Dear authors,

Thank you again for your manuscript. It has now received comments online and was reviewed by 2 reviewers.
I would suggest now that you resubmit a revised version accounting for the reviewer comments and the online discussion and we will proceed with publication.

All the best and thanks for your patience,

Philippe Jousset

Dear Martjin and Jean-Paul,

Thanks again for submitting a manuscript to the special issue. I received directly from sa reviewer and it would be necessary to address those in the revised manuscript.

"Here is [my] comments to this paper:
1. When converting strain rate to particle velocity, I didn’t see any velocity scaling. So the waveform in Fig 13e is strain? Please clarify this.
2. In section 3.2, there are several reasons to explain the DAS waveform incoherence. In the conclusion part, the author mainly ascribes the failure of DAS beamforming to the incoherence of DAS traces caused by local scattering (line 463). Maybe I was missing why the scattering is the main reason over others, like axial sensitivity of optic fiber? Fig 10 shows the pretty good coherent waveforms in each linear segment, which seems that scatterings are not strong. "

Once this is taken into account, I trust he manuscript will be able to be published.
I would like to thank you for your patience.

All the best

Philippe Jousset

Additional review from the Editorial team – Philippe Jousset

Dear Martijn and Jean-Paul,

Thanks for your patience. I reread in detail the final version of your manuscript and I noticed that the section 3.5 is entirely new, and therefore was not reviewed by anyone.

I am sorry that there things that I do not understand in this section. Note I asked advise to one of the co-editor for double checking (G. Currenti). It is not clear at all how you can go from a linear strain rate record to a “tensorial form” of the strain rate. A tensor (assuming 2D) takes into account strain (rate) components in 2 directions, with off diagonal components. However, as you mention in your manuscript line 292, DAS measure only one component in the direction of the fibre. It is indeed only the projection of the strain tensor onto the DAS inline direction. It unfortunately not possible to go back to the strain (rate) tensor (3 terms in 2D isotropic elastic) from the DAS measurements (1 direction including all components of the tensor projected). Therefore the equation line 299 is very confusing, and I would strongly advise you to reconsider, both the phrasing and the equation that you can derive from a single direction measurement. Moreover, I do not understand what you mean by “normal vector”.

In general, could you state that integration of strain rate to strain would give better beam-forming results than strain rate? This is actually the same as performing beam-forming on velocities that on acceleration.

Minors other points:

Line 119. There is a blank missing before “To visualize…”

Line 285. You indicate that the gauge length is L here, but actually at line 174 the gauge length is defined as being 2L. This is inconsistent and need to be arranged.

Line 336. minor point. You did not really demonstrated that local heterogeneity are modifying the strain rate. You used previous results from Wang et al., 2018 for instance as assumption. In addition, “Scattering” appears in the introduction and in the discussion, but never in the core of the text, so I guess you cannot claim you demonstrated that scattering is the reason. You rather processed data to remove the effect of scattering shown by others. The same applies for heterogeneity, as you point out actually at line 467.

Line 365. DAS response is flat in strain, but not is strain rate.

Line 440-445. Interesting approach, however, standard commercial cables do not necessarily follow the ideal theoretical frame. So you could mention how to cope with this issue, as deploying cables is expensive, and less easy than seismometers (need to dig a trench etc).

Line 553. The title of this paper is written twice.

Thanks for fast answer, we are almost there...

still two small checks for typoes:
Line 300: Can you check if you really mean xj to xi or the opposite?

In equation (8), check if nL should not be L only.

Thanks! I guess i did not spot any more issues, and therefore, I am happy to accept the paper. This may still be subjected to the Editor in Chief decision.
Congratulations!