We thank the reviewer for their thorough review of the manuscript and their constructive feedback that we believe has helped identify some minor shortcomings. We have attempted to address their comments appropriately and have fixed the editorial issues identified. Below we respond to the main comments in-line, with the reviewer’s original comments posted in italic text and our reply in normal text.

Main comments:

• The authors do not mention declustering implying that the rates (GR 'a-values) for zones and gridded seismicity are total catalog rates. I'm not up to speed on the state of PSHA practice in the EU, but we've only just moved away from using decluttered catalog rates (and the 2023 models that do-so are quite a few years out from becoming policy). At a minimum, I think what the rates represent bears mentioning (and I apologize if I missed it)

The omission of discussion regarding declustering is an oversight on our part, which we thank the reviewer for highlighting. Declustering is still current practice in Europe, and each of the three models applies it prior to constraining the activity rates; thus the activity rates reflect the rate of mainshocks. A new paragraph describing this comparison is added at the beginning of section 2.2, where we compare the calculation of the magnitude frequency relations. 

• In discussing GMMs, clarify what you're doing to compute mean sigma. Square-root-sum-of-squares SSRS? I think you refer to the 'median' for the ground motion implying the mean in carious plots is the weighted average of the medians, not the natural log means.

We appreciate the reviewer pointing out this unclear description in the figures (Figures 6 – 7). To compute the “Mean” labelled in the Figure 6, we take the sum of the median ground motions (μ_i) from each model i in the logic tree, weighted by their corresponding weights in the logic tree (w_i), i.e. Mean=∑_i (μ_i ⋅ w_i). Likewise, for the “Mean” aleatory variability in Figure 7,  Mean=∑_i (σ_i ⋅w_i ). This has now been made explicit in the captions.

• I don't think any change is necessary (because the conclusions of the paper will not be affected) but it is hard to compare three models. Difference and ratio maps are hard to digest when the subtrahend or denominator change. For future reference maybe consider holding ESHA20 (being the 'regional' model) fixed as the denominator and possibly making it easier to see how different the country models are relative to the regional one.

We understand the reviewer’s point here and agree that this may be preferable for presentation. However,  this particular form of presentation in the paper is deliberately selected to avoid indicating any of the specific models as a “reference”, even if it is just for the purposes of comparisons in the figures. Of course, if one wished to undertake such comparisons in practice, we would recommend the approach the reviewer suggests. A sentence is added here to clarify our motivation for this particular style of presentation of these comparisons.

• On line 553, what do you mean by the ERF approach? OpenSHA has a class/interface called ERF but its contract is pretty limited in scope and ruptures representing almost anything can be programmatically created to meet the needs of a model. Do you perhaps mean the inversion methodology applied in UCERF3, the 2014 USGS NSHM for the Conterminous U.S.? If yes, then I'd cite Field et al. (2015) instead:

Field EH, Biasi GP, Bird P, Dawson TE, Felzer KR, Jackson DD, Johnson KM, Jordan TH, Madden C, Michael AJ, Milner KR, Page MT, Parsons T, Powers PM, Shaw BE, Thatcher WR, Weldon RJ II and Zeng Y (2015) Long-term time-dependent probabilities for the third uniform California earthquake rupture forecast (UCERF3). Bulletin of the Seismological Society of America 105(2a): 511–543, https://doi.org/10.1785/0120140093. 

The reviewer is correct that what we are referring to here is the outcome of the inversion methodology for fault system modelling that was pioneered in the UCERF3 project. This sentence has been revised to clarify this and the citation to Field et al. (2015) added.

Editorial comments:

All the editorial comments have been addressed and changes implemented (see inline notes below for specific issues). We thank the reviewer for their thorough reading of the manuscript.

• Line 793 information 'theory'? I think as a discipline I don't think it should be modified to describe metrics

We have modified this to describe the metrics as “non-parametric measures based on information theory”.

• Line 971 (US NRC, 2018) not in references.... we use the following for citing the SSHAC procedure:

Budnitz RJ, Apostolakis G, Boore DM, et al. (1997) Recommendations for probabilistic seismic hazard analysis: Guidance on uncertainty and use of experts. Report no. NUREG/CR-6372. Washington, DC: U.S. Nuclear Regulatory Commission, 280 pp.

We thank the reviewer for clarifying the reference. We have added the bibliography entry for the SSHAC update document mentioned, which is now cited as Ake et al. (2018).

Reference list issues:

All the unused references have been removed from the bibliography.

We thank the reviewer for their positive assessment of the manuscript.

We thank the reviewers for their positive assessment of the manuscript. We have endeavoured to take into account their suggestions to improve the manuscript and provide our replies to the comments in-line below. The original comments of the reviewer are given in italic, while our replies are seen in normal text.

Some comments about the work are listed below:

• Other seismic hazard models in globe should be mentioned in “Introduction” with a comment on the similarities and differences with Central European Hazard models.

We appreciate the reviewer’s suggestion and understand that there may be some benefit for readers interested in understanding seismic hazard practice across the globe to gain perspective on how these Central European seismic hazard models compare. Even a cursory comparison would require a considerable expansion of the introductory section of this paper, and a more substantial treatment of similarities/differences would be a separate publication in itself. Given the focus of both the manuscript and the special issue of the journal to which it is intended for publication is on “Harmonised Seismic Hazard and Risk Assessment for Europe”, we believe that it would be better to keep the context more limited to discussing similarities and differences with respect to European models. For a more global perspective we would refer the reader to the Global Seismic Hazard Model of Pagani et al. (2020) (already cited in the introduction) and the interesting discussion paper of Gerstenberger et al. (2020) who look at the current state-of-the-art and at future challenges in regional and national PSHA models, particularly comparing different models from across the globe. The Gerstenberger et al (2020) reference is now added to the introduction.

• A preliminary paragraph can be presented with more detail for the reason in selecting these three models and the region.

In the revised manuscript we have added further sentences to the introduction to explain in more detail the reasons for selecting these models and case study region.

• Other models from Greece, Portugal, Spain beside ESHM13 (in Lines 49-51) may be commented.

We acknowledge the point that the author has made and note that there have been efforts in many other countries to update their seismic hazard maps since ESHM13 too, not just those listed here. A longer list can be found in the paper of Danciu et al (2024) in this issue of NHESS. We have added the case of Spain to the list mentioned in the current manuscript, which follows on from the update by Instituto Geográfico Nacional in 2017 (now cited). For Portugal and Greece we are not aware of specific national scale models being developed between ESHM13 and ESHM20 (though we are happy to be corrected here). However, we do know that following ESHM13, new efforts in these countries were initiated to expand and improve collections of geological and geophysical data that will be relevant for future seismic hazard models in these countries. Some of this data we were able to integrate into ESHM20. We have expanded this paragraph by a couple of sentences to reflect this.

• Gutenberg, B. and Richter, C.F. (1944), may be referred as the base for understanding seismicity rates, which is a fundamental component of probabilistic seismic hazard analysis.

Reference to the original publication of Gutenberg & Richter (1944) is now added.

• Basilic et al., 2013. (The European Database of Seismogenic Faults (EDSF) compiled in the framework of the Project SHARE https://seismofaults.eu/edsf13) may be commented/referred.

We take the reviewer’s point that reference is needed to the European Database of Seismic Faults. We have added in now the reference to the updated database that was used for the ESHM20, published as Basili et al. (2023) in this same special issue of NHESS. https://nhess.copernicus.org/preprints/nhess-2023-118/. 

• “Considerable degree of divergence in the tectonic zonations” should be explained commented in Line 261.

Clarification of the meaning of “degree of divergence” is now added to this sentence. The exact differences in the tectonic interpretations can be found in the sentences that follow.

• Discussions on using the complete logic tree with differences in France and Germany should take place.

We are keen to address the reviewer’s comment here, but unfortunately we have not understood where in the paper the shortcomings relating to this comment are to be found and what aspect of the topic we should address in detail. Differences in the logic trees in France and Germany and their implications for usage are addressed in detail throughout the paper. If possible, we would kindly ask if the reviewer could provide further clarification to help us resolve this issue to their satisfaction. 

• Line 200: … is not quite so clear…

Now edited to “… is not as clear and intentional as …”

• Line 552: The fundamental framework for PSHA is largely unchanged changed?

Now fixed

The original comments of the reviewer are given in italic, while our replies are in normal text.



The paper NHESS-2023-98 “Strategies for Comparison of Modern Probabilistic Seismic Hazard Models and Insights from the Germany and France Border Region” presents the quantitative comparison of three complex, independent seismic hazard models and accompanying maps at national and regional scales using metrics from informatic theory. The aim of this paper is of great interest to the seismic hazard community because so far the comparison of seismic hazard models with overlapping regions has been limited to the comparison of hazard curves for sites located in the same territory between the models. Instead, quantitative tools to compare the individual components of the hazard models have not been published yet as far as I know. I really appreciate the highlight of the reproducibility and transparency of seismic hazard models estimated using different software packages in the conclusion. This is one of the biggest limitations in comparing different PSHA studies for the same region.

We thank Dr Mosca for her positive assessment of the manuscript and detailed review.  We have endeavoured to take into account her suggestions to improve the manuscript and provide our replies to the comments in-line below. 

There are also a few adjustments, which could improve the manuscripts.

1) The manuscript attempts to explain very complex seismic hazard models in a reasonable length for an article and therefore some sentences are very difficult to follow. I would suggest simplifying the long sentences perhaps breaking them into two parts for better readability.

Several edits have been made to try to break the longer sentences. 

2) The introduction discusses the increasing complexity of seismic hazard models from the first and second generations (lines 34-35 and 72) but there are no citations of such models at national scales. To make this point clearer I would suggest to include one or two examples of first- and second-generation national hazard models for the same country.

The Swiss and Italian national seismic hazard models are now described more explicitly in the introduction section as examples of the increased complexity of the recent generation seismic hazard models compared to their predecessors.

3) In Section 2 the three models should be described in chronological order for the year of the publication starting with Germany, then France and ESHM20. Furthermore, the same features should be described for each model. For example, the earthquake catalogue is described for the FR2020 but not for DE2016 and ESHM20; the GMM component is described for DE2020 but not for DE2016 and ESHM20. The same order for the three models should be followed throughout the manuscript for both the text and the figures. For example, in Figure 5 the plots in the first column should be DE2016, second column for FR2020, and third column for ESHM20. It will help the reader to navigate through a manuscript that discusses many elements.

We thank the reviewer for their suggestions and have made the following changes to the manuscript to address them. The models are now presented in chronological order in Section 2, which continues through the text and figures. Some additional descriptions have been added in places, though we believe that in some cases the components of the models are already well described and juxtaposed to the maximum extent necessary. For example, the GMMs and GMM logic trees are clearly described in Table 1 and Section 2.4, so adding yet another description, however brief, would be to introduce repetition. 

4) I find it surprising that the earthquake catalogues, including strategies to homogenise the magnitude scale, decluster the catalogue, and assess the catalogue completeness, used by the three models are not discussed in more detail, except for a little mention in Section 2.3. Since the source models, especially the recurrence statistics of the three models, and how they differ are extensively described in the manuscript, the earthquake catalogues used to compute the recurrence parameters are a reason to explain the difference in the seismic hazard models. For this reason, they should be described better.

We take the reviewer’s point here and agree that the most complete comparison should address all of the points in the process of catalogue compilation, declustering and completeness assessment. It has been very difficult to keep comparisons of the models to a length and degree of detail appropriate for a journal paper, and the more detailed discussion on some of these topics (such as the catalogue compilation) were specifically removed as we felt they were not critical to the presentation of the key points that emerge from section 2. For the completeness assessment the short contrast of methods in section 2.3 captures the most important differences between the models, though we accept that there are details that may be of relevance for those wishing to develop new models here or to gain a highly detailed understanding of the process. We have, however, added a paragraph to Section 2.2 that expands upon the discussion of declustering.

Below there are a few (technical or editorial) comments on the manuscript.

Lines 34-35: Provide references for “several successive generations of seismic hazard models” and “multiple models”.

Two examples are listed here (Switzerland and Italy) to illustrate this. Other examples could include New Zealand, the United States, Japan, Taiwan, etc., but these contexts are slightly different from those contained here and are described in more detail in an interesting paper by Gerstenberger et al. (2020), which is now cited in the introduction.

Lines 50-51: I would suggest ordering the national seismic hazard models in chronological order.

Now re-ordered

Line 52: CEN (2004) is not listed in the reference section.

Now added

Line 66: The acronym “GMMs” does not correspond to ground motion model components. Should it be “ground motion model (GMM) components”?

Now edited

Line 71: “The increased in sophistication…” seems not correct.

Now fixed

Line 74: The acronym PoE is not explained.

Now added

Line 83: The word “and” between “proprietary software” and “into the open-source” should be deleted.

Fixed

Line 108: A word, probably “that” is missing between “Germany (DE2016 hereafter)” and “was prepared”. Also, the acronym DIBt does not correspond to Deutsches Institut für Bautechnik, should the “t” be deleted?

The sentence has been added for clarity. DIBt (with the small case t) is the official acronym for the Deutsches Institute for Bautechnik.

Line 109: DIN 4149 is not listed in the reference section.

The full reference is now added.

Line 120: It seems that 𝑆alpha and Sbeta are not explained.

This is now clarified.

Table 1: What does “315 (West) / 5985 (East)” indicate? Are east and west related to the region, i.e. roughly East and West Europe?

These refer to western Germany and to eastern Germany. This is now clarified in the table. Note that western/eastern here is merely an indication of general geographical location in Germany and does not correspond to the previous Bundesrepublik/Demokratische Republik (i.e. West Germany/East Germany) national boundaries.

Lines 159-160: In the sentence “large scale area zones delineating tectonically based 160 domains (“Grands Domaines”)” some wording is missing.

The sentence was incorrectly punctuated. This is now fixed for clarity.

Lines 169-170: It is difficult to understand how “the smoothed seismicity branches differ in approach between FR2020 and DE2016”. Is there a specific reference for the zoneless approach in FR2020? Similarly, for the comparison of the zoneless model for DE2016 and ESHM20, the reference of Helmstetter and Werner (2012) should be included in lines 169-170.

An additional clarification has now been made to explain the difference between the “adaptive” kernel smoothing approach used in FR2020 and ESHM20, in which the bandwidth is dependent on the local density of seismicity for a given earthquake location, and that of DE2016 in which the bandwidth is purely magnitude dependent. The Helmstetter & Werner (2012) reference is added here too (but kept in place later as it is referring to a different part of the process).

Line 184: Add the references for “existing models from Belgium, Switzerland, and the United Kingdom”.

References have been added for Switzerland and the United Kingdom; however, no relevant open publication could be identified for Belgium.

Line 210: If the comparison between the smoothed seismicity models is done earlier (i.e. lines 169-170) this reference should be also cited earlier (see also previous comment). Alternatively, such a comparison (“The smoothed seismicity branches differ in approach from those found in both FR2020 and ESHM20, as DE2016 uses an adaptive kernel with magnitude-dependent 170 bandwidth based on the method of Woo (1996).”) can be moved here.

See reply to earlier comment regarding the smoothed seismicity.

Line 246: The “;” does not seem the correct punctuation. Perhaps it can be replaced with “. This is”. In any case, this sentence is very long and could be simplified by dividing it into 2 (or even 3) parts.

The sentence has now been revised and split.

Lines 162-163: The word “define” is repeated twice in the same sentence (“one another in defining three zones of similar extent that define the Paris Basin,”). A synonym could replace one of them.

The second “define” is now switched to “delineate”.

Line 284: Is there anything missing in “… of with dm..”?

This typo has now been fixed (it should be “of width dm”)

Line 285: Add a comma between “(0,(m)” and “the epistemic…”.

This is now edited.

Line 287: The citation “Miller and Rice (1983)” is indicated as “Miller & Rice (1983)” elsewhere in the manuscript. I would suggest consistency in the notation and check the use of “and” and “&” throughout the manuscript when the citation consists of two names only.

We will try to address this in the revised manuscript.

Line 300: “Kagen” should be replaced with “Kagan”.

Now fixed

Figure 5: It would be helpful to include a legend for the size of the circles of the top plots. What is the minimum magnitude for the earthquakes plotted here? 4.5 Mw? Is the colour scale in the bottom right-hand side plots applied to the three plots? and therefore do the branches for the FR2020 have the same weight?

We had avoided adding such a legend, which would have added more clutter to the plots and was not essential to convey the main message that the catalogues appear to be different. The minimum magnitude for the earthquakes is Mw 3.0. The colour scale in the bottom right-hand site plots is applied to all three plots, which means that the branches for FR2020 have the same weight. 

Line 402: Add a comma between “(FR2020)” and “a hydrid”.

Fixed

Line 404: (USNRC, 2012) is not listed in the reference section.

The citation for the U. S. Nuclear Regulatory Commission report has now been added.

Line 430: Is the sentence “The latter is fit to NGA West 2 data but using a simpler functional form than the NGA West 2 GMMs, which more suited for the level of parameterization commonly found in moderate to low seismicity regions” related to Bindi et al. (2017)? If so, I would suggest change “(as explained), and Bindi et al. (2017). The latter is fit” with “(as explained). Bindi et al. (2017) is fit”

The sentence has been revised slightly and the explanation of the Bindi et al. (2017) model slightly expanded for clarity.

Figure 9: Is there a reason why 5.25 and 6.50 Mw were chosen for the earthquake scenarios, and not 5 and 6 Mw for example?

The magnitudes were selected to represent scenarios relevant for the France/Germany models in question. This included the minimum of the models (Mw 4.0), something close to a 1/100 year occurrence, which is similar to the 1992 Roermond earthquake (Mw 5.3), and an extreme scenario (closer to 1 / 500 to 1 / 1000 year), which is feasible but not necessarily the maximum magnitudes that are considered on the Rhine Graben faults.  

Line 539: Pagani et al. (2014) is not listed in the reference section. I assume this citation corresponds to Pagani et al., 2014a or 2014b.

One of the Pagani et al. (2014) references has been removed from the bibliography, so now the Pagani et al. (2014) in the main body is correct.

Line 555: Assatorians & Atkinson, 2014 is not listed in the reference section.

The reference has been added (and the misspelling of the name of the first author corrected).

Line 579: Add “packages” between “software” and “characterise”.

Now added.

Line 592: The words “highlighted emphasized” are redundant, one of them should be deleted.

“highlighted” has been deleted.

Line 604: Allen et al., 2020 and Abbot et al., 2020 should be listed in alphabetic order since the year of the publication is the same.

Now fixed.

Lines 693-694: It seems that the word “that” is missing between “representation” and “allows”.

Now fixed.

Lines 698-702: This sentence is difficult to follow. I would suggest rephrasing it to improve readability.

These sentences have been revised and split into smaller sentences to improve readability.

Figure 12: If I have understood correctly, the gridded activity rates plotted in Figure 12 account for the areal source models, the smoothed source models, and the fault source models for DE2016, FR2020, and ESHM20. Is that correct?

Yes, this is correct.

Figure 12: Why is North Germany white in the middle and bottom row plots? Is the activity rate very low to be white? It seems there is an abrupt change from yellowish and white.

The colour scale assigns white to regions with annual rates of M ≥ 4.5 less than 10-6 per 0.1˚ x 0.1˚cell.  Depending on the source zonation, the rates of activity can drop significantly from those zones that encapsulate parts of western and southern Germany to those that are either limited to the very low activity zone of northern Germany (or large-scale area zones for regions low activity, which yield a very low rate of occurrence per cell). So, yes, the activity is low enough to be white according to this colour scale. 

Line 745: Perhaps, the word “of” between “similarity” and “dissimilarity” should be replaced with “or”.

Now fixed.

Lines 747-748: Include references for the weighted Kolmogorov-Smirnov Statistic and Wasserstein Distance.

Appropriate references have now been added.

Figure 17: Do the extreme values in the colour scale correspond to the minimum and maximum values in the maps?

For the probabilistic seismic hazard maps themselves (in the left column) the minimum and maximum values correspond closely to the extreme values in the colour scale. For the difference maps the minima and maxima in the maps do exceed the range of the colour scale (closer to +70 % difference in some cases). Several ranges were tested to strike a balance of colour saturation across the different figures, but in order to avoid obscuring certain spatial features the current range was selected even though in certain maps the values may exceed the ranges presented in the colour scale.

Line 822: The authors should explain what “acceleration level A” is because I think it was not mentioned before.

This refers simply to the level of ground motion with a given probability of exceedance. The term “acceleration” is replaced by “ground motion”.

Line 836: Replace “difference” with “different” at the end of this line.

Fixed

Lines 849-850: Include the coordinates used for the cities of Saarbrücken and Strasbourg.

Now added

Lines 873: The word “consider” was repeated twice in the same sentence (“…we considered, we are considering seismic hazard models that are sufficiently…”). I would suggest using synonyms for one of them.

This has now been edited

Lines 871-879: Some sentences here are quite long and perhaps they could be simplified.

Some edits have been made to the sentences here.

Lines 943-949: These two sentences could be rephrased for better readability. Furthermore, the word “that” is repeated three times in the same sentences.

The sentences have been slightly rephrased and split for better readability

Line 971: US Nuclear Regulatory Commission, 2018 is not listed in the reference section.

This has now been added to the reference section as Ake et al. (2018)

Reference section: The references Goulet et al. (2021), Vilanova et al. (2014), and Weatherill and Cotton (2020) are included here but are not cited in the text. Also, the reference Meletti, D’Amico and Martinelli does not include the year (I assume it is 2013).

The unused references have now been removed and the year for the Meletti reference clarified as 2013.