Reply to Anonymous Referee #1

Dear reviewer,

Thank you for accepting and dedicating your time to review our manuscript. We are especially grateful for the constructiveness of the feedback provided and we highly appreciate your comments on the utility and potential impact of our study for the scientific community working on seismic hazards.

Regarding your comments in the interactive discussion:

• Comment #1-‘How do you express a statistical confidence that there is geologically an extra event (or 1 less), because it also affects the confidence of another event next to it?’ I guess I am a bit worried that the technique could be using age data to drive geological interpretation. I see that the authors comment on that, but is there a way to show this in a robust fashion?

The statistical confidence of the extra event is expressed by the characteristics of the probability density functions (PDFs) involved in the correlation and the rationale behind their shapes. The skewness evident in the PDFs within the chronologies from DuRoss et al. (2011) is, as explained by the authors, a forced condition to bias the event’s age towards one of the limiting stratigraphic horizons. This condition is founded on geological observations that the authors interpret as indicative of the event occurring closer in time to the age of the limiting layer in question (e.g., the presence of a colluvial wedge or paleosols).

The opposing skewness of the third PDFs in RC vs. GC sites (figure 6 in the manuscript), highlights that the first likely occurred closer in time to the older limiting layer, contrary to the second at the GC site. This is more relevant if we consider that, for both sites, the ages of the limiting units of the third event are similar. This means that, given the same constraints, the geological evidence suggests different timings of the events in relationship to the stratigraphy histories. Furthermore, the higher probability regions of both PDFs are concentrated at significantly different points in time (>500 years apart), which reinforces the two-event interpretation.

PEACH performs an interpretation that is well adjusted to the probability distributions in each site and that, at the same time, are grounded on geological observations and criteria from geologists that conducted the paleoseismic studies. In this sense, we emphasize that the approach does not drive the geological interpretation; rather it is this geological data that drives the dates of the events that are introduced as inputs of the code. With this, we remark that the outputs of PEACH should always be reviewed by the user and not be used as a rigid interpretation, but rather contextualized for the studied region.

In section 4.2.1 of the revised manuscript, we will better clarify the points made to explain the confidence of this extra event.

• Comment #2: ‘How does this go on to impact ideas/versions of fault rupture segmentation?’ e. if you can count x events on a fault system, how does the technique help differentiate whether this will represent multi-section events or smaller section events?

The method is designed to facilitate correlation between fault segments, allowing to explore rupture segmentation behavior through the graphical representations generated during the calculations (e.g., figures 5 and 6 in the manuscript). Essentially, we can geospatially position each site event PDF based on the site’s location along the fault’s strike. Then, by analyzing the contribution of each site PDF in the final chronology, we can discern whether an event results from the integration of the records from multiple adjacent sites or not.

In the framework of segmentation, for instance, if two events identified in different sites and segments were to fully overlap in time, PEACH would correlate them as the same event. Such scenario could therefore be interpreted (by the user) as a single multi-segment rupture, given these sites were both located at the tips of the neighboring segments. However, we emphasize that correlation between fault boundaries should be made carefully as there are other conditions at play that our code does not contemplate (e.g., maximum jump distance, stress rupture compatibility, among others).

In the case of the Weber segment of the Wasatch fault that we discuss, the extra event E4 primarily results from the contribution of the third event at the RC site (as illustrated in figure 6 of the manuscript). This suggests that this event likely ruptured only at that specific location in the Weber Segment. The question is whether this event belongs to an across-boundary rupture with the neighboring Brigham Segment to the north or is confined to a smaller sub-segment rupture. To discuss this, we should run the code merging the records of both involved segments, a scope that is beyond our study. But, indeed, DuRoss et al. (2016) already identified that such ruptures across the segment boundary are feasible.

While these points were already addressed in the manuscript (lines 392-399), we will emphasize them to further highlight the implications and utility of our technique for rupture segmentation.

Regarding specific comments in the manuscript document (only those that refer to scientific aspects of the manuscript):                                                                            

• Comment #3 (line 157): “In reality, how does this deal with multi-peaked calibrated C-14 calibrations?”

The choice of modelling numerical dates as normal distributions was driven by the will to accommodate not only radiocarbon dates, but also luminescence (e.g., OSL), which usually are expressed as normal distributions.  In fact, luminescence dates are more prevalent in sites dominated by older, coarser, or less complete deposits – inherently more challenging to date accurately using other, more precise techniques like radiocarbon. It is in these contexts where site-to-site correlation poses a substantial challenge, making our approach particularly valuable.

However, we acknowledge and concur with the referee that shaping radiocarbon dates as normal distributions may be an over-simplification in some cases, especially in multi-peak distributions. We acknowledged this limitation in the discussion (lines 452-457) and in the current version of our code we already introduced the option to compute correlation by directly utilizing OxCal chronologies as inputs. OxCal is a specialized software designed explicitly for radiocarbon calibration and is better suited to handle the complexities associated with radiocarbon dating, a scope that goes beyond the objectives of our approach. This addition was made to allow users to choose the most appropriate option of PEACH based on their specific dataset and requirements.

• Comment #4 (line 159): “Will it always be 4000, why?”

This comment refers to the number of samples (seeds) performed by the algorithm within the numerical date PDF to compute the event date PDF, as explained in section 3.2 of the manuscript.

The choice of a 4000-sample threshold is based on a sensitivity test conducted across several datasets, including the two shown in Figure 3 of the manuscript, as well as others tested during the development of the code. This value is conservative and is expected to yield good results in most datasets. However, because we are committed to enhance user experience and flexibility, we will make the code for running the sensitivity analysis available in the public repository of the publication. We hope this will allow the users to select the threshold that best aligns with their needs, especially considering that higher seeds imply more computation time.

• Comment #5 (line 455): “Can there be an over-interpretation of events?”

The comment refers to our statement in the manuscript (line 438) “events evident in trenches are always a minimum relative to the actual number of events that occurred”.

While we acknowledge that there can be over-interpretation of events in specific trenches, because of the localized nature of paleoseismological studies, overall, the tendency is towards under-detection. This can be due to a variety of factors, including erosion or stratigraphy gaps that fail to record the deformation of events, coarse lithologies-granulometries in sediments that mask deformation, location of the site within the tips of the paleo-surface rupture, among others (e.g., Weldon & Biasi, 2013). This phenomenon is even more apparent in sites with large date uncertainties, as the greater is the date uncertainty of an event, the higher the likelihood that multiple events occurred within that time span. In the cases we illustrate in the paper, especially in the Paganica fault, some sites exhibit considerable event uncertainties even up to a thousand of years (e.g., site TRET in figure 5 of the manuscript). This inherently raises the probability that multiple events might have taken place during that time span.

Weldon & Biasi (2013) interestingly point that the impact of over-interpretation of events in trenches is reduced by increasing the number of trench exposures and correlation among them. That is because true events are likely to be detected at more than one site, as opposed to “fake” or over-interpreted events. In our approach, due to the probabilistic modelling and product-based correlations, genuine events tend to stand out more prominently in the mean distribution and have a higher chance of being detected by the algorithm. Conversely, "fake" events are likely to be downplayed, thanks to the probabilistic framework.

Having said that, we reinforce that the scope of this work is not to engage in a re-interpretation of the paleoseismic findings presented in the studies we use to showcase our approach. Instead, we seek to refine the temporal resolution of such chronologies, while maintaining the integrity of the original interpretations.

We will add and highlight this point of discussion to the revised manuscript for clarification.

In conclusion: in the revised version of the manuscript, we will add the pertinent clarifications to the mentioned points as well as implement the minor grammatical corrections suggested in the original document of the manuscript.

Yours sincerely,

Octavi Gómez Novell, on behalf of all authors

References mentioned:

• DuRoss, C. B., Personius, S. F., Crone, A. J., Olig, S. S., and Lund, W. R.: Integration of paleoseismic data from multiple sites to develop an objective earthquake chronology: Application to the Weber segment of the Wasatch fault zone, Utah, Bull. Seismol. Soc. Am., 101, 2765–2781, https://doi.org/10.1785/0120110102, 2011.
• DuRoss, C. B., Personius, S. F., Crone, A. J., Olig, S. S., Hylland, M. D., Lund, W. R., and Schwartz, D. P.: Fault segmentation: New concepts from the Wasatch Fault Zone, Utah, USA, J. Geophys. Res. Solid Earth, 121, 1131–1157, https://doi.org/10.1002/2015JB012519, 2016.
• Weldon, R.J. & Biasi, G.P.: Probability of Detection of Ground Rupture at Paleoseismic Sites. Appendix I of Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3). https://pubs.usgs.gov/of/2013/1165/pdf/ofr2013-1165_appendixI.pdf, 2013

Dear Mauro,

Thank you for reviewing our manuscript and for highlighting the relevance of our work for the community dedicated to seismic hazard and, as such, for the publication in GMD.

Regarding your comment made in the public discussion:

• Comment #1 – ‘To add on the comments from the reviewer, I would only advise the authors to better detail and explain what I would refer to "rule of thumbs" decisions on parameters  and related assumptions that come along with them (especially those that are hardcoded in their MATLAB script, as for example the minimum/optimum sample  seeding) that any future user of the software tool would/could encounter (and possible fin tune) in his/her study. This would add to the scientific merit of the study, in addition to the examples described, and would also help potential users to better understand the underline granularity of their decisions/assumptions made and their impact on the model outcomes. ‘

We agree with the comment about the fact that detailing the specifics of the method will enhance its transparency and overall user experience. Therefore, in the revised version of the manuscript we will apply the suggestions made. Particularly we will address the following points:

• Regarding the seeding process, and in the line of our response to comment #4 of the Referee 1, we will expand the reasoning behind the determination of the seed parameter (section 3.1), with particular interest on the potential implications of the variations in such value for the model outcomes/quality. We will also make available the accompanying MATLAB code at the Zenodo repository of the publication.
• Another important assumption (addressed also by Referee 1) is the modelling of radiocarbon dates as normal distributions. To address this, we will expand the discussion on the implications of utilizing such distributions in radiocarbon dates and, accordingly, add recommendations as to when the users should consider using the OxCal implementation of the code instead. One clear example would be when datasets are highly based on radiocarbon dates.
• Along with our initial AC1, we will correct the formulation of the peak detection algorithm. The peak detection threshold (minprom) is one of the most decisive parameters of our approach. Accordingly, in the revised manuscript (section 3.2.1) we will better highlight the importance of this parameter for the correct detection of the chronology and some recommendations for the user to fast check if the detection is performing as expected. For example, if the number of peaks detected is less than the number of events in an individual site, the peak detection should be reviewed and adapted (e.g., by working with sigma-truncated PDFs).

Having said that, we remark that most of the technicalities and ‘rule of thumb’ recommendations are explicated at the user manual that we made available at the Zenodo repository of the publication. Such manual provides all the necessary technical information for the user to run the code, interpret the quality of the results and adapt parameters within it, if necessary.

Thanks again for the review.

Best regards,

Octavi Gómez-Novell, on behalf of all authors