Tectonic Stylolite Stress Inversion, Angle Correction, Validation Across Scales and Variability Within Outcrops

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, the authors test how reliable stylolite roughness inversion (SRIT) is for estimating tectonic stress. They focus on three main points: how stress tilt affects results, how scale influences crossover estimates, and how much results vary within a single outcrop. A modified version of the SRIT method is introduced, then tested through sensitivity analysis and applied to multi-scale stylolite measurements and multiple samples from one location. The results show that tilted stress fields can introduce noticeable errors (in some cases up to ~50%), that averaging measurements improves stability, and that single stylolite profiles are not reliable on their own for stress inversion. The study is solid, relevant, and useful for improving SRIT applications. I recommend minor revision.

Comments

Abstract

Clear and well written. Adding a couple of key numbers (like the tilt error range and main scale findings) would make it stronger.

Methods

The workflow is good and well thought out. The main issue is the long derivation of the new equation, which is hard to follow in places. It would read better if the detailed steps were moved to supplementary material and the main text focused on the key idea and assumptions. A bit more clarity on how vertical stress and orientation assumptions are handled would help.

Results

1. The tilt sensitivity results make sense and are clearly shown. Just make sure the extreme error values are linked to specific parameter conditions.
2. The scale analysis is one of the strongest parts of the paper. The conclusion about a minimum scale (~2.5 cm) works for this dataset, but it should not be generalized.
3. The outcrop comparison is useful, but the interpretation of stress clusters as separate tectonic phases is not strongly supported. It should be phrased more carefully.

Discussion

1. The angle correction argument is convincing, but it should be framed more conditionally, since its effect depends on tilt and anisotropy.
2. The tectonic interpretation of variability is interesting, but still speculative without independent structural evidence.

Recommendation

Minor revision -The study is strong and relevant, with good data and a clear methodological contribution. Only small improvements are needed in clarity, presentation, and how strongly some geological interpretations are stated.

Author Response

Dear reviewer 

we thank you very much for the comments that helped to improve the manuscript.

Reviewer comment 1: Abstract Clear and well written. Adding a couple of key numbers (like the tilt error range and main scale findings) would make it stronger. 

Author comment: Thank you we added two values: Our results show that the angle correction is needed for strongly tilted samples "(to reduce a potential error of up to 50%)", that one single stylolite inversion is not representative no matter what the scale, that the inversion accuracy decreases with scale but can be optimized with mean values "(down to a length of 20 x crossover length)" and that at least the orientation of stresses is very consistent within an outcrop.

Reviewer comment 2: The workflow is good and well thought out. The main issue is the long derivation of the new equation, which is hard to follow in places. It would read better if the detailed steps were moved to supplementary material and the main text focused on the key idea and assumptions. A bit more clarity on how vertical stress and orientation assumptions are handled would help. 

Author comment: Thank you we have moved most of the derivation to an appendix and have expanded the derivation so that it can be better followed (there was a small part missing). There is no vertical stress assumption necessary any, more the orientation is directly derived by the stress inversion. What is still needed is the depth. We added the following sentence at the end of the derivation of the formula.

"It should be noted that this derivation is not assuming a tilt angle, the tilt angle can be directly derived when the cross-overs are determined. However the value of the vertical stress is still needed (= depth)."

Reviewer comment 3:  Results

1. The tilt sensitivity results make sense and are clearly shown. Just make sure the extreme error values are linked to specific parameter conditions. Author reply: yes this is done
2. The scale analysis is one of the strongest parts of the paper. The conclusion about a minimum scale (~2.5 cm) works for this dataset, but it should not be generalized. Author reply: yes we have normalized this value relativ to the cross over length.
3. The outcrop comparison is useful, but the interpretation of stress clusters as separate tectonic phases is not strongly supported. It should be phrased more carefully. Author reply: yes we tried to do this  and added the following sentence:

   "Whether or not the two groups are geological relevant is debatable and is discussed further in the discussion section."

Reviewer comment 4: Discussion

1. The angle correction argument is convincing, but it should be framed more conditionally, since its effect depends on tilt and anisotropy. Author reply: yes this is done
2. The tectonic interpretation of variability is interesting, but still speculative without independent structural evidence. Author reply: yes there is one interesting point from stress inversion, we expanded the discussion  

   "Two distinct clusters of stresses can be derived: one cluster shows applied stresses of σ₁ ~ 30 MPa, σ₂ ~ 28 MPa and σ₃ ~ 23 MPa and a second cluster applied stresses of σ₁ ~ 70 MPa, σ₂ ~ 60 MPa and σ₃ ~ 10 MPa. Both are realistic stress fields but we cannot rule out that they are derived as a function of uncertainty in the data. The data shows tectonic stresses that were active during the Cretaceous inversion in central Europe in the footwall of the Eisfeld-Kulmbach reverse fault. Stress inversion data on fault slip surface [15] indicates that the stress field switched from compressional to strike slip during the inversion. This switch may be reflected in a) the consistent tilt angle of principal stresses within the stylolite plane and b) the two derived stress cluster. Stylolites record a time series and not a single event and can therefore contain overprinted stress fields. "

thank you again for the review

Reviewer 2 Report

Comments and Suggestions for Authors

This paper systematically explores three key issues in the Surface Roughness Inversion Technique (SRIT) method based on pressure solution suture lines: the correction of stress principal axis inclination, the impact of sample scale on inversion accuracy, and the representativeness of a single sample to the stress field at outcrop scale. The authors derived a correction formula considering the inclination of the stress ellipse and verified the importance of this correction formula under shallow burial depth and high anisotropy conditions through statistical analysis of a large number of samples and different scales. The study also reveals the limitations of a single suture line sample and proposes practical suggestions to improve the reliability of results through multi-segment averaging. The paper has a clear structure, detailed data, and strong methodological innovation, providing high reference value for the fields of structural geology and in-situ stress measurement. If further expanded in terms of the correlation between in-situ stress results and regional seismic potential, abnormal sample processing standards, and method applicability, it will have even broader influence. Overall, this is a solid, rigorous, and practically instructive research work.

1. The correlation between the results of in-situ stress measurements and the potential for induced earthquakes should be further discussed. In the paper, the maximum, intermediate, and minimum principal stresses (σ1, σ2, σ3) of multiple samples were calculated, and the stress ratio φ and the inclination angle of the stress ellipse were discussed. However, the relationship between these in-situ stress results and regional seismic activity or induced earthquake potential was not mentioned. It is suggested to add a discussion section: under the current stress state (e.g., σ1 is approximately 30–70 MPa, σ3 is approximately 10–23 MPa), is there a potential for fault slip? Can the Coulomb failure criterion or slip trend analysis be combined to assess the seismic risk in the region under natural or human disturbances (such as fluid injection)? This will significantly enhance the application value of the paper.
2. On pages 5-6, the author derives a corrected formula (Eq. 23) that takes into account the inclination of the stress principal axis. However, the derivation process of the formula seems somewhat abrupt, with some algebraic steps not being expanded (such as the transition from Eq. 14 to Eq. 15). It is recommended to provide a more detailed derivation process in the appendix, or provide numerical verification examples (such as comparisons with uncorrected results) to enhance the credibility and reproducibility of the formula.
3. When analyzing multiple samples (such as sample 11_6), the author points out that its cross-over length (L) and stress results significantly deviate from other samples, but does not specify whether these abnormal samples should be excluded or how they should be handled. It is recommended to propose a set of abnormal sample identification and handling standards based on statistics (such as IQR or Z-score) to improve the reliability and reproducibility of the results.
4. The author found that the cross-over length L varies between 1.2–1.5 mm across different sample lengths (1.5 cm to 30 cm), but its physical significance (such as whether it represents particle size, mineral distribution, or stress influence depth) was not discussed in depth. It is suggested to explain the reasons for L's variation in conjunction with the rock's microstructure (such as particle size, clay distribution), in order to enhance the physical interpretability of the results.
5. Although the author points out the influence of parameters such as depth, Young's modulus, and Poisson's ratio on the results, it is not clear under which geological conditions the SRIT method is not applicable (such as high strain rates, multi-stage pressure solution, dominance of inelastic deformation, etc.). It is suggested to add a discussion on "method limitations" to help readers determine whether this method is suitable for their research area.
6. The manuscript would benefit from citing a recent paper that address stress state characterization and induced seismicity in basement rocks: Zhang et al (2024). on fault reactivation mechanisms in Gonghe granite. This study provide important context for interpreting paleostress results in terms of contemporary fault stability and induced earthquake potential.

Author Response

Dear reviewer 

we thank you very much for the comments that helped to improve the manuscript.

Reviewer comment 1: The correlation between the results of in-situ stress measurements and the potential for induced earthquakes should be further discussed. In the paper, the maximum, intermediate, and minimum principal stresses (σ1, σ2, σ3) of multiple samples were calculated, and the stress ratio φ and the inclination angle of the stress ellipse were discussed. However, the relationship between these in-situ stress results and regional seismic activity or induced earthquake potential was not mentioned. It is suggested to add a discussion section: under the current stress state (e.g., σ1 is approximately 30–70 MPa, σ3 is approximately 10–23 MPa), is there a potential for fault slip? Can the Coulomb failure criterion or slip trend analysis be combined to assess the seismic risk in the region under natural or human disturbances (such as fluid injection)? This will significantly enhance the application value of the paper.

Author reply: thank you very much this is indeed interesting, however the current stress field is oriented prependicular to the paleo stress from the stylolites that we worked on. But we have added a discussion on how the stylolites could be reactivated by the current stress field: " The current stress field is oriented roughly perpendicular to the Cretaceous stylolites so that the main compressive stress is now oriented roughly parallel to the stylolite plane. Potentially that makes the Cretaceous stylolites prone to be reactivated as extensional cracks. This cannot be observed in the studied outcrop but in some other localities in Northern Bavaria. Theoretically if the main compressive stress is oriented at an angle to the plane of the Cretaceous stylolites they could also be activated as faults or shear surface (Zhang et al. 2024) but since they are very rough surfaces this is probably not the case. "

Reviewer comment 2: On pages 5-6, the author derives a corrected formula (Eq. 23) that takes into account the inclination of the stress principal axis. However, the derivation process of the formula seems somewhat abrupt, with some algebraic steps not being expanded (such as the transition from Eq. 14 to Eq. 15). It is recommended to provide a more detailed derivation process in the appendix, or provide numerical verification examples (such as comparisons with uncorrected results) to enhance the credibility and reproducibility of the formula.

Author reply: thank you very much indeed there was a small part missing. We only discuss the beginning and end of the derivation in the methods now and add a detailed derivation in an appendix.  Please see annotated file for the changes

Reviewer comment 3: When analyzing multiple samples (such as sample 11_6), the author points out that its cross-over length (L) and stress results significantly deviate from other samples, but does not specify whether these abnormal samples should be excluded or how they should be handled. It is recommended to propose a set of abnormal sample identification and handling standards based on statistics (such as IQR or Z-score) to improve the reliability and reproducibility of the results.

Author reply: thank you very much. This was mentioned:  In the following section only values falling in the IQR of the corresponding box plot diagrams are described. However it is complicated and needs a compilation of larger data sets in order to come to an advanced handling technique which is beyond the scope of this contribution.

Reviewer comment 4: The author found that the cross-over length L varies between 1.2–1.5 mm across different sample lengths (1.5 cm to 30 cm), but its physical significance (such as whether it represents particle size, mineral distribution, or stress influence depth) was not discussed in depth. It is suggested to explain the reasons for L's variation in conjunction with the rock's microstructure (such as particle size, clay distribution), in order to enhance the physical interpretability of the results.

Author reply: thank you very much but this is speculative plus we did take samples from the same layer. We think it has to do with the signal processing but this needs further research. 

Reviewer comment 5: Although the author points out the influence of parameters such as depth, Young's modulus, and Poisson's ratio on the results, it is not clear under which geological conditions the SRIT method is not applicable (such as high strain rates, multi-stage pressure solution, dominance of inelastic deformation, etc.). It is suggested to add a discussion on "method limitations" to help readers determine whether this method is suitable for their research area.

Author reply: thank you very much but his is discussed already in the manuscript. For clarity we added this to the discussion: "and is only valid for stresses stored by pressure solution"

Reviewer comment 6: The manuscript would benefit from citing a recent paper that address stress state characterization and induced seismicity in basement rocks: Zhang et al (2024). on fault reactivation mechanisms in Gonghe granite. This study provide important context for interpreting paleostress results in terms of contemporary fault stability and induced earthquake potential. 

Author reply: thank you very much we added this discussion see above.

Reviewer 3 Report

Comments and Suggestions for Authors

4257347 Köhler & Koehn

 

The authors present a well written study on tectonic stylolites and stress inversions derived from them. The manuscript is well organized and contains new data. The language is clear and grammatically sound. The figures could be improved by putting more emphasis on the nature of stylolites (photographs, drawings) and by increasing the font in the line diagrams.

 

The manuscript is heavily oriented toward methodology and statistical treatmement. Although the latter is required it makes the text difficult to read. The reader is introduced into the nomenclature in a concise and clear introduction. Later one has to go back to this introduction to grasp what is said in the discussion section.

The manuscript is submitted to a special issue which addresses new methodologies. Nevertheless, personally I would have liked to see a case study applied to a regional study to show the use of the methodology and not only the methodology by itself.

Author Response

Dear reviewer 

we thank you very much for the comments that helped to improve the manuscript.

Reviewer comment 1: The authors present a well written study on tectonic stylolites and stress inversions derived from them. The manuscript is well organized and contains new data. The language is clear and grammatically sound. The figures could be improved by putting more emphasis on the nature of stylolites (photographs, drawings) and by increasing the font in the line diagrams. 

Authors reply: We thank you very much for the comment. We only studied one set of stylolites on purpose in order to test the SRIT method. We show the stylolites and also the determined signals in detail. Sure this makes the paper technical but that was the purpose. With respect to small fonds in figures we tried to optimise this.

Reviewer comment 2: The manuscript is heavily oriented toward methodology and statistical treatment. Although the latter is required it makes the text difficult to read. The reader is introduced into the nomenclature in a concise and clear introduction. Later one has to go back to this introduction to grasp what is said in the discussion section.

Authors reply: yes thank you for this comment. We tried to optimise the discussion.

sentence added to discussion 4.1 "Stress inversion of vertically oriented tectonic stylolites normally implies that one of the main principal stresses is vertical."

Reviewer comment 3: The manuscript is submitted to a special issue which addresses new methodologies. Nevertheless, personally I would have liked to see a case study applied to a regional study to show the use of the methodology and not only the methodology by itself.

Authors reply: yes thank you for this comment. This is a case study for one inversion event we tried to make this clearer. 

changed heading 4.3 by adding "and implication for regional geology" and the following text: "

Two distinct clusters of stresses can be derived: one cluster shows applied stresses of σ₁ ~ 30 MPa, σ₂ ~ 28 MPa and σ₃ ~ 23 MPa and a second cluster applied stresses of σ₁ ~ 70 MPa, σ₂ ~ 60 MPa and σ₃ ~ 10 MPa. Both are realistic stress fields but we cannot rule out that they are derived as a function of uncertainty in the data. The data shows tectonic stresses that were active during the Cretaceous inversion in central Europe in the footwall of the Eisfeld-Kulmbach reverse fault. Stress inversion data on fault slip surface [15] indicates that the stress field switched from compressional to strike slip during the inversion. This switch may be reflected in a) the consistent tilt angle of principal stresses within the stylolite plane and b) the two derived stress cluster. Stylolites record a time series and not a single event and can therefore contain overprinted stress fields.

The current stress field is oriented roughly perpendicular to the Cretaceous stylolites so that the main compressive stress is now oriented roughly parallel to the stylolite plane. Potentially that makes the Cretaceous stylolites prone to be reactivated as extensional cracks. This cannot be observed in the studied outcrop but in some other localities in Northern Bavaria. Theoretically if the main compressive stress is oriented at an angle to the plane of the Cretaceous stylolites they could also be activated as faults or shear surface (Zhang et al. 2024) but since they are very rough surfaces this is probably not the case.

"

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors did good revisions. I therefore recommmend publishing this work.

Author Response

thank you for the positive review 

we added more references and improved the english locally 

Author Response File: Author Response.docx