Review Reports - The Hole in the Pacific LLVP and Multipathed SKS

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

see attached pdf

Comments for author File: Comments.pdf

Author Response

Please find below our point-by-point responses to the quotes from the reviewers. Our responses are highlighted in blue italics.

Review#1

In this paper, the author focuses on a region of anomalous seismic structure in the deep southwest Pacific mantle, in the vicinity of a mega ultra-low-velocity zone (ULVZ) that has been detected and studied extensively by previous authors. Using a series of 2D forward numerical simulations, he proposes a model to explain the complexity of SKS waveforms sampling this region by the presence of a fast velocity “slab” suspended above the CMB on the source side of paths from Fiji-Tonga to USArray, and argues for the presence of a “hole” in the Pacific LLSVP.

I am very supportive of any study that can demonstrate the presence of “holes” in LLSVPs, and have written several papers illustrating the fact that these LLSVPs are constructions based on long-wavelength models but in reality they do not extend as unbroken structures very high above the CMB (see our latest paper Munch et al., PNAS, 2024- https://doi.org/10.1073/pnas.2407543121; see also Davaille and Romanowicz, 2020, Tectonics).

I have no doubt that the recent global tomographic models show a dent in the contour of the Pacific LLSVP at the location targeted by this study.

It is also great that there are so numerous and densely sampled high quality waveform data from USArray, and the modeling efforts of the author should be praised for that.

However, I have some trouble with the proposed model for the following reasons.

Thank you for your overall supportive comments on the motivation of this study, as well as for the critical and expert comments you provided. We agree that although many tomographic models show “holes” within the LLVPs, their locations are not always consistent, raising questions about the robustness of these features. Furthermore, as suggested in these important references, which indicate that such structures may indeed be gaps, rather than holes. Such a structure may reflect a segmented low-velocity structure rather than a whole structure, especially for the mid-Pacific LLVP.

Thus, we have included a corresponding clarification in the “Discussion” regarding the possible origin of this “hole” structure (Lines 392-402). Nonetheless, in the revised manuscript, for simplicity, we continue to use the term “hole” to refer to this disrupted velocity structure; however, we acknowledge that it may instead represent ambient mantle between segmented low-velocity structures.

There is an ambiguity in assigning a particular travel time or waveform anomaly in SKS to the source-side or receiver-side leg in the mantle. The author starts by eliminating the possibility of an anomaly in the upper mantle on either the station or the source side which is quite fair, but he also brushes aside rather rapidly the possibility of a fast anomaly in the deep mantle on the receiver side, when in fact, tomographic models all show a rapid transition from slow to fast structure in the last 500 km of the mantle right in the region sampled by the upgoing SKS rays, on the eastern side of the LLSVP. This is quite visible in the maps and cross-sections shown in Fig. S1.

This rejection is done in one sentence:

“Comparing the obvious jump up to 6 s in the travel time of SKS and multi-pathed waveform of event A, SKKS displays very subtle change in travel time and has simpler waveform”.

First of all, the SKKS waveforms are not necessarily that simple (we are not shown many examples and no comparisons of modeled and observed SKKS), second the travel time anomalies of SKKS are not shown.

It so happens that more than 25 years ago, we published the results of a study of SKS and SKKS along very similar paths (Bréger and Romanowicz, Science, 282, 718-720 1998- DOI: 10.1126/science.282.5389.718) which proposed a model to explain the striking trends in the SKS AND SKKS travel times by invoking a strong transition from slow to fast velocity on the eastern border of the LLSVP. That study only considered travel times, and referred all measurements to the travel times of S, to reduce possible contributions from the upper mantle, and there was no USArray then, so it was much less sophisticated than the present study, however, the model fit the travel time data quite well, including trends of increasing travel times and of decreasing travel times depending on precise location of events, and including trends in SKKS-SKS differential travel times.

The very striking trend with distance of the SKS travel time anomaly is shown in Figures 3b and 4, but the author does not show the travel time predictions for SKS from any of his models (nor any travel times or waveforms for SKKS actually). The models do - very qualitatively- reproduce the waveform complexity in SKS, but that is primarily reflecting the fact that the waves encounter a sharp “edge”, which is clearly the case. The question is whether the suspended slab portion on the source side is the best interpretation, given the alternative model that we proposed in 1998.

I am not saying that the proposed model here is necessarily wrong, but given that

the 1998 model fit the then SKS and SKKS travel times quite well,
that the authors only show data from USArray (e.g in Figures 3b and c), which cover different parts of the US for different events, so the fact that the travel time anomaly for event C looks different from events A and B is possibly due to a different distance range and sampling of D” on the station side
that the proposed high velocity anomaly in this manuscript seems to be “suspended” some height above the CMB (it is not mentioned how high and why), in contrast to the 1998 model, which extends from the CMB in a region of marked higher than average velocity in tomographic models, where other authors have later also found a transition to slow and fast (e.g. He and Wen, 2012, JGR, doi:10.1029/2012JB009436, 2012; Frost and Rost, EPSL 2014, https://doi.org/10.1016/j.epsl.2014.06.046)
see also Figure below highlighting the two contrasting regions of

…I would very much like to see an evaluation of the proposed model compared to a model similar to the 1998 one, with the causative anomaly on the eastern side of the Pacific LLSVP (i.e. the station side), including quantitative arguments for potentially rejecting the latter, display of fits to travel times of the proposed models and quantitative assessment of the waveform fits for the different models.

Thank you for these important comments regarding how receiver-side anomalies at the CMB may affect the robustness of our interpretation of a slab-like structure on the source side. I apologize that the original manuscript did not clearly demonstrate these effects. I fully agree that receiver-side heterogeneities can play a significant role, particularly in explaining the travel-time variations.

To address these concerns, I have added new Figures S3–S5 to better support our preferred model. As you correctly noted, the structure proposed by Bréger and Romanowicz (1998) can substantially improve the predicted SKKS–SKS differential travel times compared with those from the GyPSuM model (new Fig. S4). Such a strong receiver side high-velocity anomaly advances SKKS arrivals at smaller distances. This type of structure can also generate multipathed SKS for event A, but only at relatively small distances (~95°; Fig. S5b), which does not match the observations, where multipathing occurs near 100°.

To test whether a shifted receiver-side anomaly could influence SKS around 100°, I shifted the high-velocity structure toward larger distances (right panel of Fig. S5a). This modified model produces multipathed SKS at the observed distances and also predicts the SKKS–SKS differential travel times, by advancing SKS at larger distances (Fig. S4), if a systematic -1.5 s shift is applied. However, this receiver-side anomaly would also be sampled by events B and D, which then exhibit similarly strong SKS multipathing (Fig. S5c)—contrary to observations, as both events show relatively simple SKS waveforms. For this reason, we still favor a source-side anomaly that is only sampled by the SKS of event A.

That said, I fully acknowledge that a receiver-side high-velocity anomaly is required to explain part of the SKKS–SKS differential travel-times, and that this feature is real, as shown in Bréger and Romanowicz (1998). I agree that the travel time should be the first and most important constraint to consider. Ideally, we should incorporate the effects from both source and receiver sides. However, given the complexities (LLVP, ULVZ, D”) along this corridor, we are not confident that these contributions can be fully resolved using our simplified models. Therefore, in the manuscript we focus primarily on the SKS waveform distortion and the ~2 s early SKS arrivals for the southwest events, rather than attempting to explain the entire pattern of SKKS–SKS travel-time variations.

To clarify the different behavior of SKS and SKKS, we have also included an MPD map for the SKKS of event A (Fig. S3), which shows that SKKS exhibits much weaker multipathing (smaller Δ_LR) compared with SKS. In the revised manuscript, the sentence—“Comparing the obvious jump up to 6 s in the travel time of SKS and multi-pathed waveform of event A, SKKS displays very subtle change in travel time and has simpler waveform”—has been removed.

We have substantially rewritten this section and added a detailed discussion of the potential receiver-side contributions to both travel times and waveforms (Lines 154–190).

Specific Comment 2: You are correct that, in Fig. 3, event C has different station coverage compared to events A and B. Unfortunately, we could not find additional northeastern events of good quality during the same time period as events A and B to perform a stable multipathing analysis. Nevertheless, in Fig. 3c, if we focus on the central U.S. stations, the multipathing feature for event C is clearly much weaker than that for event A.

Specific Comment 3: Our placement of the anomaly ~700 km above the CMB was initially guided by the high-velocity block at a similar depth in the GyPSuM model. I have included an explanation at Lines 262-265: “We use a simple idealized model by inserting a thin slab-like structure into the lower mantle of the 2D tomographic model (Fig 7a) to demonstrate its effect on the waveform. Such a model is also motivated by the observation of a high-velocity block at a depth of ~ 2000 km in GyPSuM (Fig. 5a). ”

However, I acknowledge that the depth of this anomaly is not well constrained, as shown in Fig. 10. We also include a model with the anomaly located at the CMB (4th model in Fig. 10). Although this model provides a slightly poorer fit than our preferred model, it still generally captures the observed SKS multipathing patterns.

In the end, whatever the final word on this, I do agree that the data require a sharp edge in the vicinity of the CMB and the presence of a region of faster than average velocity of limited lateral extent, and that in itself is important to write about. I do realize that I am asking the author for more work, but I hope he will take my comments as constructive and aimed at achieving the highest quality of science.

Thank you for your insightful and constructive comments. Your suggestions have helped clarify my rationale for choosing a source-side structure. We agree, however, that our current simplified model does not fit the travel-time data as well as the model of Bréger and Romanowicz (1998), highlighting the importance of receiver-side anomalies. Although exploring these additional effects did cost some time, the process has been rewarding, and I am pleased to have gained a much clearer understanding of the influence of such structures.

Now for some comments on details:

Section 2.1 line 3 from bottom: I think it should be event C (not D)

Thank you for pointing this out. It has been corrected.

Section 2.2

line 7: Dt does not appear in the equation 2 lines above…

I apologize for not making this clear. The Δ_Tis not directly derived from the equation. Instead, Δ_T represents the travel time difference between the data and the reference model and is measured with cross correlation between the data and the composed waveform with equation [S(t) + C×S (t-D_LR)]/2, where S(t) represents the predicted waveform from a reference model. This approach allows us to achieve a high cross correlation coefficient by having a more complicated composed waveform than the simple waveform predicted for most reference models. Further details can be found in the Sun and Helmberger [2013], which I have now included as a reference following this sentence.

line 6 from bottom: event D is not shown in Figure 3

It is event C. Thank you for catching up this. It has been corrected.

Figure 3 caption: “associated with the earlier arrivals” (typo).

Have corrected.

Just before Figure 4: “as suggested in Fig. 2d”: there is no Fig. 2d.

Have deleted “as suggested in Fig. 2d”.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

By studying SKS waveforms from the Fiji–Tonga earthquakes recorded by the USArray, this study investigates the seismic complexity associated to the "hole" in the Mid-Pacific Large Low Velocity Province (LLVP). assuming a mega–ultra-low velocity zone (ULVZ), the author indicates that a northeast-dipping, high-velocity block (~2% Vs increase) in the lowermost mantle can account for the observed SKS multipathing. A well-organized and data-driven discussion of LLVP morphology and its dynamic implications is presented in the article.

All things considered, the research is methodologically solid, clearly documented, and offers valuable knowledge about the fine-scale structure of the lowermost mantle. It is important to combine sensitivity testing, waveform modeling, and comparisons between SKS, SKKS, and ScS phases. The work is current and pertinent to current discussions about slab-mantle interactions and LLVP evolution.

But before publication, a few points need to be clarified or discussed further.

Key Remarks: Originality and Range
The study is comprehensive, however it would be better to highlight how innovative it is in comparison to earlier research (e.g., Thorne et al. 2013; Sun et al. 2019; Li et al. 2024). Beyond verifying the existence of a high-velocity block within the LLVP, the manuscript could more clearly state what additional limitations have been applied.
Limitations of the Model
Although a 3D test is briefly presented, the most of the modeling is 2D, and this simplification has to be addressed in greater detail. A quantitative evaluation of the potential bias in the inferred dip angle or velocity contrast caused by the absence of complete 3D geometry would be beneficial.

Quantification of Uncertainty
Though mostly qualitative, the sensitivity tests are performed well. The author should think about using numerical summaries of model–data mismatches (such as correlation coefficients or RMS values) to support claims like "provides a good fit."

Examining Different Interpretations
Given the variation in SPdKS behavior across neighboring routes, the idea of composite effects (ULVZ + fast anomaly) may be more explicitly highlighted in the discussion. The research attributes the SKS anomalies to a high-velocity slab-like block.
Visualization and Figures
Although most figures are easy to understand, others (such as Figs. 3–5, 7) would benefit from better distance range labeling and a more distinct separation between synthetic and observed traces. Simplified schematic illustrations would make the suggested geometry easier for readers to understand.

Language
Although the English is generally fluid, it may use some slight refinement to make it more clear and succinct, especially in the Discussion section (e.g., avoid unnecessarily long lines).

Minor Comments

The major conclusion—that the Mid-Pacific LLVP hole most likely represents slab–LLVP interaction rather than a pure ULVZ effect—should be emphasized in a phrase.

Figure 1: To improve reproducibility, provide coordinate labels or scale bars.

In Section 4.3, "Possible effect on ScS reverberation," it is explained whether local upper mantle heterogeneity may also have an impact on the 8s delay.

Typographical: A few small typos need to be fixed, such as "mutli-pathing" becoming "multi-pathing."

References: Make sure the format is consistent (some items don't have issue/page numbers).

Suggestion

Suggested Revision: Minor

After addressing the aforementioned concerns, the publication should be published since it makes a substantial and convincing advance to our understanding of lower mantle structures. The impact of the paper would be further increased by extending the discussion of the 3D implications and fortifying the explanation of model uncertainties.

Author Response

Please find below our point-by-point responses to the quotes from the reviewers. Our responses are highlighted in blue italics.

Review#2

I sincerely appreciate your generous comments on the contribution of the paper and am also grateful to you and the other reviewers for your insightful suggestions.

But before publication, a few points need to be clarified or discussed further.

Thank you for this constructive comment. The main difference between our work and Thorne et al. (2013) is that we examine the multipathing patterns across multiple events, rather than focusing on the waveforms within a single bin, which may include contributions from multiple events. In the latter case, multipathing effects from particular events could be misinterpreted. We have now emphasized this point in Lines 89–91: “We examine SKS data covering a wide distance range and study the different multipathing patterns for various events. Together, these approaches allow us to better resolve the lower mantle structure than previous studies, which typically focused on a more limited data range.”.

Regarding the studies by Sun et al. (2019) and Li et al. (2024), they focused on the ScS and Sdiff/S–Scd–ScS phases, respectively. In contrast, our study focuses on the SKS phases.

Limitations of the Model
Although a 3D test is briefly presented, the most of the modeling is 2D, and this simplification has to be addressed in greater detail. A quantitative evaluation of the potential bias in the inferred dip angle or velocity contrast caused by the absence of complete 3D geometry would be beneficial.

Because both comments concern the quantitative evaluation of our model, I address them together. Thank you for raising these important points. I agree that a quantitative assessment of the goodness of fit is essential. Following your suggestion, I have now calculated the cross-correlation coefficients (CCs) between the data and the synthetics and report these values for each figure with synthetics.

However, due to the large uncertainties in both the vertical extent and the length of the anomaly, it is difficult to conduct a formal grid-search–type inversion, which would be required to provide rigorous model uncertainties. I also acknowledge that although our preferred model yields the highest CCs, I am cautious about labeling it as the “best” model, given the simplified parameterization and the presence of data noise. As shown in the synthetics for different models, the differences in CCs are relatively small. Therefore, rather than providing formal uncertainties for each parameter, I now discuss the plausible ranges of these parameters in more detail by examining their CCs in the revised manuscript.

Regarding the 3-D effects, a direct comparison between the 2-D and 3-D results is currently challenging because of computational limitations. Our 3-D simulations are accurate only down to a period of ~7 s, whereas the 2-D calculations extend to ~0.5 s. Nonetheless, this is an excellent point. In the new Fig. S5, we include distance profiles for both the 3-D and 2-D synthetics, filtered to the same frequency band, and discuss the implications for the possible underestimation of velocity perturbations in the 2-D cases (Lines 353-359).

Thank you again for these valuable suggestions.

Thank you for these comments. I have added a new paragraph in the Discussion section addressing how multipathing in SKS phases affects the identification of the ULVZ (Lines 374-390).

Visualization and Figures
Although most figures are easy to understand, others (such as Figs. 3–5, 7) would benefit from better distance range labeling and a more distinct separation between synthetic and observed traces. Simplified schematic illustrations would make the suggested geometry easier for readers to understand.

I have updated all the figures accordingly.

Thank you. I have carefully reviewed the manuscript and revised the language throughout.

Minor Comments

The major conclusion—that the Mid-Pacific LLVP hole most likely represents slab–LLVP interaction rather than a pure ULVZ effect—should be emphasized in a phrase.

I have updated the conclusion section and stated this point more clearly and directly.

Figure 1: To improve reproducibility, provide coordinate labels or scale bars.

The coordinate labels have now been added. The color bar for the velocity perturbation was included in the original manuscript.

In Section 4.3, "Possible effect on ScS reverberation," it is explained whether local upper mantle heterogeneity may also have an impact on the 8s delay.

Following the academic Editor’s suggestion, I have removed the section on “ScS reverberation” In the revised manuscript.

Typographical: A few small typos need to be fixed, such as "mutli-pathing" becoming "multi-pathing."

I have carefully reviewed the entire manuscript, and the typos have been corrected.

References: Make sure the format is consistent (some items don't have issue/page numbers).

I apologize for not checking the references carefully in the previous version of the manuscript. I have now reviewed the entire reference list thoroughly and ensured that the formatting is consistent throughout.

Suggestion

Suggested Revision: Minor

Thank you for all the important comments. By including the cross-correlation coefficient analysis, we believe that the results are now more robust.

Reviewer 3 Report

Comments and Suggestions for Authors

Review of the manuscript ”The hole in the Pacific LLVP and multi-pathed SKS” by Daoyuam Sun.

The author investigates anormal SKS signal behavior (signal forms and travel times) from Tonga-Fiji deep focus events observed by USArray stations. These observations can only be explained by lateral velocity variation in the deep mantle above the CMB. The author tests several model types (published and own ones) and concludes that a slab-like high velocity body in the lower mantle north-east of Tonga is the only possible explanation for his observations.

This interesting result reminds the reviewer of research and discussions 35 to 40 years ago. To his knowledge, he was the first who proposed a high velocity body in the lower mantle to explain unnormal SKS travel time behavior (DOIs: 10.1029/GL013i013p01529, 10.23689/fidgeo-3977 and 10.23689/fidgeo-4001). It is very interesting that with today’s possibilities (higher resolution due to more and denser data, better 2 & 3D modeling tools etc.) the principal results from that time are confirmed: a high velocity body influences SKS and low velocities in D” are influencing SKKS.

Beside the missing reference to this former work, the author should consider/correct the following points:

Fig. 3 and related text: the figure shows events A & C. In the text and figure caption are in addition mentioned and discussed events B & D as shown in Fig. 3a. Something is wrong here or missing. I cannot see events B & D here. Please check this carefully through the whole manuscript. What are the broken vertical lines in Fig. 3a?

I don’t understand why IASP91 and PREM are both used as 1D reference models. Both have different lower mantle and D” structures and I think for clarity, the author should only use one of them. If you stay with IASP91 please correct in the whole text ‘IASP’ to ‘IASP91’. In any case, both models are used without reference.

Fig 11: what means ‘4.23.D’ on top of the figure?

Tables: in the text is only Table S1. Where is the mentioned Table 1? Why ‘S1’?

Events: why using as event locations the GCMT? In particular for events (depth!) in subduction zones the EHB catalogue should be by far more accurate.

Author Response

Please find below our point-by-point responses to the quotes from the reviewers. Our responses are highlighted in blue italics.

Review#3

Review of the manuscript ”The hole in the Pacific LLVP and multi-pathed SKS” by Daoyuam Sun.

Thank you for providing these important and interesting references. I apologize for having missed them. I am pleased to note that both the measurements and the proposed models in these studies are largely consistent with those presented in this manuscript. I have now included these references in both the Introduction and Results sections.

Beside the missing reference to this former work, the author should consider/correct the following points:

Sorry that I made a mistake here. The labels should refer to events A–C in Fig. 3, and I have now made this correction.The dashed vertical lines are just plotted at time of 0 for a better visualization. I have added a description in the Figure caption.

Thank you for this suggestion. For studying SPdKS and SKPdS phases, the PREM model is typically used as the reference, so we have retained the description of the waveform as “PREM-like.” For the other cases, I have corrected the text to “IASP91” and added the corresponding reference.

Fig 11: what means ‘4.23.D’ on top of the figure?

Sorry for the bad presentation. This is the section title for the next section. I have now moved this whole section before the Figure 11.

Tables: in the text is only Table S1. Where is the mentioned Table 1? Why ‘S1’?

Thank you for pointing this out. Table S1 is in Supplementary materials. Table 1 in the main text is only for the information of events A-D.

Events: why using as event locations the GCMT? In particular for events (depth!) in subduction zones the EHB catalogue should be by far more accurate.

Thank you for this important comment. I agree that the EHB catalog generally provides more accurate depth estimates. While event depth affects the absolute travel times of individual phases, switching from the EHB to the GCMT catalog has only a minor impact on the relative travel times between the phases discussed here, as well as on their waveform characteristics. Therefore, for convenience—and because we also use GCMT focal mechanisms for subsequent waveform modeling—I adopt the GCMT catalog in our analysis.

Reviewer 4 Report

Comments and Suggestions for Authors

Reviewer Comments

The manuscript titled “The Hole in the Pacific LLVP and Multi-pathed SKS” presents an insightful and technically advanced investigation into the internal heterogeneity of the Pacific Large Low Velocity Province (LLVP). Using SKS waveform multipathing and numerical modeling, the authors propose that an anomalous high-velocity block, rather than a conventional ultra-low velocity zone (ULVZ), may exist within the central Pacific LLVP. This finding, if confirmed, would have significant implications for our understanding of mantle dynamics and the thermo-chemical evolution at the core–mantle boundary.

Points Requiring Improvement

1. While the references are overall appropriate and cover major works on LLVP morphology, SPdKS-derived ULVZ interpretations, and slab–mantle interactions, several important aspects require additional citation to strengthen the discussion:

2. Although the authors use both 2D and partial 3D simulations, the transition between these is not entirely clear. Clarifying how 3D effects (e.g., lateral gradients, off-great-circle paths) could influence multipath.

3. Clarify acronyms (e.g., LLVP, ULVZ, CMB) at first occurrence in the Abstract.

4. Update the reference list to ensure consistent formatting (e.g., journal titles in italics, uniform capitalization).

5. Include uncertainties (e.g., Vs perturbation ±%) explicitly in the main text where quantitative model parameters are cited.

This is a high-quality and innovative study with potential for significant impact. I recommend minor revision before acceptance.

Author Response

Please find below our point-by-point responses to the quotes from the reviewers. Our responses are highlighted in blue italics.

Review#4

Points Requiring Improvement

While the references are overall appropriate and cover major works on LLVP morphology, SPdKS-derived ULVZ interpretations, and slab–mantle interactions, several important aspects require additional citation to strengthen the discussion:

Thank you for this important comment. I apologize for not adequately citing all the relevant and important references in the original manuscript. In the revised paper, I have added additional related references, which allow for a more thorough and informed discussion.

Although the authors use both 2D and partial 3D simulations, the transition between these is not entirely clear. Clarifying how 3D effects (e.g., lateral gradients, off-great-circle paths) could influence multipath.

Thank you for this important comment. Full 3D simulations are indeed essential for fully characterizing the geometry and properties of the lower-mantle slab-like structure, as also noted by Review#2. However, our current calculations are limited by computational resources and are accurate only down to ~7 s. Therefore, at this stage, our main conclusions rely on 2D simulations, with the 3D simulations serving primarily as a test to assess their potential impact on the results. We have added a new Fig. S5 to better illustrate how different 3D models may influence the results. In addition, we have included a more detailed discussion (Lines 353-359) on how edge effects could lead to an underestimation of the velocity perturbation.

Clarify acronyms (e.g., LLVP, ULVZ, CMB) at first occurrence in the Abstract.

Have added.

Update the reference list to ensure consistent formatting (e.g., journal titles in italics, uniform capitalization).

4. Include uncertainties (e.g., Vs perturbation ±%) explicitly in the main text where quantitative model parameters are cited.

This comment is similar to one from Review#2. I must acknowledge that, at the current stage, I am unable to provide a formal analysis of the uncertainties of the model parameters. In the revised manuscript, we calculate the cross-correlation coefficients (CCs) between the data and synthetics. However, because of the large uncertainties in both the vertical position and the length of the anomaly, a formal grid-search–type inversion is not feasible. Moreover, as shown in the synthetics from the sensitivity tests, the differences in CCs are relatively small. Therefore, instead of providing formal uncertainties for each parameter, I have now included the plausible ranges of these parameters. I hope this provides an adequate characterization of the model.

This is a high-quality and innovative study with potential for significant impact. I recommend minor revision before acceptance.

Thank you again for your thoughtful and important comments.