Editor comments to HESS-2019-2015 ‘An extended trajectory-mechanics approach for calculating the pathof a pressure transient: Hydraulic tomographic imaging’ by Donald W. Vasco, Joseph Doetsc, and Ralf Brauchler.

The reviewers gave diverging recommendations. I therefore studied the paper in detail with both reviews in mind. As a consequence I add some review comments of my own.

The title does needs to reflect the actual contents of the paper more accurately. It oversells things a bit.

P2 L20: What is ‘source assembly coupling’? And what is the connection between ‘voltage’ and the propagation of a pressure signal in an aquifer?

P3 L15: replace ‘length‒1 [1/L]’ with ‘[L‒1]’.

P3 L20: Equation (1) applies to saturated flow. How can you have a fluid front in a porous medium that contains only a single fluid?

P4 L29: declare T as the pressure pulse travel time and give its dimension.

P5 L7: Why is this confinement of the non-linearity valid for Eq. (12) but not for Eq. (10)?

P5, L18: In Eq. (15), the perturbed path should then be labelled differently from the unperturbed path. Also, give references after ‘it has been shown’.

P5 L27: Isotropy is often absent in sedimentary strata. Or does it apply to the conductivity of a single model node?

P6 L4-6: This suggests that the storativity depends only on the porosity. In fact it depends on the pore space architecture, and hence on the water retention curve (arguably only on the wet end of that curve).

P10 L26: delete ‘a’.

Test cases: I agree with R1 that the test cases have severe limitations. Both cover spatial extents that are too small for any practical groundwater flow problem. Test case 1 starts with a pretty good initial model, and noise that is unbiased and has a small standard deviation and range, making the job of parameter identification relatively easy.

All things considered, I think the paper has potential, but with a more limited scope than the title suggests. I agree with R1 that the treatment of the paper of fitting a trajectory-based solution to derive the spatial distribution of hydraulic aquifer properties is not complete. Still, the contribution of the paper is clear and can be viewed as a step towards that completeness, with further studies tackling other aspects. But this needs to be reflected in the title, which currently does not describe the contents of the paper terribly well.

Given the positive comments of R2, I have the impression that the authors should be able to address at least some of the concerns by R1 as well, bearing in mind that not all aspects of the parameter identification problem need to be addressed in this paper, as long as this is made clear to the reader early on.

I therefore ask the authors to revise the paper accordingly. If a more challenging test case can be developed that would be very nice. If that is not feasible, I believe the paper should be recast as an exploratory pilot study to examine the potential of the trajectory-based approach in combination with a solution to the eikonal equation.

Sincerely,

Gerrit de Rooij
Editor

Dear authors,

I asked one of the reviewers to have a look at your revision. The reviewer gave a positive assessment with which I concur. The reviewer noted a single typo: in line 3 on page 3, 'discussion' should read 'discuss'.

I am therefore happy to inform you I can now accept your paper for publication.

Yours sincerely,

Gerrit de Rooij
Editor