Detailed investigation of multi-scale fracture networks in glacially abraded crystalline bedrock at &Aring;land Islands, Finland

Ovaskainen, Nikolas Aleksi; Skyttä, Pietari Mikael; Nordbäck, Nicklas Johan; Engström, Jon Oskar

doi:https://doi.org/10.5194/egusphere-2022-1363

Preprints

https://doi.org/10.5194/egusphere-2022-1363

Preprints

12 Dec 2022

| 12 Dec 2022

Detailed investigation of multi-scale fracture networks in glacially abraded crystalline bedrock at Åland Islands, Finland

Nikolas Aleksi Ovaskainen, Pietari Mikael Skyttä, Nicklas Johan Nordbäck, and Jon Oskar Engström

Abstract. Using multiple scales of observation in studying the fractures of the bedrock increases the reliability and representativeness of the respective studies. This is because the discontinuities, i.e., the fractures, in the bedrock lack any characteristic length and instead occur within a large range of scales of approximately 10 orders of magnitude. Consequently, fracture models need to be constructed based on representative multi-scale datasets to enable valid interpolation and extrapolation of common scaling laws to all fracture sizes.

In this paper, we combine a detailed bedrock fracture study from an extensive bedrock outcrop area with lineament interpretation using Light Detection And Ranging (LiDAR) and geophysical data. Our study offers lineament data in an intermediary length range missing from Discrete Fracture Network -modelling conducted at Olkiluoto, a nuclear spent fuel facility in Finland. In addition, this study also provides a robust multi-scale fracture and lineament dataset which has been thoroughly analysed for the purposes of understanding the uncertainties and differences in the different datasets. Our analysis further covers the topological, scale-independent, fracture network characteristics.

Results of our study include the discovery of three distinct azimuth sets, N-S, NE-SW and WNW-ESE, both single scale and multi-scale power-law models for fracture and lineaments and further insight into a trend of decreasing apparent connectivity of fracture networks as the scale of observation increases. Specifically, a multi-scale power-law exponent of -1.13 is fitted to fracture and lineament lengths although we found that individually the fractures and lineaments might follow distinct power-laws rather than a common one.

Received: 29 Nov 2022 – Discussion started: 12 Dec 2022

Nikolas Aleksi Ovaskainen et al.

Status: closed

CC1:
'Comment on egusphere-2022-1363', Matthis Frey, 28 Dec 2022

Dear Nikolas,

I saw that you cited our paper 'Interdisciplinary Fracture Network Characterization in the Crystalline Basement: A case study from the Southern Odenwald, SW Germany' (Frey et al. 2021) in your preprint. Thanks for this. Please note however that your citation refers to the preprint. The accepted article was published earlier this year: https://doi.org/10.5194/se-13-935-2022

Please change the reference accordingly.

Kind regards

Matthis Frey

Citation: https://doi.org/10.5194/egusphere-2022-1363-CC1
- AC1: 'Reply on CC1', Nikolas Ovaskainen, 02 Jan 2023
  
  Hey Matthis,
  Thank you for taking the time to notify about this! We will update to the proper citation as we continue our work on the manuscript. Using the preprint was an oversight.
  Cheers,
  Nikolas
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC1
RC1:
'Comment on egusphere-2022-1363', Anonymous Referee #1, 10 Jan 2023
The paper is well written, the methods up-to-date and the related results very interesting and statistically robust. The methods are adequately described, the limitation discussed and their reliability and representativeness of the obtained results considered as well. However, some further discussions on methods/results reliability and robustness are needed.

There is a main problem which undermines the possibility to publish the present manuscript in Solid Earth: the aim of the research is not clearly stated and thus it is not clear if the presented methods and results are significant or have any relevant implications for the case study or what are the broader implications for the general analyses of lineament maps from remote sensing. Stating clearly what are the aims and how the presented methods/results can answer to the research questions will also help in reorganizing logically the discussion sections. The paper would be also good if it was clearly focused on the presentation of the new analytical tools and the results adopted for the characterization of a case study, but still the case study need to have a clear aim. I think that the Authors can re-arrange the present manuscript with little effort in order to solve this main issue, otherwise I would suggest to redirect the manuscript to a more specialized journal.

Main issues:

The aim of the research and the conclusions/implications of the results need to be explained a little bit more, they are not immediately understandable from reading the present manuscript. Especially in the Abstract, Introduction (where the aims are sparsely presented in bit and pieces) and in the conclusions.

There is a discrepancy between the “results and conclusions” (sparsely) reported in the introduction section and the final Conclusions of the paper in Section 6. Are the methods and results presented here resolutive for the problem they aim to solve?

The cut-off issue needs to be properly discussed in depth. What is the statistical significance of a results based on the analysis of only the 3% of the total dataset? Is it representative of the whole distribution? This needs to be discussed from the methodological point of view (is the analytical method adequate to analyse our dataset?). Is the results based on the 3% of the data representing the entire length distribution?

Minor comments.

Some part need to be rephrased to be a little bit more concise (the part of the discussion regarding glacial erosion)

Reconsider the use of “e.g.”,

Rephrase the section Lines 92-99 : to be moved to the method section and integrated with the exiting description of the data source.

Line 206: “?”?
Citation: https://doi.org/10.5194/egusphere-2022-1363-RC1
- AC2:
  'Reply on RC1', Nikolas Ovaskainen, 05 Apr 2023
  Dear Reviewer 1,
  Thank you for the constructive review and comments. Specifically, the
  
  criticism on the lack of clear motivation in the introduction resulted in
  
  a major revision of the introduction to better highlight the motivation and
  
  to link the contents of the introduction to the rest of the paper. See
  
  below for specific responses to your comments. All comments are numbered to
  
  allow referencing from other responses. Line number references are to the PDF document with the changes highlighted.
  On behalf of all the authors,
  
  Turku, Finland, April 2023, Nikolas Ovaskainen
  The paper is well written, the methods up-to-date and the related
  
  results very interesting and statistically robust. The methods are
  
  adequately described, the limitation discussed and their reliability and
  
  representativeness of the obtained results considered as well. However,
  
  some further discussions on methods/results reliability and robustness
  
  are needed.
  There is a main problem which undermines the possibility to publish the
  
  present manuscript in Solid Earth: the aim of the research is not
  
  clearly stated and thus it is not clear if the presented methods and
  
  results are significant or have any relevant implications for the case
  
  study or what are the broader implications for the general analyses of
  
  lineament maps from remote sensing. Stating clearly what are the aims
  
  and how the presented methods/results can answer to the research
  
  questions will also help in reorganizing logically the discussion
  
  sections. The paper would be also good if it was clearly focused on the
  
  presentation of the new analytical tools and the results adopted for the
  
  characterization of a case study, but still the case study need to have
  
  a clear aim. I think that the Authors can re-arrange the present
  
  manuscript with little effort in order to solve this main issue,
  
  otherwise I would suggest to redirect the manuscript to a more
  
  specialized journal.
  Main issues
  
  -----------
  The aim of the research and the conclusions/implications of the results
  
  need to be explained a little bit more, they are not immediately
  
  understandable from reading the present manuscript. Especially in the
  
  Abstract, Introduction (where the aims are sparsely presented in bit and
  
  pieces) and in the conclusions. There is a discrepancy between the “results
  
  and conclusions” (sparsely) reported in the introduction section and the
  
  final Conclusions of the paper in Section 6. Are the methods and results
  
  presented here resolutive for the problem they aim to solve?
  1. We have clarified our motivation and aim primarily in the introduction
  
  and added discussion on data, method and statistical reliability based on
  
  comments by both Reviewers. The methods for multi-scale analysis of
  
  fractures and lineaments have been developed for decades but there still
  
  lacks any easily usable common convention for the analysis. Therefore,
  
  some "method development" text must be included in the manuscript to
  
  explain the methods we used. Furthermore, there does not exist any
  
  multi-scale datasets from Finland outside of our very limited prior
  
  research. So there is demand for both datasets and method development and
  
  therefore the focus is on both goals in this manuscript. Multi-scale data
  
  collection, geologic setting and the analysis all cause uncertainties in
  
  the results and in the discussion section we therefore have to consider
  
  all with limited ability to completely separate the discussions about
  
  them as their effect in the results cannot be separated either.
  The cut-off issue needs to be properly discussed in depth. What is the
  
  statistical significance of a results based on the analysis of only the 3% of
  
  the total dataset? Is it representative of the whole distribution? This needs
  
  to be discussed from the methodological point of view (is the analytical method
  
  adequate to analyse our dataset?). Is the results based on the 3% of the data
  
  representing the entire length distribution?
  2. This issue was also pointed out by Reviewer 2. See the answer we gave
  
  there in response number 11.
  Minor comments
  
  --------------
  Some part need to be rephrased to be a little bit more concise (the part of
  
  the discussion regarding glacial erosion)
  3. We have made the discussion section more concise around the
  
  discussion on the effect of glacial erosion. See lines 495-516.
  Reconsider the use of “e.g.”,
  4. The copernicus template for latex submissions that we used
  
  had "e.g." with the comma in numerous examples. If this paper enters the
  
  typesetting phase we will fix these details as instructed.
  Rephrase the section Lines 92-99 : to be moved to the method section and
  
  integrated with the exiting description of the data source.
  5. We moved much of the repeated information about the data to the
  
  method section where we added any missing information that was
  
  only in the introduction. See lines 120-136 in the introduction.
  Line 206: “?”?
  6. The reference is fixed to Rohrbaugh et al. 2002 as was intended.
  Additional fixes unrelated to specific referee comments:
  Modified Figure 3 to include the second, missing, eastern 1:20 000 circular target area.
  
  Fixed small reference errors.
  
  Modified all figure sub-labels to use "(a)", "(b)", ... instead of "A.", ... in figures captions and in text.
  
  Increased font size in Figure 4.
  
  Headers were fixed to only have the first letter capitalized.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC2
RC2:
'Comment on egusphere-2022-1363', Marco Mercuri, 13 Mar 2023
General comments

The manuscript by Ovaskainen and coauthors deals with a multi-scale analysis of the fracture network affecting the crystalline bedrock at the Åland Islands in Finland. The main aim of the study is to contribute to filling the gap of data sets dealing with multi-scale fracture network analyses of crystalline rocks, which might have important applications, including nuclear waste disposal. The multi-scale approach also allows filling the knowledge gap on the local fracture network at an intermediate scale length range (i.e., 100-500 m). The authors highlight that certain fracture network properties, such as length distribution and connectivity might be scale-dependent. I think this study represents an interesting example of a multi-scale analysis of a fracture network. The study is very well performed, particularly for the collection of a very robust dataset and for the usage of up-to-date methods for fracture analysis, including a new software. Consequently my opinion is that the study deserves to be published in Solid Earth.
A point which does not fully convince me is the analysis of length distribution. As described in lines 249-251 (see also Figure 5) the power law, lognormal, and exponential fit hypotheses for fitting length distribution have all been tested on the range of the lengths (traces or branches) above the power-law cut-off length. For testing the power law fit, I have no doubts on the procedure, but I would like to see also the goodness of fit for exponential and lognormal distributions calculated for the whole data set. Moreover, the data (black dots) below the cut-off are not showed on the figures (Figure 5). Such a procedure also impacts the multi-scale analysis of length distribution (Figure 6). In my opinion, all the cumulative length data should be shown in the Figures 5 and 6. To summarize, I think that the procedure for the best fitting equation should be revised or better motivated, and some Figures (5 and 6) should be revised accordingly.
I suggest publication in Solid Earth after moderate revisions. Please find below specific comments and technical corrections.

Marco Mercuri

Specific comments
The Introduction section is well written and the contents are appropriate for this work. However, I find it quite long and composed by a single sub-section (Review). I suggest reorganizing the Introduction section into subsections and, if possible, reducing its length to better highlight the main aim of the work. Perhaps some parts could be moved to the Discussion section.

Very interesting part of the introduction at lines 56-64

Line 83; 103-104; Please refer to literature and/or briefly explain with text or a table or a figure the different topological parameters (connection per branch, fracture intensity, dimensionless intensity …)

I am not an expert in this area, so I find lines 127-130 not easily understandable. What is the kinematics of the E-W faults? I assume it is left-lateral from the presence of NE-SW extension fractures in their damage zone. Is it?

Data & Methods. Looking at the different scales of observation, I noticed that a scale similar to 1:1000 has not been considered. I suppose a “basemap” for mapping fractures at such a scale does not exist for the study area, and perhaps this should be stated in the text. Just a curiosity: have you considered the usage of Bing Maps/Google Maps, or is there too much vegetation?

Table 1. What do you mean by “cell size”? Please explain it better in the text

Table 3. What is the difference between Number of Traces and “Number of Traces (Real)”. Please, explain it in the caption or in the text.

Table 3. I suggest accompanying the absolute number of each type of node and branch with the relative percentage for higher clarity.

L295. “Same trend is seen with Dimensionless Intensity B22”. The values of B22 are quite similar at different scales, but the trend of P21 with scale is actually the opposite. Please fix the sentence.

L295-297. “Connections per Trace and Connections per Branch display a trend with values decreasing as the scale increases with the 1:10 scale having the lowest value”. I agree, but values of connection per Branch at 1:20.000 and 1:200.000 scales are actually pretty similar (1.75 and 1.85). I suggest underlying this point.

L316-317 and Fig. 5. “The cut-off proportion (i.e., amount of data removed by the application of the cut-off) for the 1:10 scale is very high with 97.82 % of data being cut off.” Maybe I do not understand this sentence correctly. Do you mean the power law fit is performed on the remaining data (i.e. about 2% of data), or that the fit is performed on 97.82% of data? I am not sure that a fit performed on 2% of data is statistically significant. Have you tested the exponential and lognormal fit on the whole dataset, or only on lengths longer than the power law cut-off length? If not, my suggestion is to compare the PL fit as it is with the exponential and lognormal fit performed on the whole datasets.

L363-365: “This cut-off can be estimated to be the lowest length lineaments which we can consistently interpret without truncation effects caused by resolution of the LiDAR DEM, assuming that the lineament trace lengths follow a power-law.” In my opinion, such an assumption should be better justified.

Section 5.3. I think that all the data should be shown on the plots and not only the data which are above the cut-off power law length. I think that (and it is also somewhat stated in section 5.3), as presented now, the effect of the left tail (truncation) on the potential multi-scale fit is considered (too much?), but there is also a censoring effect due to the fact that the cumulative number of longer fractures is affected by the size of the sampling window. My suggestion is to plot all the data, trying to manually fit them with a power-law which is tangent to the central part of each distribution (see also Ceccato et al., 2022).

L467-469. In my opinion, this option is very reliable. Isn't it part of the "source raster differences" (L466)?

Conclusion no 4 (Lines 491-495). OK, but you also said before that such type of analysis can be affected by a lot of biases. In my opinion, it's hard to imagine that the connectivity of a fracture network decreases with increasing detail of the analysis. I suggest removing or toning down this conclusion.

Technical corrections
Line 28. Consider using “multiple” instead of “multi-scale” to improve readability.

Lines 35-36: There is repetition from Line 27. Please remove one of them.

Line 111: The wording "The main part of Åland Islands bedrock is comprised of the 1.58 Ga Åland Batholith" is odd. Please rephrase.

Figure 1: The text in the image is very small. Perhaps enlarging the figure in the final version could fix this.

Line 132 (and in many other parts): "e.g." should not be capitalized.

Line 138: Consider using "As an example" or similar instead of "e.g." at the beginning of the sentence.

Lines 141-142: Please use consistent nomenclature here with Table 1 for better clarity.

Line 206: There is a "?" in the brackets. Please remove it.

Lines 215-217: Please use P22 instead of P21.

Figure 3: The white text in the image is not easily readable. Please change the color of the text.

Figure 6: Please provide an explanation of the acronyms (e.g., ANCCM) in the caption.

Line 392: Please rephrase as "[...] with high geophysical but low topographic signals."

Lines 481-483: Please rephrase the sentence to be more concise.

References: Please pay attention to the formatting of some references (e.g. capital letters for the reference at Line 610).
Citation: https://doi.org/10.5194/egusphere-2022-1363-RC2
- AC3:
  'Reply on RC2', Nikolas Ovaskainen, 05 Apr 2023
  Dear Reviewer 2, Marco Mercuri,
  Thank you for the constructive review and comments. The comments on the
  
  data analysis resulted in the additional analysis in the Appendix to
  
  satisfy a missing part in our length distribution analysis. Furthermore, it
  
  resulted in more clear explanations in the text for our decisions regarding
  
  the analysis. Your indepth line-wise comments further resulted in a number
  
  of small fixes that overall make the paper more cohesive. See below for
  
  more specific responses to your comments. All comments are numbered
  
  to allow referencing from other responses.
  
  Line number references are to the PDF document with the changes highlighted.
  On behalf of all the authors,
  
  Turku, Finland, April 2023, Nikolas Ovaskainen
  General comments
  
  ----------------
  The manuscript by Ovaskainen and coauthors deals with a multi-scale analysis of
  
  the fracture network affecting the crystalline bedrock at the Åland Islands in
  
  Finland. The main aim of the study is to contribute to filling the gap of data
  
  sets dealing with multi-scale fracture network analyses of crystalline rocks,
  
  which might have important applications, including nuclear waste disposal. The
  
  multi-scale approach also allows filling the knowledge gap on the local
  
  fracture network at an intermediate scale length range (i.e., 100-500 m). The
  
  authors highlight that certain fracture network properties, such as length
  
  distribution and connectivity might be scale-dependent. I think this study
  
  represents an interesting example of a multi-scale analysis of a fracture
  
  network. The study is very well performed, particularly for the collection of
  
  a very robust dataset and for the usage of up-to-date methods for fracture
  
  analysis, including a new software. Consequently my opinion is that the study
  
  deserves to be published in Solid Earth.
  A point which does not fully convince me is the analysis of length
  
  distribution. As described in lines 249-251 (see also Figure 5) the power law,
  
  lognormal, and exponential fit hypotheses for fitting length distribution have
  
  all been tested on the range of the lengths (traces or branches) above the
  
  power-law cut-off length. For testing the power law fit, I have no doubts on
  
  the procedure, but I would like to see also the goodness of fit for exponential
  
  and lognormal distributions calculated for the whole data set. Moreover, the
  
  data (black dots) below the cut-off are not showed on the figures (Figure 5).
  
  Such a procedure also impacts the multi-scale analysis of length distribution
  
  (Figure 6). In my opinion, all the cumulative length data should be shown in
  
  the Figures 5 and 6. To summarize, I think that the procedure for the best
  
  fitting equation should be revised or better motivated, and some Figures (5 and
  
  6) should be revised accordingly.
  1. We acknowledge the issue of representation for all length data in the
  
  individual scale length distribution plots (Figure 5). The truncated
  
  data, i.e. lengths below the cut-off, are not well represented. This is
  
  intentional and it is done to focus the plots on the data above the
  
  cut-off where all the statistical fits are done. We remedy this lack of
  
  representation in this revision by adding a figure in the Appendix with
  
  all length data and associated lognormal and exponential fits. However,
  
  such analysis is difficult to tie to multi-scale analysis without
  
  confusion for the readers (and writers) and the fits are not comparable
  
  to the fits done to cut-off truncated data (Clauset et al. 2009;
  
  lines 346-348) and
  
  consequently, the discussion around the appendix results is minimal.
  In the multi-scale plot (Figure 6), all length data is shown. The length
  
  data points above the cut-offs are colored while the greyed out points
  
  represent the data below the cut-offs. Some data points are covered by
  
  others.
  I suggest publication in Solid Earth after moderate revisions. Please find
  
  below specific comments and technical corrections.
  Marco Mercuri
  Specific comments
  
  -----------------
  The Introduction section is well written and the contents are appropriate
  
  for this work. However, I find it quite long and composed by a single
  
  sub-section (Review). I suggest reorganizing the Introduction section into
  
  subsections and, if possible, reducing its length to better highlight the
  
  main aim of the work. Perhaps some parts could be moved to the Discussion
  
  section.
  2. We have revised the introduction based on this comment and Reviewer 1
  
  comments. Text was made more concise and some was moved to the method
  
  section to remove repetition. The length has been reduced and the
  
  research questions and aims are better highlighted in the new structure.
  
  The introduction starts with a review subsection which is followed
  
  with the "Agenda of our study" subsection which should make apparent
  
  the aims of this work. The word count of the introduction was
  
  shortened from circa 1400 words to circa 1100 words.
  Very interesting part of the introduction at lines 56-64
  Line 83; 103-104; Please refer to literature and/or briefly explain with
  
  text or a table or a figure the different topological parameters
  
  (connection per branch, fracture intensity, dimensionless intensity …)
  3. We added references to the parts in the introduction where we refer
  
  to these parameters.
  I am not an expert in this area, so I find lines 127-130 not easily
  
  understandable. What is the kinematics of the E-W faults? I assume it is
  
  left-lateral from the presence of NE-SW extension fractures in their damage
  
  zone. Is it?
  4. We clarified the text to specify the varying kinematics of the E-W
  
  faults, and specified that the sinistral faults were associated with
  
  the extension fractures, as you pointed out.
  Data & Methods. Looking at the different scales of observation, I noticed
  
  that a scale similar to 1:1000 has not been considered. I suppose
  
  a “basemap” for mapping fractures at such a scale does not exist for the
  
  study area, and perhaps this should be stated in the text. Just
  
  a curiosity: have you considered the usage of Bing Maps/Google Maps, or is
  
  there too much vegetation?
  5. We have tried using satellite images from different sources and found
  
  Google Maps to be the most accurate and easily available dataset.
  
  However, as you pointed out, the vegetation is the problem. We are only
  
  able to use the images in almost perfectly exposed areas without any
  
  vegetation. In comparison, in LiDAR data the vegetation is (mostly)
  
  filtered so it can be used in more extensive areas.
  
  We have clarified this in text on lines 441-451.
  Table 1. What do you mean by “cell size”? Please explain it better in the
  
  text
  6. We clarified "cell size" on line 189.
  Table 3. What is the difference between Number of Traces and “Number of
  
  Traces (Real)”. Please, explain it in the caption or in the text.
  7. We added the "b" symbol to the parameter and explained it in the caption
  
  of Table 3.
  Table 3. I suggest accompanying the absolute number of each type of node
  
  and branch with the relative percentage for higher clarity.
  8. We have included the relative percentages of node and branch counts
  
  in Table 3.
  L295. “Same trend is seen with Dimensionless Intensity B22”. The values of
  
  B22 are quite similar at different scales, but the trend of P21 with scale
  
  is actually the opposite. Please fix the sentence.
  9. This was an error and we fixed the sentence.
  L295-297. “Connections per Trace and Connections per Branch display a trend
  
  with values decreasing as the scale increases with the 1:10 scale having
  
  the lowest value”. I agree, but values of connection per Branch at 1:20.000
  
  and 1:200.000 scales are actually pretty similar (1.75 and 1.85). I suggest
  
  underlying this point.
  10. We have noted this point in text but did also point out that the range of
  
  values for Connections per Branch is limited between 0.0 and 2.0. This
  
  amplifies these numerically small differences so the difference should be
  
  considered as at least somewhat significant.
  L316-317 and Fig. 5. “The cut-off proportion (i.e., amount of data removed
  
  by the application of the cut-off) for the 1:10 scale is very high with
  
  97.82 % of data being cut off.” Maybe I do not understand this sentence
  
  correctly. Do you mean the power law fit is performed on the remaining data
  
  (i.e. about 2% of data), or that the fit is performed on 97.82% of data?
  
  I am not sure that a fit performed on 2% of data is statistically
  
  significant.
  11. The fits are performed on only ~2 % of the fracture data so your
  
  interpretation is correct. The majority of
  
  the digitized fractures are seemingly affected by the
  
  resolution truncation effect (Pickering et al. 1995). Though this makes
  
  the fits statistically very uncertain we wished to be consistent in the
  
  analysis we performed for all data. Even though the fracture length
  
  distribution by itself might not adequately follow a power-law, it
  
  does not mean that in a multi-scale length analysis they could not still
  
  follow a common trend with the lineament data, at least partly. Therefore
  
  we wished to keep the analysis results for the individual scales to use
  
  as reference to the multi-scale results. Furthermore, another motivation
  
  for the use of the power-law comes from the physical rationale (Bonnet et
  
  al. 2001) that fractures follow some scale-independent and possibly
  
  fractal law as we mention in text on lines 319-321.
  Have you tested the exponential and lognormal fit on the whole
  
  dataset, or only on lengths longer than the power law cut-off length? If
  
  not, my suggestion is to compare the PL fit as it is with the exponential
  
  and lognormal fit performed on the whole datasets.
  12. We refer to Clauset et al. 2009 on why we cannot compare the fits to
  
  the full data to the fits on the truncated data. Clauset et al. 2009
  
  state that it is not statistically valid to compare fits that have been
  
  conducted on different data. However, we added both a figure and a table
  
  in the appendix which contains the lognormal and exponential fits to the
  
  full length data for both traces and branches (See also response 1.).
  L363-365: “This cut-off can be estimated to be the lowest length lineaments
  
  which we can consistently interpret without truncation effects caused by
  
  resolution of the LiDAR DEM, assuming that the lineament trace lengths
  
  follow a power-law.” In my opinion, such an assumption should be better
  
  justified.
  13. We have expanded the discussion around this assumption after the sentence
  
  which you pointed out on lines 428-433.
  Section 5.3. I think that all the data should be shown on the plots and not
  
  only the data which are above the cut-off power law length. I think that
  
  (and it is also somewhat stated in section 5.3), as presented now, the
  
  effect of the left tail (truncation) on the potential multi-scale fit is
  
  considered (too much?), but there is also a censoring effect due to the
  
  fact that the cumulative number of longer fractures is affected by the size
  
  of the sampling window. My suggestion is to plot all the data, trying to
  
  manually fit them with a power-law which is tangent to the central part of
  
  each distribution (see also Ceccato et al., 2022).
  14. See response 1. in regards to the missing data
  
  points (all data should be visible in the multi-scale plot). You are
  
  correct that the censoring effect of the sampling area also affects the
  
  results. We touch this issue on lines 522-527 in the "Multi-scale
  
  analysis" discussion chapter and issue recommendations for method
  
  development. We are skeptical on the use of a manual method to fit the
  
  power-law to the multi-scale data as these kinds of methods lack
  
  reproducibility and are not statistically consistent. Instead, as we
  
  discuss on lines 527-530, we recommend the development of a
  
  multi-scale fitting method which considers both the head and tail of the
  
  distribution. Furthermore, we recommend the use of the density
  
  distribution in place of the complementary cumulative number that we use
  
  in this paper. We do however still claim that there is some use in
  
  publishing the results that we have as is, as the complementary
  
  cumulative number method is used in many other studies and the results
  
  are therefore comparable to them and are more reproducible without
  
  manual fitting.
  L467-469. In my opinion, this option is very reliable. Isn't it part of the
  
  "source raster differences" (L466)?
  15. We did not fully understand your point here, as we do already state
  
  "Another option related to the raster differences ..." i.e. we already
  
  link the option to the source raster differences. We do not wish to
  
  amplify this option in our study as we provide no examination of its
  
  possibility in our digitizations but just point it out from prior
  
  studies.
  Conclusion no 4 (Lines 491-495). OK, but you also said before that such
  
  type of analysis can be affected by a lot of biases. In my opinion, it's
  
  hard to imagine that the connectivity of a fracture network decreases with
  
  increasing detail of the analysis. I suggest removing or toning down this
  
  conclusion.
  16. We appended the conclusion with the suggestion that it might be related
  
  to methods rather than nature itself. This is the point we wished
  
  to bring out and it should be more clear now thanks to your suggestion.
  Technical corrections
  
  ---------------------
  Line 28. Consider using “multiple” instead of “multi-scale” to improve
  
  readability.
  17. We changed the word to "multiple" as per your suggestion and
  
  brought up the importance of using multiple scales.
  Lines 35-36: There is repetition from Line 27. Please remove one of them.
  18. We removed the repeated lines which were originally at 35-36.
  Line 111: The wording "The main part of Åland Islands bedrock is comprised
  
  of the 1.58 Ga Åland Batholith" is odd. Please rephrase.
  19. We rephrased to clarify that we mean by the main island.
  Figure 1: The text in the image is very small. Perhaps enlarging the figure
  
  in the final version could fix this.
  20. We enlarged the figure in the pdf and the text is consequently more
  
  clear.
  Line 132 (and in many other parts): "e.g." should not be capitalized.
  21. Thank you, we fixed the capitalizations.
  Line 138: Consider using "As an example" or similar instead of "e.g." at
  
  the beginning of the sentence.
  22. We have changed some uses of "e.g.", particularly at beginnings
  
  of sentences to use "for example". This should improve readability.
  Lines 141-142: Please use consistent nomenclature here with Table 1 for
  
  better clarity.
  23. We have added clarifications both to the Table 1 caption and to the text.
  
  We specify by what terms we refer to the resolution and areal extent.
  
  However, we believe including the specific terms we use ("Cell Size" and
  
  "Total Target Area") along with the more general terms is justified.
  
  Resolution is a more general term compared to the "Cell Size" which more
  
  specifically states how we defined the resolution for raster datasets.
  
  We also refer to "target areas" many times in text.
  Line 206: There is a "?" in the brackets. Please remove it.
  24. We fixed the citation to Rohrbaugh et al. 2002 as was originally
  
  intended.
  Lines 215-217: Please use P22 instead of P21.
  25. We fixed the reference from "Dimensionless Intensity P21" to "Dimensionless
  
  Intensity P22" as you pointed out!
  Figure 3: The white text in the image is not easily readable. Please change
  
  the color of the text.
  26. We changed to color of the labels in Figure 3 to have a orange foreground.
  
  This makes them stand out more in the images. We also increased
  
  the size of the points that were associated with the labels as they
  
  were almost imperceptible before as you pointed out.
  Figure 6: Please provide an explanation of the acronyms (e.g., ANCCM) in
  
  the caption.
  27. We included explanations of both ANCCM and MSLE in the Figure 6 caption.
  Line 392: Please rephrase as "[...] with high geophysical but low
  
  topographic signals."
  28. We removed the "and" word to fix the sentence.
  Lines 481-483: Please rephrase the sentence to be more concise.
  29. We made the conclusion more concise as suggested.
  References: Please pay attention to the formatting of some references (e.g.
  
  capital letters for the reference at Line 610).
  30. We fixed the capitalized letters in the titles of some references
  
  including the referred Middleton et al. 2015 reference on line 610.
  Additional fixes unrelated to specific referee comments:
  Modified Figure 3 to include the second, missing, eastern 1:20 000 circular target area.
  
  Fixed small reference errors.
  
  Modified all figure sub-labels to use "(a)", "(b)", ... instead of "A.", ... in figures captions and in text.
  
  Increased font size in Figure 4.
  
  Headers were fixed to only have the first letter capitalized.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC3

Status: closed

CC1:
'Comment on egusphere-2022-1363', Matthis Frey, 28 Dec 2022

Dear Nikolas,

I saw that you cited our paper 'Interdisciplinary Fracture Network Characterization in the Crystalline Basement: A case study from the Southern Odenwald, SW Germany' (Frey et al. 2021) in your preprint. Thanks for this. Please note however that your citation refers to the preprint. The accepted article was published earlier this year: https://doi.org/10.5194/se-13-935-2022

Please change the reference accordingly.

Kind regards

Matthis Frey

Citation: https://doi.org/10.5194/egusphere-2022-1363-CC1
- AC1: 'Reply on CC1', Nikolas Ovaskainen, 02 Jan 2023
  
  Hey Matthis,
  Thank you for taking the time to notify about this! We will update to the proper citation as we continue our work on the manuscript. Using the preprint was an oversight.
  Cheers,
  Nikolas
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC1
RC1:
'Comment on egusphere-2022-1363', Anonymous Referee #1, 10 Jan 2023
The paper is well written, the methods up-to-date and the related results very interesting and statistically robust. The methods are adequately described, the limitation discussed and their reliability and representativeness of the obtained results considered as well. However, some further discussions on methods/results reliability and robustness are needed.

There is a main problem which undermines the possibility to publish the present manuscript in Solid Earth: the aim of the research is not clearly stated and thus it is not clear if the presented methods and results are significant or have any relevant implications for the case study or what are the broader implications for the general analyses of lineament maps from remote sensing. Stating clearly what are the aims and how the presented methods/results can answer to the research questions will also help in reorganizing logically the discussion sections. The paper would be also good if it was clearly focused on the presentation of the new analytical tools and the results adopted for the characterization of a case study, but still the case study need to have a clear aim. I think that the Authors can re-arrange the present manuscript with little effort in order to solve this main issue, otherwise I would suggest to redirect the manuscript to a more specialized journal.

Main issues:

The aim of the research and the conclusions/implications of the results need to be explained a little bit more, they are not immediately understandable from reading the present manuscript. Especially in the Abstract, Introduction (where the aims are sparsely presented in bit and pieces) and in the conclusions.

There is a discrepancy between the “results and conclusions” (sparsely) reported in the introduction section and the final Conclusions of the paper in Section 6. Are the methods and results presented here resolutive for the problem they aim to solve?

The cut-off issue needs to be properly discussed in depth. What is the statistical significance of a results based on the analysis of only the 3% of the total dataset? Is it representative of the whole distribution? This needs to be discussed from the methodological point of view (is the analytical method adequate to analyse our dataset?). Is the results based on the 3% of the data representing the entire length distribution?

Minor comments.

Some part need to be rephrased to be a little bit more concise (the part of the discussion regarding glacial erosion)

Reconsider the use of “e.g.”,

Rephrase the section Lines 92-99 : to be moved to the method section and integrated with the exiting description of the data source.

Line 206: “?”?
Citation: https://doi.org/10.5194/egusphere-2022-1363-RC1
- AC2:
  'Reply on RC1', Nikolas Ovaskainen, 05 Apr 2023
  Dear Reviewer 1,
  Thank you for the constructive review and comments. Specifically, the
  
  criticism on the lack of clear motivation in the introduction resulted in
  
  a major revision of the introduction to better highlight the motivation and
  
  to link the contents of the introduction to the rest of the paper. See
  
  below for specific responses to your comments. All comments are numbered to
  
  allow referencing from other responses. Line number references are to the PDF document with the changes highlighted.
  On behalf of all the authors,
  
  Turku, Finland, April 2023, Nikolas Ovaskainen
  The paper is well written, the methods up-to-date and the related
  
  results very interesting and statistically robust. The methods are
  
  adequately described, the limitation discussed and their reliability and
  
  representativeness of the obtained results considered as well. However,
  
  some further discussions on methods/results reliability and robustness
  
  are needed.
  There is a main problem which undermines the possibility to publish the
  
  present manuscript in Solid Earth: the aim of the research is not
  
  clearly stated and thus it is not clear if the presented methods and
  
  results are significant or have any relevant implications for the case
  
  study or what are the broader implications for the general analyses of
  
  lineament maps from remote sensing. Stating clearly what are the aims
  
  and how the presented methods/results can answer to the research
  
  questions will also help in reorganizing logically the discussion
  
  sections. The paper would be also good if it was clearly focused on the
  
  presentation of the new analytical tools and the results adopted for the
  
  characterization of a case study, but still the case study need to have
  
  a clear aim. I think that the Authors can re-arrange the present
  
  manuscript with little effort in order to solve this main issue,
  
  otherwise I would suggest to redirect the manuscript to a more
  
  specialized journal.
  Main issues
  
  -----------
  The aim of the research and the conclusions/implications of the results
  
  need to be explained a little bit more, they are not immediately
  
  understandable from reading the present manuscript. Especially in the
  
  Abstract, Introduction (where the aims are sparsely presented in bit and
  
  pieces) and in the conclusions. There is a discrepancy between the “results
  
  and conclusions” (sparsely) reported in the introduction section and the
  
  final Conclusions of the paper in Section 6. Are the methods and results
  
  presented here resolutive for the problem they aim to solve?
  1. We have clarified our motivation and aim primarily in the introduction
  
  and added discussion on data, method and statistical reliability based on
  
  comments by both Reviewers. The methods for multi-scale analysis of
  
  fractures and lineaments have been developed for decades but there still
  
  lacks any easily usable common convention for the analysis. Therefore,
  
  some "method development" text must be included in the manuscript to
  
  explain the methods we used. Furthermore, there does not exist any
  
  multi-scale datasets from Finland outside of our very limited prior
  
  research. So there is demand for both datasets and method development and
  
  therefore the focus is on both goals in this manuscript. Multi-scale data
  
  collection, geologic setting and the analysis all cause uncertainties in
  
  the results and in the discussion section we therefore have to consider
  
  all with limited ability to completely separate the discussions about
  
  them as their effect in the results cannot be separated either.
  The cut-off issue needs to be properly discussed in depth. What is the
  
  statistical significance of a results based on the analysis of only the 3% of
  
  the total dataset? Is it representative of the whole distribution? This needs
  
  to be discussed from the methodological point of view (is the analytical method
  
  adequate to analyse our dataset?). Is the results based on the 3% of the data
  
  representing the entire length distribution?
  2. This issue was also pointed out by Reviewer 2. See the answer we gave
  
  there in response number 11.
  Minor comments
  
  --------------
  Some part need to be rephrased to be a little bit more concise (the part of
  
  the discussion regarding glacial erosion)
  3. We have made the discussion section more concise around the
  
  discussion on the effect of glacial erosion. See lines 495-516.
  Reconsider the use of “e.g.”,
  4. The copernicus template for latex submissions that we used
  
  had "e.g." with the comma in numerous examples. If this paper enters the
  
  typesetting phase we will fix these details as instructed.
  Rephrase the section Lines 92-99 : to be moved to the method section and
  
  integrated with the exiting description of the data source.
  5. We moved much of the repeated information about the data to the
  
  method section where we added any missing information that was
  
  only in the introduction. See lines 120-136 in the introduction.
  Line 206: “?”?
  6. The reference is fixed to Rohrbaugh et al. 2002 as was intended.
  Additional fixes unrelated to specific referee comments:
  Modified Figure 3 to include the second, missing, eastern 1:20 000 circular target area.
  
  Fixed small reference errors.
  
  Modified all figure sub-labels to use "(a)", "(b)", ... instead of "A.", ... in figures captions and in text.
  
  Increased font size in Figure 4.
  
  Headers were fixed to only have the first letter capitalized.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC2
RC2:
'Comment on egusphere-2022-1363', Marco Mercuri, 13 Mar 2023
General comments

The manuscript by Ovaskainen and coauthors deals with a multi-scale analysis of the fracture network affecting the crystalline bedrock at the Åland Islands in Finland. The main aim of the study is to contribute to filling the gap of data sets dealing with multi-scale fracture network analyses of crystalline rocks, which might have important applications, including nuclear waste disposal. The multi-scale approach also allows filling the knowledge gap on the local fracture network at an intermediate scale length range (i.e., 100-500 m). The authors highlight that certain fracture network properties, such as length distribution and connectivity might be scale-dependent. I think this study represents an interesting example of a multi-scale analysis of a fracture network. The study is very well performed, particularly for the collection of a very robust dataset and for the usage of up-to-date methods for fracture analysis, including a new software. Consequently my opinion is that the study deserves to be published in Solid Earth.
A point which does not fully convince me is the analysis of length distribution. As described in lines 249-251 (see also Figure 5) the power law, lognormal, and exponential fit hypotheses for fitting length distribution have all been tested on the range of the lengths (traces or branches) above the power-law cut-off length. For testing the power law fit, I have no doubts on the procedure, but I would like to see also the goodness of fit for exponential and lognormal distributions calculated for the whole data set. Moreover, the data (black dots) below the cut-off are not showed on the figures (Figure 5). Such a procedure also impacts the multi-scale analysis of length distribution (Figure 6). In my opinion, all the cumulative length data should be shown in the Figures 5 and 6. To summarize, I think that the procedure for the best fitting equation should be revised or better motivated, and some Figures (5 and 6) should be revised accordingly.
I suggest publication in Solid Earth after moderate revisions. Please find below specific comments and technical corrections.

Marco Mercuri

Specific comments
The Introduction section is well written and the contents are appropriate for this work. However, I find it quite long and composed by a single sub-section (Review). I suggest reorganizing the Introduction section into subsections and, if possible, reducing its length to better highlight the main aim of the work. Perhaps some parts could be moved to the Discussion section.

Very interesting part of the introduction at lines 56-64

Line 83; 103-104; Please refer to literature and/or briefly explain with text or a table or a figure the different topological parameters (connection per branch, fracture intensity, dimensionless intensity …)

I am not an expert in this area, so I find lines 127-130 not easily understandable. What is the kinematics of the E-W faults? I assume it is left-lateral from the presence of NE-SW extension fractures in their damage zone. Is it?

Data & Methods. Looking at the different scales of observation, I noticed that a scale similar to 1:1000 has not been considered. I suppose a “basemap” for mapping fractures at such a scale does not exist for the study area, and perhaps this should be stated in the text. Just a curiosity: have you considered the usage of Bing Maps/Google Maps, or is there too much vegetation?

Table 1. What do you mean by “cell size”? Please explain it better in the text

Table 3. What is the difference between Number of Traces and “Number of Traces (Real)”. Please, explain it in the caption or in the text.

Table 3. I suggest accompanying the absolute number of each type of node and branch with the relative percentage for higher clarity.

L295. “Same trend is seen with Dimensionless Intensity B22”. The values of B22 are quite similar at different scales, but the trend of P21 with scale is actually the opposite. Please fix the sentence.

L295-297. “Connections per Trace and Connections per Branch display a trend with values decreasing as the scale increases with the 1:10 scale having the lowest value”. I agree, but values of connection per Branch at 1:20.000 and 1:200.000 scales are actually pretty similar (1.75 and 1.85). I suggest underlying this point.

L316-317 and Fig. 5. “The cut-off proportion (i.e., amount of data removed by the application of the cut-off) for the 1:10 scale is very high with 97.82 % of data being cut off.” Maybe I do not understand this sentence correctly. Do you mean the power law fit is performed on the remaining data (i.e. about 2% of data), or that the fit is performed on 97.82% of data? I am not sure that a fit performed on 2% of data is statistically significant. Have you tested the exponential and lognormal fit on the whole dataset, or only on lengths longer than the power law cut-off length? If not, my suggestion is to compare the PL fit as it is with the exponential and lognormal fit performed on the whole datasets.

L363-365: “This cut-off can be estimated to be the lowest length lineaments which we can consistently interpret without truncation effects caused by resolution of the LiDAR DEM, assuming that the lineament trace lengths follow a power-law.” In my opinion, such an assumption should be better justified.

Section 5.3. I think that all the data should be shown on the plots and not only the data which are above the cut-off power law length. I think that (and it is also somewhat stated in section 5.3), as presented now, the effect of the left tail (truncation) on the potential multi-scale fit is considered (too much?), but there is also a censoring effect due to the fact that the cumulative number of longer fractures is affected by the size of the sampling window. My suggestion is to plot all the data, trying to manually fit them with a power-law which is tangent to the central part of each distribution (see also Ceccato et al., 2022).

L467-469. In my opinion, this option is very reliable. Isn't it part of the "source raster differences" (L466)?

Conclusion no 4 (Lines 491-495). OK, but you also said before that such type of analysis can be affected by a lot of biases. In my opinion, it's hard to imagine that the connectivity of a fracture network decreases with increasing detail of the analysis. I suggest removing or toning down this conclusion.

Technical corrections
Line 28. Consider using “multiple” instead of “multi-scale” to improve readability.

Lines 35-36: There is repetition from Line 27. Please remove one of them.

Line 111: The wording "The main part of Åland Islands bedrock is comprised of the 1.58 Ga Åland Batholith" is odd. Please rephrase.

Figure 1: The text in the image is very small. Perhaps enlarging the figure in the final version could fix this.

Line 132 (and in many other parts): "e.g." should not be capitalized.

Line 138: Consider using "As an example" or similar instead of "e.g." at the beginning of the sentence.

Lines 141-142: Please use consistent nomenclature here with Table 1 for better clarity.

Line 206: There is a "?" in the brackets. Please remove it.

Lines 215-217: Please use P22 instead of P21.

Figure 3: The white text in the image is not easily readable. Please change the color of the text.

Figure 6: Please provide an explanation of the acronyms (e.g., ANCCM) in the caption.

Line 392: Please rephrase as "[...] with high geophysical but low topographic signals."

Lines 481-483: Please rephrase the sentence to be more concise.

References: Please pay attention to the formatting of some references (e.g. capital letters for the reference at Line 610).
Citation: https://doi.org/10.5194/egusphere-2022-1363-RC2
- AC3:
  'Reply on RC2', Nikolas Ovaskainen, 05 Apr 2023
  Dear Reviewer 2, Marco Mercuri,
  Thank you for the constructive review and comments. The comments on the
  
  data analysis resulted in the additional analysis in the Appendix to
  
  satisfy a missing part in our length distribution analysis. Furthermore, it
  
  resulted in more clear explanations in the text for our decisions regarding
  
  the analysis. Your indepth line-wise comments further resulted in a number
  
  of small fixes that overall make the paper more cohesive. See below for
  
  more specific responses to your comments. All comments are numbered
  
  to allow referencing from other responses.
  
  Line number references are to the PDF document with the changes highlighted.
  On behalf of all the authors,
  
  Turku, Finland, April 2023, Nikolas Ovaskainen
  General comments
  
  ----------------
  The manuscript by Ovaskainen and coauthors deals with a multi-scale analysis of
  
  the fracture network affecting the crystalline bedrock at the Åland Islands in
  
  Finland. The main aim of the study is to contribute to filling the gap of data
  
  sets dealing with multi-scale fracture network analyses of crystalline rocks,
  
  which might have important applications, including nuclear waste disposal. The
  
  multi-scale approach also allows filling the knowledge gap on the local
  
  fracture network at an intermediate scale length range (i.e., 100-500 m). The
  
  authors highlight that certain fracture network properties, such as length
  
  distribution and connectivity might be scale-dependent. I think this study
  
  represents an interesting example of a multi-scale analysis of a fracture
  
  network. The study is very well performed, particularly for the collection of
  
  a very robust dataset and for the usage of up-to-date methods for fracture
  
  analysis, including a new software. Consequently my opinion is that the study
  
  deserves to be published in Solid Earth.
  A point which does not fully convince me is the analysis of length
  
  distribution. As described in lines 249-251 (see also Figure 5) the power law,
  
  lognormal, and exponential fit hypotheses for fitting length distribution have
  
  all been tested on the range of the lengths (traces or branches) above the
  
  power-law cut-off length. For testing the power law fit, I have no doubts on
  
  the procedure, but I would like to see also the goodness of fit for exponential
  
  and lognormal distributions calculated for the whole data set. Moreover, the
  
  data (black dots) below the cut-off are not showed on the figures (Figure 5).
  
  Such a procedure also impacts the multi-scale analysis of length distribution
  
  (Figure 6). In my opinion, all the cumulative length data should be shown in
  
  the Figures 5 and 6. To summarize, I think that the procedure for the best
  
  fitting equation should be revised or better motivated, and some Figures (5 and
  
  6) should be revised accordingly.
  1. We acknowledge the issue of representation for all length data in the
  
  individual scale length distribution plots (Figure 5). The truncated
  
  data, i.e. lengths below the cut-off, are not well represented. This is
  
  intentional and it is done to focus the plots on the data above the
  
  cut-off where all the statistical fits are done. We remedy this lack of
  
  representation in this revision by adding a figure in the Appendix with
  
  all length data and associated lognormal and exponential fits. However,
  
  such analysis is difficult to tie to multi-scale analysis without
  
  confusion for the readers (and writers) and the fits are not comparable
  
  to the fits done to cut-off truncated data (Clauset et al. 2009;
  
  lines 346-348) and
  
  consequently, the discussion around the appendix results is minimal.
  In the multi-scale plot (Figure 6), all length data is shown. The length
  
  data points above the cut-offs are colored while the greyed out points
  
  represent the data below the cut-offs. Some data points are covered by
  
  others.
  I suggest publication in Solid Earth after moderate revisions. Please find
  
  below specific comments and technical corrections.
  Marco Mercuri
  Specific comments
  
  -----------------
  The Introduction section is well written and the contents are appropriate
  
  for this work. However, I find it quite long and composed by a single
  
  sub-section (Review). I suggest reorganizing the Introduction section into
  
  subsections and, if possible, reducing its length to better highlight the
  
  main aim of the work. Perhaps some parts could be moved to the Discussion
  
  section.
  2. We have revised the introduction based on this comment and Reviewer 1
  
  comments. Text was made more concise and some was moved to the method
  
  section to remove repetition. The length has been reduced and the
  
  research questions and aims are better highlighted in the new structure.
  
  The introduction starts with a review subsection which is followed
  
  with the "Agenda of our study" subsection which should make apparent
  
  the aims of this work. The word count of the introduction was
  
  shortened from circa 1400 words to circa 1100 words.
  Very interesting part of the introduction at lines 56-64
  Line 83; 103-104; Please refer to literature and/or briefly explain with
  
  text or a table or a figure the different topological parameters
  
  (connection per branch, fracture intensity, dimensionless intensity …)
  3. We added references to the parts in the introduction where we refer
  
  to these parameters.
  I am not an expert in this area, so I find lines 127-130 not easily
  
  understandable. What is the kinematics of the E-W faults? I assume it is
  
  left-lateral from the presence of NE-SW extension fractures in their damage
  
  zone. Is it?
  4. We clarified the text to specify the varying kinematics of the E-W
  
  faults, and specified that the sinistral faults were associated with
  
  the extension fractures, as you pointed out.
  Data & Methods. Looking at the different scales of observation, I noticed
  
  that a scale similar to 1:1000 has not been considered. I suppose
  
  a “basemap” for mapping fractures at such a scale does not exist for the
  
  study area, and perhaps this should be stated in the text. Just
  
  a curiosity: have you considered the usage of Bing Maps/Google Maps, or is
  
  there too much vegetation?
  5. We have tried using satellite images from different sources and found
  
  Google Maps to be the most accurate and easily available dataset.
  
  However, as you pointed out, the vegetation is the problem. We are only
  
  able to use the images in almost perfectly exposed areas without any
  
  vegetation. In comparison, in LiDAR data the vegetation is (mostly)
  
  filtered so it can be used in more extensive areas.
  
  We have clarified this in text on lines 441-451.
  Table 1. What do you mean by “cell size”? Please explain it better in the
  
  text
  6. We clarified "cell size" on line 189.
  Table 3. What is the difference between Number of Traces and “Number of
  
  Traces (Real)”. Please, explain it in the caption or in the text.
  7. We added the "b" symbol to the parameter and explained it in the caption
  
  of Table 3.
  Table 3. I suggest accompanying the absolute number of each type of node
  
  and branch with the relative percentage for higher clarity.
  8. We have included the relative percentages of node and branch counts
  
  in Table 3.
  L295. “Same trend is seen with Dimensionless Intensity B22”. The values of
  
  B22 are quite similar at different scales, but the trend of P21 with scale
  
  is actually the opposite. Please fix the sentence.
  9. This was an error and we fixed the sentence.
  L295-297. “Connections per Trace and Connections per Branch display a trend
  
  with values decreasing as the scale increases with the 1:10 scale having
  
  the lowest value”. I agree, but values of connection per Branch at 1:20.000
  
  and 1:200.000 scales are actually pretty similar (1.75 and 1.85). I suggest
  
  underlying this point.
  10. We have noted this point in text but did also point out that the range of
  
  values for Connections per Branch is limited between 0.0 and 2.0. This
  
  amplifies these numerically small differences so the difference should be
  
  considered as at least somewhat significant.
  L316-317 and Fig. 5. “The cut-off proportion (i.e., amount of data removed
  
  by the application of the cut-off) for the 1:10 scale is very high with
  
  97.82 % of data being cut off.” Maybe I do not understand this sentence
  
  correctly. Do you mean the power law fit is performed on the remaining data
  
  (i.e. about 2% of data), or that the fit is performed on 97.82% of data?
  
  I am not sure that a fit performed on 2% of data is statistically
  
  significant.
  11. The fits are performed on only ~2 % of the fracture data so your
  
  interpretation is correct. The majority of
  
  the digitized fractures are seemingly affected by the
  
  resolution truncation effect (Pickering et al. 1995). Though this makes
  
  the fits statistically very uncertain we wished to be consistent in the
  
  analysis we performed for all data. Even though the fracture length
  
  distribution by itself might not adequately follow a power-law, it
  
  does not mean that in a multi-scale length analysis they could not still
  
  follow a common trend with the lineament data, at least partly. Therefore
  
  we wished to keep the analysis results for the individual scales to use
  
  as reference to the multi-scale results. Furthermore, another motivation
  
  for the use of the power-law comes from the physical rationale (Bonnet et
  
  al. 2001) that fractures follow some scale-independent and possibly
  
  fractal law as we mention in text on lines 319-321.
  Have you tested the exponential and lognormal fit on the whole
  
  dataset, or only on lengths longer than the power law cut-off length? If
  
  not, my suggestion is to compare the PL fit as it is with the exponential
  
  and lognormal fit performed on the whole datasets.
  12. We refer to Clauset et al. 2009 on why we cannot compare the fits to
  
  the full data to the fits on the truncated data. Clauset et al. 2009
  
  state that it is not statistically valid to compare fits that have been
  
  conducted on different data. However, we added both a figure and a table
  
  in the appendix which contains the lognormal and exponential fits to the
  
  full length data for both traces and branches (See also response 1.).
  L363-365: “This cut-off can be estimated to be the lowest length lineaments
  
  which we can consistently interpret without truncation effects caused by
  
  resolution of the LiDAR DEM, assuming that the lineament trace lengths
  
  follow a power-law.” In my opinion, such an assumption should be better
  
  justified.
  13. We have expanded the discussion around this assumption after the sentence
  
  which you pointed out on lines 428-433.
  Section 5.3. I think that all the data should be shown on the plots and not
  
  only the data which are above the cut-off power law length. I think that
  
  (and it is also somewhat stated in section 5.3), as presented now, the
  
  effect of the left tail (truncation) on the potential multi-scale fit is
  
  considered (too much?), but there is also a censoring effect due to the
  
  fact that the cumulative number of longer fractures is affected by the size
  
  of the sampling window. My suggestion is to plot all the data, trying to
  
  manually fit them with a power-law which is tangent to the central part of
  
  each distribution (see also Ceccato et al., 2022).
  14. See response 1. in regards to the missing data
  
  points (all data should be visible in the multi-scale plot). You are
  
  correct that the censoring effect of the sampling area also affects the
  
  results. We touch this issue on lines 522-527 in the "Multi-scale
  
  analysis" discussion chapter and issue recommendations for method
  
  development. We are skeptical on the use of a manual method to fit the
  
  power-law to the multi-scale data as these kinds of methods lack
  
  reproducibility and are not statistically consistent. Instead, as we
  
  discuss on lines 527-530, we recommend the development of a
  
  multi-scale fitting method which considers both the head and tail of the
  
  distribution. Furthermore, we recommend the use of the density
  
  distribution in place of the complementary cumulative number that we use
  
  in this paper. We do however still claim that there is some use in
  
  publishing the results that we have as is, as the complementary
  
  cumulative number method is used in many other studies and the results
  
  are therefore comparable to them and are more reproducible without
  
  manual fitting.
  L467-469. In my opinion, this option is very reliable. Isn't it part of the
  
  "source raster differences" (L466)?
  15. We did not fully understand your point here, as we do already state
  
  "Another option related to the raster differences ..." i.e. we already
  
  link the option to the source raster differences. We do not wish to
  
  amplify this option in our study as we provide no examination of its
  
  possibility in our digitizations but just point it out from prior
  
  studies.
  Conclusion no 4 (Lines 491-495). OK, but you also said before that such
  
  type of analysis can be affected by a lot of biases. In my opinion, it's
  
  hard to imagine that the connectivity of a fracture network decreases with
  
  increasing detail of the analysis. I suggest removing or toning down this
  
  conclusion.
  16. We appended the conclusion with the suggestion that it might be related
  
  to methods rather than nature itself. This is the point we wished
  
  to bring out and it should be more clear now thanks to your suggestion.
  Technical corrections
  
  ---------------------
  Line 28. Consider using “multiple” instead of “multi-scale” to improve
  
  readability.
  17. We changed the word to "multiple" as per your suggestion and
  
  brought up the importance of using multiple scales.
  Lines 35-36: There is repetition from Line 27. Please remove one of them.
  18. We removed the repeated lines which were originally at 35-36.
  Line 111: The wording "The main part of Åland Islands bedrock is comprised
  
  of the 1.58 Ga Åland Batholith" is odd. Please rephrase.
  19. We rephrased to clarify that we mean by the main island.
  Figure 1: The text in the image is very small. Perhaps enlarging the figure
  
  in the final version could fix this.
  20. We enlarged the figure in the pdf and the text is consequently more
  
  clear.
  Line 132 (and in many other parts): "e.g." should not be capitalized.
  21. Thank you, we fixed the capitalizations.
  Line 138: Consider using "As an example" or similar instead of "e.g." at
  
  the beginning of the sentence.
  22. We have changed some uses of "e.g.", particularly at beginnings
  
  of sentences to use "for example". This should improve readability.
  Lines 141-142: Please use consistent nomenclature here with Table 1 for
  
  better clarity.
  23. We have added clarifications both to the Table 1 caption and to the text.
  
  We specify by what terms we refer to the resolution and areal extent.
  
  However, we believe including the specific terms we use ("Cell Size" and
  
  "Total Target Area") along with the more general terms is justified.
  
  Resolution is a more general term compared to the "Cell Size" which more
  
  specifically states how we defined the resolution for raster datasets.
  
  We also refer to "target areas" many times in text.
  Line 206: There is a "?" in the brackets. Please remove it.
  24. We fixed the citation to Rohrbaugh et al. 2002 as was originally
  
  intended.
  Lines 215-217: Please use P22 instead of P21.
  25. We fixed the reference from "Dimensionless Intensity P21" to "Dimensionless
  
  Intensity P22" as you pointed out!
  Figure 3: The white text in the image is not easily readable. Please change
  
  the color of the text.
  26. We changed to color of the labels in Figure 3 to have a orange foreground.
  
  This makes them stand out more in the images. We also increased
  
  the size of the points that were associated with the labels as they
  
  were almost imperceptible before as you pointed out.
  Figure 6: Please provide an explanation of the acronyms (e.g., ANCCM) in
  
  the caption.
  27. We included explanations of both ANCCM and MSLE in the Figure 6 caption.
  Line 392: Please rephrase as "[...] with high geophysical but low
  
  topographic signals."
  28. We removed the "and" word to fix the sentence.
  Lines 481-483: Please rephrase the sentence to be more concise.
  29. We made the conclusion more concise as suggested.
  References: Please pay attention to the formatting of some references (e.g.
  
  capital letters for the reference at Line 610).
  30. We fixed the capitalized letters in the titles of some references
  
  including the referred Middleton et al. 2015 reference on line 610.
  Additional fixes unrelated to specific referee comments:
  Modified Figure 3 to include the second, missing, eastern 1:20 000 circular target area.
  
  Fixed small reference errors.
  
  Modified all figure sub-labels to use "(a)", "(b)", ... instead of "A.", ... in figures captions and in text.
  
  Increased font size in Figure 4.
  
  Headers were fixed to only have the first letter capitalized.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1363-AC3

Nikolas Aleksi Ovaskainen et al.

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Short summary

We have studied fracturing of the bedrock at Åland Islands from bedrock outcrops and digital elevation models using multiple scales of observation. Using the results we can compare properties of the fractures of different sizes to find similarities and differences. E.g., we found that glacial erosion has probable effect on the study of larger bedrock structures. Furthermore, we collected data from 100 to 500 m long fractures which have previously been proven to be difficult to sample.


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