the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Apr 2024
The effect of stiffness contrasts at faults on stress orientation
Abstract. Even though the crustal stress state is primarily driven by gravitational volume forces and plate tectonics, interpretations of borehole breakout observations show occasionally abrupt rotations of horizontal stress orientation of up to 90° when faults are crossed. This indicates the influence of faults on the local stress state, which parameter control the degree of rotation. Herein, we investigate the phenomenon of principal stress rotation at a fault by means of a 2D generic numerical model. We parametrised the fault as a rock stiffness contrast and investigate systematically the full model parameter space in terms of the ratio of the applied principal stresses, the rock stiffness contrast, as well as the angle between fault strike and orientation of the principal stress axis. General findings are that the stress rotation is negatively correlated with the ratio of principal stresses. A small angle between the far field stress orientation and the fault facilitates stress rotation. A high contrast in rock stiffness further increases the stress rotation angle. Faults striking perpendicular to the maximum principal stress orientation experience no rotation at all. However, faults oriented parallel to the maximum principal stress orientation experience either no rotation or a 90° rotation, dependent on the ratio of principal stresses and the rock stiffness contrast. A comparison with observations from various boreholes worldwide shows that in general, the findings are well in agreement, even though the dip angle proves to have an influence on the stress rotation, in particular for shallow dipping faults.
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RC1: 'Comment on egusphere-2024-1109', Anonymous Referee #1, 01 May 2024
Review
The effect of stiffness contrasts at faults on stress orientation
Ziegler et al.
submitted to Solid Earth
General comments and recommendation
This is a useful contribution that expands on the present knowledge about the influence of mechanical inhomogeneities (faults and fractures) on stress magnitude and orientation in homogeneous rock. It is well suited for publication in Solid Earth.
The manuscript still has some serious shortcomings in its present form:
- The Results chapter lacks a proper introduction that explains the problem focused upon and which strategy is selected to solve those. This chapter and its affiliated figures seem to me to be not to utilized to its full potential (see comments below) and gives a slightly whimsical impression.
- I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated (it should harmonized with the introduction to the Results-chapter). This list of scientific items should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and sometimes also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned. My recommendation will be that the Discussion-chapter is completely re-written. It seems that the observations given in Results and Discussion/evaluation-chapters have not been consequently systematized in all cases.
- I think some figures (Figures 2 and 3) should be redrafted to display some more details clearly. If I understand correctly that the outer part of the zonation is an artifact (see comment Lines 127-130) the color code should be modified: Artifacts should not have a color code in the fiure). I also suggst that other figures (particularly 4 and 5) are described and discussed more coherently in the text. The figure cations should also be more focused on explaining the meaasge to he reader.
- The English language needs some more attention. It is sometimes a little clumsy and some phrasings and sometimes ambiguous or unclear. It is therefore recommended that the authors approach a colleague (who is familiar with this field of research) with English as his/her first language to assist in linguistic matters.
It is concluded that this article deserves publication in Solid Earth after rewriting of the description and discussion, reworking of a couple of figures and affiliated figure captions and improvement of the English language in general.
Specific comments
Title
I suggest that the authors adjust the title of the paper slightly, perhaps something like:
“The influence of rock stiffness contrast on stress configuration along and within faults”.
Abstract
Generally, I find the abstract to be a little “soft”. The initial sentence has the flare of a general introduction and should be condensed. I suggest that the abstract separate clearly between 1) the definition of the problem investigated in this study, 2) specification of which methods were and 3) sharpen even more the conclusions of this work and that all three items are expanded upon, more completely to cover the intention of the paper and its important findings.
Line 1: I think “body forces” are better than “gravitational volume forces”. Perhaps “contemporary stress” and associated concepts as defined by e.g. Engelder (1983) is preferrable (Engelder,T.,1993: Stress Regimes in the Lithosphere. Princeton University Press, 467pp.)
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Line 4: This is fine and is where the important information really starts: “We investigate….”
Lines 2-3: “when faults are crossed …..”. Suggestion: “along or in the vicinity of faults ….. control the amount of principal stress axes.”
Line 7: “General findings….” You mean findings in the present work. Please clarify.
Introduction
Line 15: parameter in the stability assessment
Line 16: “exploitation” rather than “usage”? Add safety assessment?
Line 17: Most frequently? You mean: “Information about SHmax is most easily obtained from…”?
Lines 19-24: You mean far-field stress, locally imposed by stress imposed by local……. like topography. Perhaps an advanced textbook (e.g. Engelder 1983) with a summary of such stress systems should be referred to and nomenclature and definitions adapted to that source (see also above).
e.g. Lines 23-28 and generally: The authors have a tendency to over-use adverbs in beginnings of phrases: “Furthermore, it has……”, “However, Reiter ….”, “Nevertheless, on a meters scale….”. These examples are taken from sentences that follow each other.
Line 29: “across the world” is a surplice phrase: (Where else?)
Line 33: Borehole breakouts: Again, I think it would be convenient to refer to an advanced textbook – Again, I think Engelder (1983) can be used.
Line 47: Perhaps this section should start with reference to empiric data/observations: Examples are given in lines 58-60, so I suggest that this is moved here.
Lines 43-49: Not well phrased. Please separate int two statements and clarify.
Line 50: Rather: “This raises questions as to which parameters determine….”
Lines52-53: Rephrase. Suggestion: (if this is what the authors mean to say. If I misread this, a full rephrasing is necessary). “The potential for stress rotation and the magnitude for such rotation are assumed to be determined by…. , the contrast in rock stiffness between ….. and the angle between SHmax and the fault strike”.
Lines 61-74: I think this is well phrased. Please include a short version of this in the abstract.
Line 76: I do see the rationale in the application of a plain strain situation in a strike-slip regime. Most faults will be influenced by shear whatever the overall tectonic regime. Perhaps this generic situation should be explained (to the unprepared reader), and perhaps the term shear” (rather than-strike slip) should be applied (for the same reason).
Line 77: Why SHmax and Shmin: Misprint or some hidden significance? Either correct or explain.
Line 84: Isn’t the term tria-elements commonly written with capital T?
Line 85: In the order of about 75,00 elements?? Either 75,000 elements were used or not? Or did the model define the grid itself? If so, based on what? Whatever: “In the order of about” is a superfluous double description.
Lines 90ff: Why not Ehost and Efault to bring it in harmony with e.g. SHmax
Line 93: “Non-existence of a fault”: Why not “intact rock”? When I walk in a street, the street may be empty, which is congruent with “filled with non-existent cars”. But we don’t say that.
Line 94ff: In my opinion care should be taken so that the conclusions gave a consequent grammatical time sence in distinguishing between what was observed in the experiments and what is generally valid for such systems. In other words: We tested the influence…., scenarios were analysed…. .
Results
This important section of the paper comes on a little abruptly. Perhaps a short introduction that describes the dynamics of the experiments should serve as an introduction to this section. Particularly, the reader should be reminded which relations and which hypoteses are subject to investigation, and informed about the strategy selected to attack the problem (which parameters are at stake, which are kept constant and which are varied). Some of the general statements on the experiments given in the previous section and also spread out in the following description could perhaps be moved here.
At this stage he authors should reveal to the reader also their strategy for illustration of the observations and the analyses, which is revealed in Figures 3, 4 and 5: In oher words, The relation between figures 3 - 5 showing the stress configuration within the faults should be highlighted from the start in this section.
I think the use of tables 1 and 2 should be utilized more actively in the descriptive part. Now a very summaric summary is given in the text: “A more comprehensive comparison is shown in Table 2” (line 113).
Some crucial information seems to be lacking: Are the situations illustrated in Figure 3 initial or advanced stress configurations? In other words: did the configuration change with time or did it become stabilised?
The general observaton should be stated and highlighted in the closing part of this section: Now the summary of the key observations are a little bit spread out and the (important) observatios are presented rather summarily.
General: See comment to line 94ff above.
Line 98: Please rephrase: this sentence is complex to the extent that is messsage is obscured. Start with the subject “The orientation of ……”, refer immediately to Figure 3, and use Figure 2 more actively.
Line 98 -101: Again, why not sxx, syy etc, since s and xx describe different qualities, namely principal stress and vector components?
Line 103: Please expand the text somewhat to help the reader a bit here, e.g. “….. an angle (g) of 15o between the strike of the fault and the far field stress (S1) a moderate stiffness contrast (RE)…”.
Line 104: Take out “There,”
Lines 103-105: I think that the potential of Figure 3 is not fully exploited here, and the reader should be informed to read Figure 3 in concert with Figures 4 and 5. And why is only Figure 3a referred to in the text, completely neglecting b-f?
Furthermore, Figure 3 is rather nitty-gritty and it is mpossible to read all the details. (Particularly 3b is unclearly displayed). I understand that the displayed zonation (e.g.yellow-red-magneta) in e.g. is an artifact (lines 126-130). If so, the color symbols are misleading and the “artifical” color zones should be removed from the figure display and rather commented upon in the figure caption.
Lines 105-108: I think this information should be given in the very inroduction to the Results-section on a general basis and combined with a description of the strategy for the prsentation of the results (see general comments to the Results-chapter above).
Line 108: You mean: “S1-S2 remains constant”. Please state clearly whether this implies absolute stress magnitude, or the difference only?
Line 115: Rather: “Thus, greater RE promotes less stress rotation”
Line 123: Moved to introductory remarks in this chapter?
Line 127-130: This is a strange phrasing and rather confusing.You mean: “The data on stress orientation at the material borders show here are not valid, because…..the apparent stress rotation result from interpolation of what?...... please rephrase/explain” Also the following sentence (“At material contrasts….”) needs to be rewritten e.g.: “At the borders between bodies with different material properties ….”.
I understand that the apparent zonation (displayed in Figures 3a, b,c,d) are artifacts. This is technical information that should be kept isolated form the valid observations done in the interpretation of the data (perhaps transferred to the introductory section of “Results”).
Lines 130-150: I think I understand what the authors try to state her, but the messages are blurred by overly complex sentences and uclear language: Pleaese straighten out and avoid over-complex statements like “…(g = 0o) may exhibit the maximally possible stress rotation of 90o which signifies a mutual replacement of S1 and S2 orientation, respectively”. This is unclear at the best, and should be rephrased.
Figure 3, figure caption: “… dependent on different setting” meaning what? I assme you mean: ”resulting from contrasting sets of model input parameters”. Details in this figure are not easily readable (see e.g. 3b). A better explanation is needed and the crucial differnces should be pinted out. E.g. The only difference between a and b is the Rs-value of 1,4 and 1,2. So please axplain what you want to demonstrate.
Figure 4, figure caption: This figure is not well explained. Rather: “Intrinsic stress rotation in the fault zone as a function of increasing ……”. The figure caption needs much more attention. Please lead the attention of the reader more clearly to the important relations here, for example the abrupt termination of stress rotation at the fault border. A comment on geological consequences and limitations would be appropriate (see e.g. Gabrielsen et al. 2017 referred to below).
- Discussion
After a very short introduction the discussion chapter jumps directly onto a mention of the practical application of the results (4.1 Application). Thereby the entire scientific discussion and the evaluation of the results in the framework of established knowledge of stress configurations in the framework of present knowledge becomes deluted. This is a bit disappointing and particularly so because elements several principal elemnts for discussion pop up.
I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated. This list should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned.
Thereafter the chapter on practical applications of the reults could be included before the Conclusions are given
Since I reommend that the Discussion-chapter is re-written, I have not included specific comments here.
In the present version the “Discussion” slides over from “4.1 Application” to “Implementation (4.2)”. Relevant elements that should be addressed in a scientific discussion are touched upon, but are immeiately abandoned, preventing discussion in any depth (e.g. the element of plastic (vs brittle, which is not mentioned) deformation and strain softening/hardening).
The authors touch upon the complexities of mature fault zones “Material gradient (4.3)”. I do agree that mature natural fault zones frequently host damage zones (as mentioned) and often include structural elements sparated by abrupt changes in mechanical properties (see e.g. Gabrielsen et al. 2017; Figure1; (Gabrielsen,R.H., Braathen,A., Kjemperud,M. & Valdresbåten,M.L.R., 2017: The geometry and dimensions of fault core lenses, Geological Society London, Special Publication, 439, 249-269, doi.org/10.1144/SP439.4). Nevertheless, the present contribution has a nucleus for a more profound discussion of this in the light of their new data, that I think it could be expanded upon.
The authors use data well data to illustrate patterns of break-out (4.4 Well data vs modeling results). The concept of wellbore break-out is well established in the literature and I again miss reference to basic advanced textbooks (again Engelder 1983). I think these would give a good background for the discussion of rotated stress, which is tricky in wellbores since the drilling process can influence the stress and fracture patterns.
The final part of the Discussion (4.5 Limitations) has a flare of afterthought. I think it would be better that elements from this section be transferred to the discussions of in subchapters 4.1 - 4.4 and placed where there should is a limitation in the conclusion for each topic.
4.6. Other reasons for stress rotations. I think this section should be amalgamated with section. 4.4.
- Conclusions
The most significant conclusions from Chapter 4 should be summarized here and referred to in the abstract.
References
The references have not been controlled by me, neither when consistency between text and reference list, nor when format is concerned.
Citation: https://doi.org/10.5194/egusphere-2024-1109-RC1 -
AC1: 'Reply on RC1', Moritz Ziegler, 29 May 2024
We thank the reviewer for the detailed and thorough comments that are very helpful to improve and clarify the manuscript. In our replies, we follow the report structure of the reviewer. First, we address the major points that were raised. Individual and specific remarks will be addressed later in the reply.
Results: We agree with the reviewer, that an introduction to the question that is to be answered is beneficial for the results section. In order to avoid to many repetitions, the introduction will remain rather brief in the revised version of the manuscript. The results section will be updated accordingly in the revised version in order to be more to the point and better structured.
Discussion: We thank the reviewer for pointing out the weakness in the Discussion section. In particular, the names of the Subsections (and their order) may be confusing (see also comments and reply to reviewer #2). We will re-write the Discussion section in order to put it in line with the results. The discussed topics will be better sorted along the line of:
- Implications of the results
- Application examples
- Clearly discuss, identify (and if possible eliminate) possible shortcomings of the model (2D, mesh convergence – see reviewer #2)
Figures: We agree with the reviewer that the figures and captions can be improved and thank for the ideas and suggestions. Individually, we have to disagree with the suggestion to decolourize artifacts. They are a part of the model results and their existence needs to be taken into account. A mentioning of the features being artifacts in the text and figure caption – in our opinion – should be sufficient to advise readers on this issue.
Language: We will have the manuscript read by a colleague with proficient English language knowledge.
In the following you can find point-by-point remarks on the raised issues. We thank the reviewer for finding some typos or minor technical and other issues. To keep the reply brief and focussed, we do not acknowledge them individually but of course will correct them in the revised version of the manuscript.
Title:
Apparently, the title of the manuscript is not appropriate since also reviewer #2 suggests a change of the title. Our suggestion for an updated title is “Stress state at faults: The influence of rock stiffness contrast, stress orientation, and ratio”. This incorporates also the comments made by reviewer #2 that an inclusion of stress ratio and far-field stress state are required.
Abstract:
We agree that the abstract should be clearer and more to the point. For most of the comments and suggestions we will take according actions to include them in the revised version of the manuscript.
Line 1: We disagree with the reviewer to replace “gravitational volume forces” with “body forces”. The former term is clearly more specific and unambiguous while the latter can be misinterpreted by readers unfamiliar with the subject.
Line 4: Agreed
Lines 2-3: We assume the reviewer means “controls the amount of principal stress axes rotation” and agree with that.
Line 7: Agreed
Introduction & Model setup:
Line 15, Line 16: Agreed
Line 17: Actually, we mean “most frequently” in that most (publicly) available data is on stress orientations rather than magnitudes. It is also often most easily obtained but not necessarily. It will be expanded to include both.
Lines 19-24: References to some according textbooks will be included here and in other appropriate locations in the text.
Lines 23-28, Line 29, Line 33, Line 47, Lines 43-49, Line 50: Minor comments to add references or clarify, language issues. Will be revised.
Lines 52-53: We thank the reviewer for the suggestion to clarify this phrase and will adapt it accordingly.
Lines 61-74: Thank you. Will be included in the abstract.
Line 76: We agree with the reviewer in general and will revise accordingly. However, at the same time we try to be cautious about the influence of the intermediate stress component which is shown in the Discussion to be likely of importance.
Line 77: The capital H in SHmax and the lower-case h in Shmin are commonly used to further highlight the difference between the two horizontal stress components including maximum and minimum horizontal stresses (see e.g. the World Stress Map and associated publications).
Line 84: Agreed
Line 85: We agree with the reviewer that this reads somewhat peculiar. Furthermore, we thank the reviewer for pointing this out, which allowed us to identify a typo. Indeed, the number of elements is higher. Since a variety of models for the variations in strike are setup, the exact number of elements is also variable. Depending on the model set-up, the total number of elements is variable, and it is between 145,612 and 172,484 elements. An exceptionally high number of elements (732,526) was used for a strike of 15° in order to generate high resolution figures (Figure 3). We will clarify this issue in the revised version accordingly.
Lines 90ff: It was intended to write subscript host and fault. It will be corrected in the revised version.
Line 93, Lines 94ff: Agreed and will be implemented.
Results:
We agree with the reviewer that the results section needs some more explanation of the actual results. This will be included in the revised version of the manuscript, in particular the results presented in Figure 5. We will also include a better description of the visualization.
Instead of the suggested explanation of the visualization strategy in the beginning (or introduction section of the Results section), we prefer to subdivide the Results section into subsections. This allows to guide the reader from the easily understandable Figure 3 to the advanced Figure 4 and mainly 5. Furthermore, we will ensure during typesetting that the figures are closer to the corresponding text which will also help in understanding.
Line 98: Agreed.
Lines 98-101: Again, this was intended but somehow got lost in typesetting.
Line 103, Line 104: Agreed.
Lines 103-105: We agree with the reviewer that a closer interlinkage of Figures 3, 4, and 5 is required. However, all subpanels of Figure 3 are referred to and discussed in detail in lines 106-120. We will also include information in the figure caption that the displayed stress states are “advanced” stress states in that they show a change due to a stiffness contrast. Detailed comments on Figure 3 are also made in the beginning of our reply and are quoted in the following: “Individually, we have to disagree with the suggestion to decolourize artifacts. They are a part of the model results and their existence needs to be taken into account. A mentioning in the text and figure caption – in our opinion – should be sufficient to advise readers on this issue.”
Lines 105-108: Agreed.
Line 108: We agree that it has to be more clearly stated that the magnitude of the differential stress remains constant.
Line 115, Line 123: Agreed.
Lines 127-130: The artifacts occur for numerical reasons. The modelled stress state is computed by the numerical solver not at the nodes but at so called “integration points”. They are located within the elements. The stress state is then interpolated from the integration points to the nodes that connect elements. The stress state at a node is thus influenced by the stress state from each bordering integration point. In particular, for significant material contrasts, this results in an averaging of the stress states exactly at the border. And that is the artifact which is observed.
Lines 130-150: Will be revised.
Figure 3: Agreed and will be improved.
Figure 4: The figure caption will be improved. It will be highlighted that the abrupt change in stress rotation angle at the border of the fault is a result of the abrupt change in rock properties. According references to the (un)likeliness of this behaviour in geological situations will be included.
Discussion:
We agree with both reviewers that the Discussion section needs to be thoroughly revised or re-written. We thank the reviewer for the suggestions and comments that are much appreciated and will help to structure a revised version of the Discussion. We will name the Subsections in a clearer and unambiguous way and update the order. We will pay attention to more in-depth discussions of the raised topics and dismiss superfluous insets and sidetracks to keep the focus.
Further comments on the Discussion can be found in the above general section and in the reply to reviewer #2.
Citation: https://doi.org/10.5194/egusphere-2024-1109-AC1
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RC2: 'Comment on egusphere-2024-1109', Anonymous Referee #2, 20 May 2024
The paper conducted extensive numerical studies to investigate the effect of stiffness contrasts, stress ratio, and the angle on stress orientation. It has essential contribution to the community to understand the difference between in situ stress and local stress field. It also calls for attention that breakouts do not necessarily correspond to the far field Shmin direction, but need more in-depth investigation since local stress fields could be rotated. Revisions are required before publication to address questions/clarifications that have been listed below:
Title: The study is not only about stiffness contrasts, but also includes stress ratio, and the angle between strike and SHmax. Please consider changing the title.
Line 25: Reiter et al. (2024) says stress changes beyond a few hundred meters are too small to see. However, from Fig 4, the rotation is zero as when the distance is >=3m. Could you please explain the order difference (hundred meters in Reiter versus only 3m in Fig 4)? In the current study, it seems the stress changes are indiscernible whenever the distance is >= 3m.
Line 77: In the Strike-slip stress regime, shouldn’t S1=SHmax and S3=Shmin? I understand the model is in 2D, but I feel it is a bit confusing to say S2=Shmin. Please consider change that.
Line 79: Have you conducted a mesh convergence study in FEM? It could be great to have plots (maybe in the supplement) to show the validation of mesh convergence.
Table 2: The row name should be “S1-S2 [MPa]”, instead of “S1-2 [MPa]”.
Line 113: “A reduction of RE=0.4 to RE=0.7” seems to be an increase, not reduction. I understand that from the value, it is “increase”. However, based on the meaning, it could say a reduction of stiffness contrast between fault and the host rock. Please make it clear in the text.
Figure 6: the color-coding looks different as it is in the legend.
Section 4.2: section 4.2 could be combined with section 2 model setup. It is all about how you set the model. You didn’t do contact modelling, right?
Section 4.4 and Table 3: The table caption of table 3 shows “parameters in italics are derived”. However, the parameters in Table 3 is in italics. In addition, in order to do comparison of well data with the modelling result, intuitively, I will expect authors use Rs, Re, angle from the reference, and have a column called “modeled stress rotation” and compare it with the column “observed stress rotation”. However, in the manuscript, it seems authors sometime derived for input parameters, not for modeled stress rotation. Please have more clarifications in the text.
Citation: https://doi.org/10.5194/egusphere-2024-1109-RC2 -
AC2: 'Reply on RC2', Moritz Ziegler, 29 May 2024
We thank reviewer #2 for the detailed comments and thorough reading of the manuscript. Please find detailed replies to the raised points in the following. We thank the reviewer for finding some typos or minor technical issues. To keep the reply brief and focussed, we do not acknowledge them individually but of course will correct them in the revised version of the manuscript.
Title: Apparently, the title of the manuscript is not appropriate since also reviewer #1 suggests a change of the title. Our suggestion for an updated title is “Stress state at faults: The influence of rock stiffness contrast, stress orientation, and ratio”.
Line 25: The reviewer is correct in this observation. However, Reiter et al. (2024) state that there is NO rotation in a distance of several hundred of meters from the fault. Given the different scope of the work (Reiter et al: far-field, this work: near-field), the numerical resolution is also very different in that Reiter et al. cannot resolve any stress rotation in the immediate vicinity (meters to 10 meters) of a fault. Eventually, Reiter et al. mainly refer to the effect of an explicit discontinuity (technically speaking a contact surface with a frictional behaviour) on the stress state. In contrast, in this manuscript a continuous model is applied. This discrepancy will be clarified in a revised version of the manuscript.
Line 77: We agree with the reviewer that this is confusing. However, the choice was made in order to avoid suggesting the modelling has been done in 3D. A clarification will be added.
Line 79: The influence of element size has been investigated prior to the final computations. The main influence is expected to be the number of elements that represent the stiffness contrast perpendicular to its strike (in contrast to the overall element sizes). The results could be briefly shown in the appendix.
Table 2: Agreed.
Line 113: We agree that this is indeed confusing. This will be clarified in the text.
Figure 6: Agreed and will be revised.
Section 4.2: We agree with both reviewers on the criticism of the Discussion and naming of the subsections. The reasoning behind Section 4.2 is to discuss possible influence of the modelling method (FEM). At this point, the earlier suggested mesh convergence checks will be displayed and discussed. This will more clearly show the intention of Section 4.2. In addition, the Section will be renamed to “Numerical implementation”.
Table 3: Indeed, for some reason, the parameters in italics are not printed in the table correctly. This will be changed in the revised version of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-1109-AC2
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AC2: 'Reply on RC2', Moritz Ziegler, 29 May 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1109', Anonymous Referee #1, 01 May 2024
Review
The effect of stiffness contrasts at faults on stress orientation
Ziegler et al.
submitted to Solid Earth
General comments and recommendation
This is a useful contribution that expands on the present knowledge about the influence of mechanical inhomogeneities (faults and fractures) on stress magnitude and orientation in homogeneous rock. It is well suited for publication in Solid Earth.
The manuscript still has some serious shortcomings in its present form:
- The Results chapter lacks a proper introduction that explains the problem focused upon and which strategy is selected to solve those. This chapter and its affiliated figures seem to me to be not to utilized to its full potential (see comments below) and gives a slightly whimsical impression.
- I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated (it should harmonized with the introduction to the Results-chapter). This list of scientific items should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and sometimes also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned. My recommendation will be that the Discussion-chapter is completely re-written. It seems that the observations given in Results and Discussion/evaluation-chapters have not been consequently systematized in all cases.
- I think some figures (Figures 2 and 3) should be redrafted to display some more details clearly. If I understand correctly that the outer part of the zonation is an artifact (see comment Lines 127-130) the color code should be modified: Artifacts should not have a color code in the fiure). I also suggst that other figures (particularly 4 and 5) are described and discussed more coherently in the text. The figure cations should also be more focused on explaining the meaasge to he reader.
- The English language needs some more attention. It is sometimes a little clumsy and some phrasings and sometimes ambiguous or unclear. It is therefore recommended that the authors approach a colleague (who is familiar with this field of research) with English as his/her first language to assist in linguistic matters.
It is concluded that this article deserves publication in Solid Earth after rewriting of the description and discussion, reworking of a couple of figures and affiliated figure captions and improvement of the English language in general.
Specific comments
Title
I suggest that the authors adjust the title of the paper slightly, perhaps something like:
“The influence of rock stiffness contrast on stress configuration along and within faults”.
Abstract
Generally, I find the abstract to be a little “soft”. The initial sentence has the flare of a general introduction and should be condensed. I suggest that the abstract separate clearly between 1) the definition of the problem investigated in this study, 2) specification of which methods were and 3) sharpen even more the conclusions of this work and that all three items are expanded upon, more completely to cover the intention of the paper and its important findings.
Line 1: I think “body forces” are better than “gravitational volume forces”. Perhaps “contemporary stress” and associated concepts as defined by e.g. Engelder (1983) is preferrable (Engelder,T.,1993: Stress Regimes in the Lithosphere. Princeton University Press, 467pp.)
.
Line 4: This is fine and is where the important information really starts: “We investigate….”
Lines 2-3: “when faults are crossed …..”. Suggestion: “along or in the vicinity of faults ….. control the amount of principal stress axes.”
Line 7: “General findings….” You mean findings in the present work. Please clarify.
Introduction
Line 15: parameter in the stability assessment
Line 16: “exploitation” rather than “usage”? Add safety assessment?
Line 17: Most frequently? You mean: “Information about SHmax is most easily obtained from…”?
Lines 19-24: You mean far-field stress, locally imposed by stress imposed by local……. like topography. Perhaps an advanced textbook (e.g. Engelder 1983) with a summary of such stress systems should be referred to and nomenclature and definitions adapted to that source (see also above).
e.g. Lines 23-28 and generally: The authors have a tendency to over-use adverbs in beginnings of phrases: “Furthermore, it has……”, “However, Reiter ….”, “Nevertheless, on a meters scale….”. These examples are taken from sentences that follow each other.
Line 29: “across the world” is a surplice phrase: (Where else?)
Line 33: Borehole breakouts: Again, I think it would be convenient to refer to an advanced textbook – Again, I think Engelder (1983) can be used.
Line 47: Perhaps this section should start with reference to empiric data/observations: Examples are given in lines 58-60, so I suggest that this is moved here.
Lines 43-49: Not well phrased. Please separate int two statements and clarify.
Line 50: Rather: “This raises questions as to which parameters determine….”
Lines52-53: Rephrase. Suggestion: (if this is what the authors mean to say. If I misread this, a full rephrasing is necessary). “The potential for stress rotation and the magnitude for such rotation are assumed to be determined by…. , the contrast in rock stiffness between ….. and the angle between SHmax and the fault strike”.
Lines 61-74: I think this is well phrased. Please include a short version of this in the abstract.
Line 76: I do see the rationale in the application of a plain strain situation in a strike-slip regime. Most faults will be influenced by shear whatever the overall tectonic regime. Perhaps this generic situation should be explained (to the unprepared reader), and perhaps the term shear” (rather than-strike slip) should be applied (for the same reason).
Line 77: Why SHmax and Shmin: Misprint or some hidden significance? Either correct or explain.
Line 84: Isn’t the term tria-elements commonly written with capital T?
Line 85: In the order of about 75,00 elements?? Either 75,000 elements were used or not? Or did the model define the grid itself? If so, based on what? Whatever: “In the order of about” is a superfluous double description.
Lines 90ff: Why not Ehost and Efault to bring it in harmony with e.g. SHmax
Line 93: “Non-existence of a fault”: Why not “intact rock”? When I walk in a street, the street may be empty, which is congruent with “filled with non-existent cars”. But we don’t say that.
Line 94ff: In my opinion care should be taken so that the conclusions gave a consequent grammatical time sence in distinguishing between what was observed in the experiments and what is generally valid for such systems. In other words: We tested the influence…., scenarios were analysed…. .
Results
This important section of the paper comes on a little abruptly. Perhaps a short introduction that describes the dynamics of the experiments should serve as an introduction to this section. Particularly, the reader should be reminded which relations and which hypoteses are subject to investigation, and informed about the strategy selected to attack the problem (which parameters are at stake, which are kept constant and which are varied). Some of the general statements on the experiments given in the previous section and also spread out in the following description could perhaps be moved here.
At this stage he authors should reveal to the reader also their strategy for illustration of the observations and the analyses, which is revealed in Figures 3, 4 and 5: In oher words, The relation between figures 3 - 5 showing the stress configuration within the faults should be highlighted from the start in this section.
I think the use of tables 1 and 2 should be utilized more actively in the descriptive part. Now a very summaric summary is given in the text: “A more comprehensive comparison is shown in Table 2” (line 113).
Some crucial information seems to be lacking: Are the situations illustrated in Figure 3 initial or advanced stress configurations? In other words: did the configuration change with time or did it become stabilised?
The general observaton should be stated and highlighted in the closing part of this section: Now the summary of the key observations are a little bit spread out and the (important) observatios are presented rather summarily.
General: See comment to line 94ff above.
Line 98: Please rephrase: this sentence is complex to the extent that is messsage is obscured. Start with the subject “The orientation of ……”, refer immediately to Figure 3, and use Figure 2 more actively.
Line 98 -101: Again, why not sxx, syy etc, since s and xx describe different qualities, namely principal stress and vector components?
Line 103: Please expand the text somewhat to help the reader a bit here, e.g. “….. an angle (g) of 15o between the strike of the fault and the far field stress (S1) a moderate stiffness contrast (RE)…”.
Line 104: Take out “There,”
Lines 103-105: I think that the potential of Figure 3 is not fully exploited here, and the reader should be informed to read Figure 3 in concert with Figures 4 and 5. And why is only Figure 3a referred to in the text, completely neglecting b-f?
Furthermore, Figure 3 is rather nitty-gritty and it is mpossible to read all the details. (Particularly 3b is unclearly displayed). I understand that the displayed zonation (e.g.yellow-red-magneta) in e.g. is an artifact (lines 126-130). If so, the color symbols are misleading and the “artifical” color zones should be removed from the figure display and rather commented upon in the figure caption.
Lines 105-108: I think this information should be given in the very inroduction to the Results-section on a general basis and combined with a description of the strategy for the prsentation of the results (see general comments to the Results-chapter above).
Line 108: You mean: “S1-S2 remains constant”. Please state clearly whether this implies absolute stress magnitude, or the difference only?
Line 115: Rather: “Thus, greater RE promotes less stress rotation”
Line 123: Moved to introductory remarks in this chapter?
Line 127-130: This is a strange phrasing and rather confusing.You mean: “The data on stress orientation at the material borders show here are not valid, because…..the apparent stress rotation result from interpolation of what?...... please rephrase/explain” Also the following sentence (“At material contrasts….”) needs to be rewritten e.g.: “At the borders between bodies with different material properties ….”.
I understand that the apparent zonation (displayed in Figures 3a, b,c,d) are artifacts. This is technical information that should be kept isolated form the valid observations done in the interpretation of the data (perhaps transferred to the introductory section of “Results”).
Lines 130-150: I think I understand what the authors try to state her, but the messages are blurred by overly complex sentences and uclear language: Pleaese straighten out and avoid over-complex statements like “…(g = 0o) may exhibit the maximally possible stress rotation of 90o which signifies a mutual replacement of S1 and S2 orientation, respectively”. This is unclear at the best, and should be rephrased.
Figure 3, figure caption: “… dependent on different setting” meaning what? I assme you mean: ”resulting from contrasting sets of model input parameters”. Details in this figure are not easily readable (see e.g. 3b). A better explanation is needed and the crucial differnces should be pinted out. E.g. The only difference between a and b is the Rs-value of 1,4 and 1,2. So please axplain what you want to demonstrate.
Figure 4, figure caption: This figure is not well explained. Rather: “Intrinsic stress rotation in the fault zone as a function of increasing ……”. The figure caption needs much more attention. Please lead the attention of the reader more clearly to the important relations here, for example the abrupt termination of stress rotation at the fault border. A comment on geological consequences and limitations would be appropriate (see e.g. Gabrielsen et al. 2017 referred to below).
- Discussion
After a very short introduction the discussion chapter jumps directly onto a mention of the practical application of the results (4.1 Application). Thereby the entire scientific discussion and the evaluation of the results in the framework of established knowledge of stress configurations in the framework of present knowledge becomes deluted. This is a bit disappointing and particularly so because elements several principal elemnts for discussion pop up.
I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated. This list should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned.
Thereafter the chapter on practical applications of the reults could be included before the Conclusions are given
Since I reommend that the Discussion-chapter is re-written, I have not included specific comments here.
In the present version the “Discussion” slides over from “4.1 Application” to “Implementation (4.2)”. Relevant elements that should be addressed in a scientific discussion are touched upon, but are immeiately abandoned, preventing discussion in any depth (e.g. the element of plastic (vs brittle, which is not mentioned) deformation and strain softening/hardening).
The authors touch upon the complexities of mature fault zones “Material gradient (4.3)”. I do agree that mature natural fault zones frequently host damage zones (as mentioned) and often include structural elements sparated by abrupt changes in mechanical properties (see e.g. Gabrielsen et al. 2017; Figure1; (Gabrielsen,R.H., Braathen,A., Kjemperud,M. & Valdresbåten,M.L.R., 2017: The geometry and dimensions of fault core lenses, Geological Society London, Special Publication, 439, 249-269, doi.org/10.1144/SP439.4). Nevertheless, the present contribution has a nucleus for a more profound discussion of this in the light of their new data, that I think it could be expanded upon.
The authors use data well data to illustrate patterns of break-out (4.4 Well data vs modeling results). The concept of wellbore break-out is well established in the literature and I again miss reference to basic advanced textbooks (again Engelder 1983). I think these would give a good background for the discussion of rotated stress, which is tricky in wellbores since the drilling process can influence the stress and fracture patterns.
The final part of the Discussion (4.5 Limitations) has a flare of afterthought. I think it would be better that elements from this section be transferred to the discussions of in subchapters 4.1 - 4.4 and placed where there should is a limitation in the conclusion for each topic.
4.6. Other reasons for stress rotations. I think this section should be amalgamated with section. 4.4.
- Conclusions
The most significant conclusions from Chapter 4 should be summarized here and referred to in the abstract.
References
The references have not been controlled by me, neither when consistency between text and reference list, nor when format is concerned.
Citation: https://doi.org/10.5194/egusphere-2024-1109-RC1 -
AC1: 'Reply on RC1', Moritz Ziegler, 29 May 2024
We thank the reviewer for the detailed and thorough comments that are very helpful to improve and clarify the manuscript. In our replies, we follow the report structure of the reviewer. First, we address the major points that were raised. Individual and specific remarks will be addressed later in the reply.
Results: We agree with the reviewer, that an introduction to the question that is to be answered is beneficial for the results section. In order to avoid to many repetitions, the introduction will remain rather brief in the revised version of the manuscript. The results section will be updated accordingly in the revised version in order to be more to the point and better structured.
Discussion: We thank the reviewer for pointing out the weakness in the Discussion section. In particular, the names of the Subsections (and their order) may be confusing (see also comments and reply to reviewer #2). We will re-write the Discussion section in order to put it in line with the results. The discussed topics will be better sorted along the line of:
- Implications of the results
- Application examples
- Clearly discuss, identify (and if possible eliminate) possible shortcomings of the model (2D, mesh convergence – see reviewer #2)
Figures: We agree with the reviewer that the figures and captions can be improved and thank for the ideas and suggestions. Individually, we have to disagree with the suggestion to decolourize artifacts. They are a part of the model results and their existence needs to be taken into account. A mentioning of the features being artifacts in the text and figure caption – in our opinion – should be sufficient to advise readers on this issue.
Language: We will have the manuscript read by a colleague with proficient English language knowledge.
In the following you can find point-by-point remarks on the raised issues. We thank the reviewer for finding some typos or minor technical and other issues. To keep the reply brief and focussed, we do not acknowledge them individually but of course will correct them in the revised version of the manuscript.
Title:
Apparently, the title of the manuscript is not appropriate since also reviewer #2 suggests a change of the title. Our suggestion for an updated title is “Stress state at faults: The influence of rock stiffness contrast, stress orientation, and ratio”. This incorporates also the comments made by reviewer #2 that an inclusion of stress ratio and far-field stress state are required.
Abstract:
We agree that the abstract should be clearer and more to the point. For most of the comments and suggestions we will take according actions to include them in the revised version of the manuscript.
Line 1: We disagree with the reviewer to replace “gravitational volume forces” with “body forces”. The former term is clearly more specific and unambiguous while the latter can be misinterpreted by readers unfamiliar with the subject.
Line 4: Agreed
Lines 2-3: We assume the reviewer means “controls the amount of principal stress axes rotation” and agree with that.
Line 7: Agreed
Introduction & Model setup:
Line 15, Line 16: Agreed
Line 17: Actually, we mean “most frequently” in that most (publicly) available data is on stress orientations rather than magnitudes. It is also often most easily obtained but not necessarily. It will be expanded to include both.
Lines 19-24: References to some according textbooks will be included here and in other appropriate locations in the text.
Lines 23-28, Line 29, Line 33, Line 47, Lines 43-49, Line 50: Minor comments to add references or clarify, language issues. Will be revised.
Lines 52-53: We thank the reviewer for the suggestion to clarify this phrase and will adapt it accordingly.
Lines 61-74: Thank you. Will be included in the abstract.
Line 76: We agree with the reviewer in general and will revise accordingly. However, at the same time we try to be cautious about the influence of the intermediate stress component which is shown in the Discussion to be likely of importance.
Line 77: The capital H in SHmax and the lower-case h in Shmin are commonly used to further highlight the difference between the two horizontal stress components including maximum and minimum horizontal stresses (see e.g. the World Stress Map and associated publications).
Line 84: Agreed
Line 85: We agree with the reviewer that this reads somewhat peculiar. Furthermore, we thank the reviewer for pointing this out, which allowed us to identify a typo. Indeed, the number of elements is higher. Since a variety of models for the variations in strike are setup, the exact number of elements is also variable. Depending on the model set-up, the total number of elements is variable, and it is between 145,612 and 172,484 elements. An exceptionally high number of elements (732,526) was used for a strike of 15° in order to generate high resolution figures (Figure 3). We will clarify this issue in the revised version accordingly.
Lines 90ff: It was intended to write subscript host and fault. It will be corrected in the revised version.
Line 93, Lines 94ff: Agreed and will be implemented.
Results:
We agree with the reviewer that the results section needs some more explanation of the actual results. This will be included in the revised version of the manuscript, in particular the results presented in Figure 5. We will also include a better description of the visualization.
Instead of the suggested explanation of the visualization strategy in the beginning (or introduction section of the Results section), we prefer to subdivide the Results section into subsections. This allows to guide the reader from the easily understandable Figure 3 to the advanced Figure 4 and mainly 5. Furthermore, we will ensure during typesetting that the figures are closer to the corresponding text which will also help in understanding.
Line 98: Agreed.
Lines 98-101: Again, this was intended but somehow got lost in typesetting.
Line 103, Line 104: Agreed.
Lines 103-105: We agree with the reviewer that a closer interlinkage of Figures 3, 4, and 5 is required. However, all subpanels of Figure 3 are referred to and discussed in detail in lines 106-120. We will also include information in the figure caption that the displayed stress states are “advanced” stress states in that they show a change due to a stiffness contrast. Detailed comments on Figure 3 are also made in the beginning of our reply and are quoted in the following: “Individually, we have to disagree with the suggestion to decolourize artifacts. They are a part of the model results and their existence needs to be taken into account. A mentioning in the text and figure caption – in our opinion – should be sufficient to advise readers on this issue.”
Lines 105-108: Agreed.
Line 108: We agree that it has to be more clearly stated that the magnitude of the differential stress remains constant.
Line 115, Line 123: Agreed.
Lines 127-130: The artifacts occur for numerical reasons. The modelled stress state is computed by the numerical solver not at the nodes but at so called “integration points”. They are located within the elements. The stress state is then interpolated from the integration points to the nodes that connect elements. The stress state at a node is thus influenced by the stress state from each bordering integration point. In particular, for significant material contrasts, this results in an averaging of the stress states exactly at the border. And that is the artifact which is observed.
Lines 130-150: Will be revised.
Figure 3: Agreed and will be improved.
Figure 4: The figure caption will be improved. It will be highlighted that the abrupt change in stress rotation angle at the border of the fault is a result of the abrupt change in rock properties. According references to the (un)likeliness of this behaviour in geological situations will be included.
Discussion:
We agree with both reviewers that the Discussion section needs to be thoroughly revised or re-written. We thank the reviewer for the suggestions and comments that are much appreciated and will help to structure a revised version of the Discussion. We will name the Subsections in a clearer and unambiguous way and update the order. We will pay attention to more in-depth discussions of the raised topics and dismiss superfluous insets and sidetracks to keep the focus.
Further comments on the Discussion can be found in the above general section and in the reply to reviewer #2.
Citation: https://doi.org/10.5194/egusphere-2024-1109-AC1
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RC2: 'Comment on egusphere-2024-1109', Anonymous Referee #2, 20 May 2024
The paper conducted extensive numerical studies to investigate the effect of stiffness contrasts, stress ratio, and the angle on stress orientation. It has essential contribution to the community to understand the difference between in situ stress and local stress field. It also calls for attention that breakouts do not necessarily correspond to the far field Shmin direction, but need more in-depth investigation since local stress fields could be rotated. Revisions are required before publication to address questions/clarifications that have been listed below:
Title: The study is not only about stiffness contrasts, but also includes stress ratio, and the angle between strike and SHmax. Please consider changing the title.
Line 25: Reiter et al. (2024) says stress changes beyond a few hundred meters are too small to see. However, from Fig 4, the rotation is zero as when the distance is >=3m. Could you please explain the order difference (hundred meters in Reiter versus only 3m in Fig 4)? In the current study, it seems the stress changes are indiscernible whenever the distance is >= 3m.
Line 77: In the Strike-slip stress regime, shouldn’t S1=SHmax and S3=Shmin? I understand the model is in 2D, but I feel it is a bit confusing to say S2=Shmin. Please consider change that.
Line 79: Have you conducted a mesh convergence study in FEM? It could be great to have plots (maybe in the supplement) to show the validation of mesh convergence.
Table 2: The row name should be “S1-S2 [MPa]”, instead of “S1-2 [MPa]”.
Line 113: “A reduction of RE=0.4 to RE=0.7” seems to be an increase, not reduction. I understand that from the value, it is “increase”. However, based on the meaning, it could say a reduction of stiffness contrast between fault and the host rock. Please make it clear in the text.
Figure 6: the color-coding looks different as it is in the legend.
Section 4.2: section 4.2 could be combined with section 2 model setup. It is all about how you set the model. You didn’t do contact modelling, right?
Section 4.4 and Table 3: The table caption of table 3 shows “parameters in italics are derived”. However, the parameters in Table 3 is in italics. In addition, in order to do comparison of well data with the modelling result, intuitively, I will expect authors use Rs, Re, angle from the reference, and have a column called “modeled stress rotation” and compare it with the column “observed stress rotation”. However, in the manuscript, it seems authors sometime derived for input parameters, not for modeled stress rotation. Please have more clarifications in the text.
Citation: https://doi.org/10.5194/egusphere-2024-1109-RC2 -
AC2: 'Reply on RC2', Moritz Ziegler, 29 May 2024
We thank reviewer #2 for the detailed comments and thorough reading of the manuscript. Please find detailed replies to the raised points in the following. We thank the reviewer for finding some typos or minor technical issues. To keep the reply brief and focussed, we do not acknowledge them individually but of course will correct them in the revised version of the manuscript.
Title: Apparently, the title of the manuscript is not appropriate since also reviewer #1 suggests a change of the title. Our suggestion for an updated title is “Stress state at faults: The influence of rock stiffness contrast, stress orientation, and ratio”.
Line 25: The reviewer is correct in this observation. However, Reiter et al. (2024) state that there is NO rotation in a distance of several hundred of meters from the fault. Given the different scope of the work (Reiter et al: far-field, this work: near-field), the numerical resolution is also very different in that Reiter et al. cannot resolve any stress rotation in the immediate vicinity (meters to 10 meters) of a fault. Eventually, Reiter et al. mainly refer to the effect of an explicit discontinuity (technically speaking a contact surface with a frictional behaviour) on the stress state. In contrast, in this manuscript a continuous model is applied. This discrepancy will be clarified in a revised version of the manuscript.
Line 77: We agree with the reviewer that this is confusing. However, the choice was made in order to avoid suggesting the modelling has been done in 3D. A clarification will be added.
Line 79: The influence of element size has been investigated prior to the final computations. The main influence is expected to be the number of elements that represent the stiffness contrast perpendicular to its strike (in contrast to the overall element sizes). The results could be briefly shown in the appendix.
Table 2: Agreed.
Line 113: We agree that this is indeed confusing. This will be clarified in the text.
Figure 6: Agreed and will be revised.
Section 4.2: We agree with both reviewers on the criticism of the Discussion and naming of the subsections. The reasoning behind Section 4.2 is to discuss possible influence of the modelling method (FEM). At this point, the earlier suggested mesh convergence checks will be displayed and discussed. This will more clearly show the intention of Section 4.2. In addition, the Section will be renamed to “Numerical implementation”.
Table 3: Indeed, for some reason, the parameters in italics are not printed in the table correctly. This will be changed in the revised version of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-1109-AC2
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AC2: 'Reply on RC2', Moritz Ziegler, 29 May 2024
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Robin Seithel
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Oliver Heidbach
Thomas Kohl
Birgit Müller
Mojtaba Rajabi
Karsten Reiter
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