This is an interesting and, in general, is well written paper. However, I believe that some of the results can be and should be presented in a more informative and spectacular way and the entire text and figures should be polished! Therefore, my recommendation “Acceptable after revision”.

(1) My main suggestion is related to Figure 4 and the respective text. The most noteworthy point of this event and the corresponding study is that there were TWO earthquakes with an interval less than 2 hours between them. The authors declare that the tsunami waves associated with both events are clearly seen in Figure 4. But for readers (in contrast to the authors) this is not obvious! What the authors should do is to construct the theoretical dispersion curves for both events (following papers of González and Kulikov, 1993 and Kulikov, 2006) and demonstrate that the observed f-t extrema are in good agreement with the theory. BTW, the source regions of these two events are relatively small; therefore, the dispersive effects for propagating waves should be clearly seen in the wavelet plots. All details and necessary equations can be found in Fine et al. (2019).

The dispersion curves and corresponding f-t diagrams are constructed as functions of frequency (not of period!) (e.g. Thomson and Emery, 2014); now all plots in Figure 4 are upside down and wave dispersion is difficult to identify. (Actually, the authors themselves call these plots “frequency-time analyses”, not “period-time”). So the figures should be presented in the standard way.

I believe that if the authors prepare everything in the best way, the corresponding figure will become striking and highly quoted! The authors of the listed papers used the f-t diagrams to identify a specific event and to examine the dispersive properties of tsunami waves. However, I do not know any study where this approach has been used to identify and separate two events following each other!

(2) Spectral analysis, Figure 3. This figure is prepared in a very “unfriendly manner”! I know that the second author loves to combine a numerous number of plots in one figure. However, in that case the value of each plot tends to zero. What are the specific spectral features that the authors would like to demonstrate? Spectral peaks? The differences of the tsunami spectra from the background spectra? The differences between two tsunamis? Any of these features are unclear in this figure.

The spectra are strongly vertically compressed; the scale of the Y-axis looks strange: 10^-5, then 10⁰ and nothing between! As a result, all spectra look flat. BTW, I believe that the dimension of the Y-axis is cm²/Hz, not cm/Hz.

An additional question is units. Typical periods of seismic waves are second; therefore, it is natural use Hz for their frequencies. However, typical periods of tsunami waves are minutes and fractures of an hour. Besides, the sampling interval of the data is 1 min. Thus, it would be natural for tsunami spectra to use cycles per minute (cpm) or cycles per hour (cph). This will be helpful for readers, and they will not need to use a calculator to estimate the period of a specific spectral peak. (The same comment is just for Figures 5c and 5d).

Also, what is the meaning of the magic numbers for periods: 1,7, 16.7 and 166.7 min in the scale of periods?! The Nyquist period for these spectra is 2 min, the fundamental period is 120 min (2 hours). The meaning of the shown magic periods remains totally unclear and does not help a reader to detect the periods of spectral maxima.

The last but not least comment to these spectra: the confidence levels are not shown and without confidence levels all results of spectral analysis are senseless (e.g. Thomson and Emery, 2014).

(3) Figure 5c. The idea to estimate “relative spectra of tsunamis” as the ratio of various tsunami events was first proposed by Miller (1972). The authors mention this study (Line 44), but it is absent in the List of references. Also, they do not mention this paper when they discuss their Figure 5c.

It should be emphasized that this approach (the authors call it “empirical Green’s function”, EGF) does not allow to reconstruct the tsunami source spectrum because it shows not the properties of the second source themselves, but the differences of the second source from the first one. As was indicated by the authors (e.g. Lines 168-169), the seismic mechanisms of the two events are very similar. Therefore, the mutual part of the two sources (in particular, mutual spectral peaks) is not seen in Figure 5c. From this point of view, it would be interesting to see the tsunami/background ratio for the first event (i.e. a figure similar to Figure 5d, but for the first tsunami).

(4) Equation (1) (Line 183) is the exact solution for periods of standing (eigen) modes in a closed rectangular basin of uniform depth h = const. This equation for n = 1 allows to estimate very roughly the order of periods of generated tsunami waves. However, a real tsunami source is far away from being uniform and rectangular; thus, even for the first mode, this estimate is a very approximate. So, this estimate is rather qualitative than quantitative. From this point of view, it is strange to see that the authors use this equation for PRECISE estimation (with fractures of minutes!) the “source periods”, and even not only for the first but also for the secondary modes.

(5) The authors use a high-pass filter to remove tides from the original records; this is definitely not the best way to suppress tides! Any unnoticed spike, shift or gap (small in comparison with tides) will strongly distort the tsunami signal (and even create some “artificial tsunamis”; the corresponding examples are well known!). It is much better to subtract predicted or calculated tides (as was done by the authors in some other their papers. BTW, the authors write: “…we applied a second-order high-pass filter with the corner frequency of 0.00014 Hz (7,200 s) to remove the tidal components”. Why “Hz”, why “seconds”?! The sampling interval of the data is not seconds, but 1 min; it would be much easier for readers if the authors write: “We applied a 2-hour (or 120-min) high-pass window”!

Some polishing of the paper language will be useful; there are some problems with articles, etc.

Alexander Rabinovich

References

Fine, I. V., Thomson, R. E., Chadwick, W. W., Jr, and Fox, C. G. (2019), Toward a universal frequency of occurrence distribution for tsunamis: statistical analysis of a 32‐year bottom pressure record at Axial Seamount, Geophysical Research Letters, 47, e2020GL087372. https://doi.org/10.1029/2020GL087372

González, F. I., & Kulikov, E. A. (1993). Tsunami dispersion observed in the deep ocean. In S. Tinti (Ed.), Tsunamis in the World (pp. 7–16). Dordrecht: Kluwer Acad. Publ.

Kulikov, E. (2006), Dispersion of the Sumatra Tsunami waves in the Indian Ocean detected by satellite altimetry, Russian Journal of Earth Sciences, 8, ES4004, doi:10.2205/2006ES000214.

Miller, G.R. (1972), Relative spectra of tsunamis. Publ. HIG-72-8, Hawaii Institute of Geophysics, University of Hawaii, Honolulu, 7 pp.

Thomson, R. E., & Emery, W. J. (2014). Data Analysis Methods in Physical Oceanography (3rd ed., p. 716). New York: Elsevier Science.

Overview

This paper describes the source spectrum of the tsunamis generated by two earthquakes (Mw 7.4 and Mw 8.1) that occurred in the Kermadec subduction zone on 4 March 2021 using tsunami data recorded at tide gauges. The study produced the dominant wave period range for each event and the spectral ratio for the larger earthquake (second event) by utilizing the data from the smaller event (first event) as Green’s Functions.

Comments

1. High-quality water level data at DART stations are available for this event. The DART stations are in the deep ocean which means the records are not affected by the coastal geomorphology, unlike tide gauges. It is not clear why the study is only using tide gauge but not DART data. I suggest the inclusion of spectral analysis of DART data in this study.
2. The paper provides the dominant wave period ranges for the first and second events. But what the meaning of those numbers is not explained. The dominant period ranged from 8 to 28 minutes for the Mw8.1 earthquake (the range is 7-28 min in lines 175-180, which one is the correct one). Is this a normal range for this kind of earthquake?
3. It is not clear how the period range was determined. Was it from the Fourier or the wavelet analysis? Lines 130-135 describe that the range was determined from the peak spectral power. But the peak for the first event at some of the stations like Owenga is longer than the upper limit of the 5-17 min range. Please indicate the peak at each station for each event with an inverted triangle in Figure 3.
4. Similarly, the period range determination using the wavelets is also not so clear. The period range for the second event detected at Ouinne was 20-30 min. But the paper finally concluded the period range of 8-28 min for the second event. Was the period at Ouinne simply ignored? Moreover, if we chose the peaks in the Ouinne wavelet using the contours, we would get a range of 10-30 min instead of 20-30 min. Please provide a table with the range for each station.
5. Figure 4: Provide purple and red boxes for the other tide stations.
6. Lines 185-190: the paper argues that the spectral analysis validates the USGS source model. But the calculation of the model source periods used the total fault length and width instead of the dimension of the main slip region, which is about 120 km long and 120 km wide. Outside this main slip region, the slip amounts are almost zero, so the total fault dimension should not be used in the calculation.
7. Provide the spectral ratios from the simulated waveforms and then compare them with the observed ones.
8. Error bars are required for Figure 5c and 5d.

In the manuscript entitled ‘Characteristics of two tsunamis generated by successive Mw 7.4 and Mw 8.1 earthquakes in Kermadec Islands on March 4, 2021’, the authors have addressed a not trivial case capturing tsunami characteristics generated by two successive earthquakes. This study provides insights of the source spectrum based on the empirical Green’s function (EGF) and tsunami/background ratio methods. The spectral analysis allows distinguishing the dominant wave periods and ranges. The paper is well written but the discussion and conclusions should be improved. I suggest further revision to the following comments.

General comments:

(1) While the selection of a second-order high-pass filter has been tested (e.g. Heiderzadeh and Satake, 2013; Heiderzadeh et al., 2015), the justification of the window or frequency corner is not clearly stated. This selection may affect results.

(2) Considering that this is a peculiar case where two tsunamis are generated from close sources, I’ve found that the Section 5 and the Conclusions are weak. These sections could be enhanced by exploiting more the results, and providing a thorough discussion that is lacking. Also, consider to add limitations of this study (e.g. not using the DART records).

(3) The authors are encouraged to provide further interpretation of the results higher frequencies, decaying processes and source characteristics, specially in light of one of the main observations of this study described in Line 195.

(4) The overall structure of the paper is fine, but some elements of the Methods appear in the Section 5, where instead, discussion is expected. Also, the results of the subsection 2.3 ‘Earthquake Slip Models and Tsunami Numerical Simulation’, where simulations based on the USGS source models need further contextualization/discussion, for example, in Figure 5.

Specific details:

Lines 83-84, articles needed.

Line 127, needs rephrasing: Similar patterns were also be observed at Ouinne…

Line 133, modify ‘at most stations. At most stations …’

The figures of this manuscript have been greatly improved in the answers to previous comments, but I suggest to modify the green point that shows the spectral peaks in Figure 3. Instead, consider using a stronger color.

References:

Heidarzadeh, M., and Satake, K. (2013). Waveform and spectral analyses of the 2011 Japan tsunami records on tide gauge and DART stations across the Pacific Ocean. Pure Appl. Geophys., 170, 1275–1293. Doi:10.1007/s00024- 012-0558-5

Heidarzadeh, M., Pranantyo, I. R., Okuwaki, R., Dogan, G. G., and Yalciner, A.C. (2021). Long tsunami oscillations following the 30 October 2020 Mw 7.0 Aegean Sea earthquake: Observations and modelling. Pure Appl. Geophys., 178, 1531–250. Doi:10.1007/s00024-021-02761-8