tensor rotations are not controlled by faults, but by rock properties seems a great jump. I have chosen an area in the attached figure (Kenya Rift) with an admittedly high density of faults to make the point, that you have to consider the effects of a fault population, not a single fault, if you are going to discuss basins. In the image these are quite large faults because they are visible on satellite data, the yellow line is 30 km long, and 30 faults intersect that line. Hence the fault spacing is 1 km. Hence, since this study has concluded that near field stresses are significant around 1000-1500 m from a fault, then such fault spacing should significantly influence the stress tensor orientation. The problem with trying to address faulting is that the issue is not just an individual fault core and its damage zone. Faults tend to come in large populations of fractures.  A large fault (kms displacement) maybe accompanied zones of secondary faults (10’s-100’s m displacement) that are present in zones kilometers away from the main faults (just one example are the areas of conjugate faulting that can be >5 km wide, that  develop in the hangingwalls of major listric faults, and are located several kilometers into the hangingwall). We haven’t even got into what fault-related joints might do to rock properties. Consequently, I would contend that a basin with its highly variable distributions of faults, at a variety of scales is a very different proposition, in terms of its potential effects on the stress tensor, to the single fault investigated in this study, and as a result the second conclusion needs to be reconsidered. 

Chris Morley

Review for Solid Earth

Title: Impact of faults on the remote stress state.

Authors: Karsten Reiter, Oliver Heidbach, and Moritz. O. Ziegler

General comments

The paper uses a numerical modelling approach to investigate the changes in stress magnitudes due to fault movement. The tested models include a cohesionless fault with various element resolutions, fault frictions, fault inclinations, strike directions, rock stiffnesses, and fault sizes, focusing on the far-field perturbation. Then, after presenting the results highlighting the effects of the different parameters, the authors discuss the model simplifications, parameterization and the impacts of other potential controls. I think this manuscript's topic is relevant to the journal, with the paper providing important general insights into stress perturbation broadening to various applications such as geothermal systems, CCS or geological disposal. The modelling design, methodology and parameters seem appropriate. The paper is well-written, but I found the structures a bit repetitive, and there are many figures. Also, I have a few main comments below and suggest publication after moderate/major revisions.

Specific comments:

Far-field vs. near-field: This paper focuses on the far-field stress perturbations due to faults instead of the near-field. I think such far-field is defined as a distance beyond 100 m from the fault (l.67) and is supposed to be in the intact host rock, away from the fault core and the damage zone, according to Fig. 1. Broadly, this dimension of the damage zone seems correct for a 10 km fault, but I will suggest nevertheless the authors provide some information on fault scaling supporting their chosen geometry (e.g. Childs et al., 2009, Torabi et al., 2011). Such a definition is also scale-dependent, and the far-field for a minor fault may not be the same as for a major fault. Maybe the authors could discuss their view on such a topic as well.

Faulting regime: The boundary conditions correspond to a horizontal shortening perpendicular to the fault's strike and extension parallel to the fault. However, according to Fig. 4, such boundary conditions result in a complex stress regime, with a thrust fault regime down to 660 m, strike-slip down to  2 km, and normal faulting below that. According to the authors, this stress state generally agrees with Northern Switzerland's. Then, the observation well for the results intersects the fault at 660 m, which is the level at which the stress regime changes from thrust to strike-slip. Therefore, it seems the result involves a rather singular transverse isotropic stress state (SV = Shmin). I will suggest that the authors explain how this impacts the results to broaden the scope of the manuscript to other stress regimes.

Reference model and faulting regime: The reference geometry consists of a 60◦ dipping fault, which looks like a normal fault. But the normal stress regime only occurs down 2 km depth according to Fig. 4. So I think the authors should explain the rationale for using a reactivated normal fault as a reference rather than a more traditional normal fault in extension or a thrust fault in compression, for example. Maybe this is related to the context in Northern Switzerland, but I think this is worth discussing.

Stress rotation: The authors investigate primarily the variation and SV, SH and Sh magnitudes, assuming those are the principal stresses. However, this is only the case if there is no rotation of the vertical stress. By contrast, if there is vertical rotation, this should induce modifications in the magnitude of SV, Sh and Sh, while the von Mises criteria should remain the same. Maybe the existence or absence of such rotations is worth discussing.

Critical stress and failure: Some models test fault friction and fault dip. However, I am unsure if this case's boundary conditions are modified. If they are not, the stress state applied to the fault may change and not always be at the same level relative to a critical state of stress. It can even be greater than a critical stress state, which may be unrealistic. Maybe the authors should discuss the importance of this in their results.

Planar geometry: The tested faults are planar in the models over 10 km long and 3 km deep. By contrast, faults are often complex, with bends and steps (Roche et al., 2023). Although such complexities may affect the near-field more than far-field stress, I suggest the authors discuss this point further in section 4.6, as geometry may ultimately be the main controlling factor.

Figures and structures: The paper has many figures (i.e. 25) and many sections. I will suggest the authors try to group some figures and results less repetitively.

Technical corrections:

• 21-27: Stress perturbations are also important for assessing secondary fracturing near faults and associated permeability, including joint direction, secondary faulting and bed-parallel slip (e.g. Maerten et al., 2002; Kattenhorn et al., 2000; Delogkos et al., 2022).
• 1: I think the modelling by Maerten et al., 2002 about stress perturbation is worth adding.
• 50: Photoelastic modelling has also been used to study the effects of faults on stress (de Joussineau, Soliva et al., 2010).
• 49: "Geomechnanical"
• 126: "1.000" Maybe use 1000 to avoid confusion.
• 132: "This shows," remove coma.
• 160: "decreas"
• 236: I will be curious to know the model's results with different Young's modulus on the HW and FW.
• See also Roche et al. (2013) for the effect of fault aspect ratio on stress perturbation.

I hope this helps to improve the manuscript.

Vincent Roche

References

Childs, C., Manzocchi, T., Walsh, J. J., Bonson, C. G., Nicol, A., & Schöpfer, M. P. (2009). A geometric model of fault zone and fault rock thickness variations. Journal of Structural Geology, 31(2), 117-127.

Delogkos, Efstratios, Vincent Roche, and John J. Walsh. "Bed-parallel slip associated with normal fault systems." Earth-Science Reviews 230 (2022): 104044.

de Joussineau, G., Petit, J. P., & Gauthier, B. D. (2003). Photoelastic and numerical investigation of stress distributions around fault models under biaxial compressive loading conditions. Tectonophysics, 363(1-2), 19-43.

Kattenhorn, S. A., Aydin, A., & Pollard, D. D. (2000). Joints at high angles to normal fault strike: an explanation using 3-D numerical models of fault-perturbed stress fields. Journal of structural Geology, 22(1), 1-23.

Maerten, L., Gillespie, P., & Pollard, D. D. (2002). Effects of local stress perturbation on secondary fault development. Journal of Structural Geology, 24(1), 145-153.

Roche, V., Homberg, C., & Rocher, M. (2013). Fault nucleation, restriction, and aspect ratio in layered sections: Quantification of the strength and stiffness roles using numerical modeling. Journal of Geophysical Research: Solid Earth, 118(8), 4446-4460.

Roche, V., Camanni, G., Childs, C., Manzocchi, T., Walsh, J., Conneally, J., ... & Delogkos, E. (2021). Variability in the three-dimensional geometry of segmented normal fault surfaces. Earth-Science Reviews, 216, 103523.

Soliva, R., Maerten, F., Petit, J. P., & Auzias, V. (2010). Field evidences for the role of static friction on fracture orientation in extensional relays along strike-slip faults: comparison with photoelasticity and 3-D numerical modeling. Journal of Structural Geology, 32(11), 1721-1731.

Torabi, A., & Berg, S. S. (2011). Scaling of fault attributes: A review. Marine and petroleum geology, 28(8), 1444-1460.