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

    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.

    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.