Dear authors,

I received a second review from Dr. Booth. He is overall positive and made some editorial suggestions. I assessed the revised manuscript by myself as well. Revision is significant and this manuscript can be acceptable with additional revisions suggested below. Please provide a mark-up manuscript and point-to-point responses in which corresponding revisions are clearly indicated by line numbers or by pasting the revised text.

Kenny Matsuoka
TC/TCD Editor

1. Expansion of the methods section 2.2 improved the manuscript significantly. The general description at lines 138-160 (in the marked up manuscript) is satisfactory. However, the revision at lines 177-200 should be improved, though I don’t expect the full description of the method here. It is helpful if you mention how HV in Equation (2) and HV^(theo) in Equation (3) are connected in a clearer way, first of all. Sigma and m are not defined in the text. Are P1, P2, and P3 the average energy densities of a diffuse field? If so, define P more explicitly. Do you need to connect P and Green’s tensor components using this equation? if so, explanation on its physical meaning is helpful.

2. Define three different H/V estimates of ice thickness more clearly, namely Equation (1), DFA + Model A, and DFA + Model B (or even define symbols). To a certain point in this manuscript, I thought that Model A is used with Equation (1), not with DFA. These estimates are stated many times but in slightly different ways and thus confusing. It’s better to clearly define them once and stick with these terms.

3. I am not convinced yet how independent ice-thickness estimates can be retrieved using the H/V method, because BEDMAP2 ice thicknesses are used to constrain the method (lines 229-230). What happens, if there is not such constraint? To rigorously argue this independence, it is necessary to make the H/V estimate without BEDMAP2’s guidance and compare these results with BEDMAP2’s ice thickness.

Editorial points (all line numbers refer those in the mark-up manuscript)

Rough estimation:I am not a native English speaker but I think that “approximate estimate” or “first-order estimate” can show the nature of this estimate much clearer than “rough estimate”. Maybe this is a personal taste so I leave it with the authors.

Wittlinger (2012) and Wittlinger (2015): are they Wittlinger and Farra?

L141: Define SH.

Lines 143-144: Revise the sentence.

Lines 188-189: check sets of parentheses and brackets to show the imaginary components.

L261ff: what does this error stand for? It is said at L285-286 “Error of Thickness I is associated with BEDMAP2’s uncertainty”. Is the error of the resonance frequency here also related to BEDMAP2’s error or relevant to the quality of the resonance peak?

Line 262: Fig. 3, not Fig. 2.

Line 351: cite Table 1.

Line 373: remove “(Fig. 5)”?

Lines 400-404: Do you really need this paragraph? I feel that this conclusion section can be stronger if you start with the second paragraph.

Table 1 caption: Please clarify thickness I and II in a better way. See the main point #2 above. Also, explain the error shown for Thickness I in the caption briefly.

Figure 3: change the order of individual panels or add lines between panels to group these 9 panels into 3 sub-groups. Explain what the vertical bars mean (thick gray and thin red).

Figure 4: scale all four profiles. Now the profile A-A’ takes the full page width (2 columns) for 2000 km, whereas the profile D-D’ of 1000-km long takes only about one third of the page width. The use of the same scale is important because the H/V method can be more useful to estimate ice thickness when the topography is less variable. Please make sure that all fonts are larger than 8 pt (feel free to use full page width and height). Separately I think that it is more appropriate to show the four stations without corresponding peaks in gray, not in red, and highlight the nine representative stations presented in Fig. 3, 5, 6 (e.g. different color or thicker curve).

Figures 6 and 8: Explain red and thin dotted vertical lines. If it shows what the thick brown bars in Fig. 3 show, consider using the same legends all in Figs. 3, 6, and 8.

Figure 7: Do you really need this figure, or can you show the same information by adding the Model A estimates to Figure 4? Figure 4 already show BEDMAP2, Equation (1), and Model B estimates. If you judge that this figure is necessary, please provide justification (would the figure be too busy to read details if all info is shown in Fig. 4?). Do you really need three panels for Fig. 7? You can show BEDMAP2 using mask, and three different estimates using markers (but then such figure is very similar to the current Fig. 4). In any case, clarify how the station number is given (is it in the same order listed in Table 1?).

Figure 9: I think that this figure can easily cause misleading, because blue dots perfectly match with the interfaces and thus Wittlinger and Farra make better estimates than this study. I recommend using BEDMAP2 thickness to mask the bed and ice.

Dear authors,

I am happy to accept this manuscript subject to a technical correction.

Technical correction:
Shorten the Table 1 caption and move equations and most description to footnote. You can use asterisks etc in cells at table's top row and define these errors in the footnote.

Thanks for submitting your work to TC/TCD.

Kenny Matsuoka
TC/TCD editor