This work provides a methodology to evaluate geomechanical properties of subsurface materials based on Earth and atmospheric tides (EAT). The methodology is based on the observation of head and uses models that are taken from available literature studies. The approach is demonstrated with a few numerical examples related to real case studies.

I found the paper and the proposed methodology interesting and I support publication of this work. I think that the paper is not very easy to read and I suggest some restructuring and streamlining of the presentation, ultimately leading to a number of revisions concerning the presentation of the methods and results. Detailed comments are reported below.

General comments on the methods:

The methodology is quite articulated and includes the integration of several models and mathematical formulations. It was not easy to follow the presentation of the method. For example, two models are presented for post or pre-strain response. While after reading the whole manuscript I (probably) understood the reason for this, the way the models are integrated is only explained in section 2.2.5 after the models are presented in 2.2.3-4. There is an itemized list, presenting the whole method step by step, but this comes only in section 3. I suggest presenting a flowchart presenting the general idea of the whole methodology at the beginning of section 2, to clarify the explanation and presentation of the methods.

To me it is not intuitive to understand the meaning of a pre-strain water response. After reading the whole manuscript I understand that the authors are offering here a quantitative interpretation to a phenomenon that is not clearly understood and, in these terms, I completely support their work. However, all the discussion related to this point, should be given earlier (see e.g., section 4.2 495-505) to give the reader the possibility to properly assess and understand all the assumptions. On this note, the caption of figure 3 distinguishes confined from semi-confined, and this is related to post and pre-strain as far as I undertand. This is not clear from the figure caption.

General comments on the results and discussion:

In general, there is little appreciation in the paper for the uncertainty associated with the estimated quantities. I suggest reporting more details about parameter estimation via curve fitting, e.g., the value assumed by residuals, RMSE or other similar error indicators, and the confidence bounds associated with the key estimated properties. Following up on this comment I have a particular concern: the method prescribes the selection of pre- or post-strain model according to a phase shift evaluation, where the two models are assumed to be both possible if the shift is between -1deg and 0deg. However, I wonder if this overlap is not too restricted as, in principle, the estimation of the phase shift from observed data may be affected by a larger interval of uncertainty.  

I found the discussion of the results quite interesting, particularly the fact that they seem to disclose non trivial response of subsurface materials to EAT. These could be due to multiple factors, as extensively discussed in the paper. I have three comments on this point, which in my view should be considered in a revision:

• I wonder if the observed results may be the results of some particular assumption embedded in the parameter estimation procedure. In particular, can the authors demonstrate that the proposed methodology leads to consistent results when applied to synthetic data (i.e. data numerically generated with known parameters and artificially perturbed)? This would demonstrate that the estimation method is robust in terms of parameter identification, at least when the data are consistent with the assumptions.
• Regarding the discussion of the negative Poisson ratio (section 4.4), and given the fact that the measurement sampling volume is unknown, is it possible that this result is due to boundary effects?
• The authors state that the results could be used to infer poroelastic properties to be used in civil and mining construction. However, I have the impression that some of the estimated parameters may be driven by the very specific conditions associated with EAT, and may not be portable to different conditions and loading. For instance, I wonder if some of the observed parameters may be associated with different time scales associated with material responses.

In section 4.2 the authors provide a sort of sensitivity analysis. (e.g., eq. 36-37). This is hard to follow because the discussion is only qualitative. I suggest either dropping it or expanding it. However, the paper is already dense and long and I wonder if the author really need to include this point.

Other minor points:

Data Figure 3 are scarcely readable, please improve readability of the Figure.

Line 405: if bounds are imposed it seems quite logical that no none of the parameters exceeded the fitting bounds. I suggest rephrasing and, as mentioned above, provide more quantitative details about the estimates.

At line 648 the authors state that the model offers the advantage to rely on information on grain compressibility, available in the literature. However, at line 629 they state the opposite, i.e. that grain compressibility data are generally lacking. Please reconcile the two statements.

Summary

This paper presents a methodology to estimate hydro-geo-mechanical properties of semi-confined sub-surface using the groundwater response of a borehole to Earth and atmospheric tides. The methodology is based on previously developed methods that were independently used either to investigate a tidal dilatation response or a surface load response. The originality of the present work is to combine both approaches and to successfully retrieve the hydro-geomechanical parameters of the sub-surface only by measuring the water-level pressure heads and using hydraulic and linear poro-elasticity theories. I suggest this paper to be published after some revisions mentioned here after are performed.

General comments

The paper is very long and organization of the sections is quite confusing. The methodology is described only on page 19, even after the description of the 4 studied sites. In order to better understand the sections on the pre- and post-strain response of the water level response and the discussions on the compressibility or incompressibility of grains, the methodology should be introduced right after the introduction.

In the different stages of the methodology, the hypotheses behind the employed theories should appear more distinguishly: drained or undrained conditions, consolidated or unconsolidated, lateral flows or only vertical flow etc.

Finally, the title should be more precise since the groundwater response was studied only at semi-diurnal periods (for instance add “semi-diurnal” before Earth and atmospheric tides) and precise M2 and S2 tides in the abstract. The surface load model used in the pre-strain water level response and the model used in the post-strain response are frequency-dependent, elastic parameters too. We may expect different results when analyzing diurnal or longer-period tides for instance.

Detailed remarks

p.2 line 45: please define ETs

p.2 line 46: “separating tidal components” it depends mostly on the spectral resolution, hence on the length of the time-records used.

p.3 line 71: You applied a moving average spanning across a time period of 3 days; such a process is equivalent to a low-pass filtering not high-pass filtering. It filters out higher frequency signals. Please replace “longer frequency” by “higher”, since I do not know what means a longer frequency.

p.3 section 2.1: how well are identified the M2 and S2 tidal components in the data using HALS? How large are the uncertainties on the amplitudes and phases? Particularly on the phase, how precise it is, since it will affect the phase-shift value used to determine the use of a pre-strain or post-strain model.

p.5 equation (2): the superscript “p” in the following equations designs “pore” but here is this “p” for potential? Please clarify.

p.6 line 138 typo: dilation à dilatation

p.7 section 2.2.3 the figure 3 is referenced here before Figure 2. Please reorganize figures in order they are numerated in the order of citation.

p.8 section 2.2.3 some discussion on the boundary layer depth associated with the parameter a_w/r_w should be done in regard with the pre-strain model depth here after.

p.8 section 2.2.4 more discussion on the boundary layer depth is missing. For instance, at which depth/diffusivity the amplitude A_M2 is maximum?

Interpretation of Fig. 2 is missing. For instance, with respect to the plots shown in Fig. 6.11 in the book by Wang (2000), at what depth the diffusive pore-pressure effects are confined? What is the limit in terms of thickness for using this theory as a good approximation? What about the phase of eq. (14), if you plot it wrt z/d, in which depth/diffusivity range does the sign change?

p.8 line 196 is this 10 m the value obtained for d when the pore-pressure is equal to surface load? How much larger the pore-pressure can be wrt surface load (when loading efficiency is larger than 1)? Please explain better the adequacy (the valid depths ranges) when combining ET and AT.

p.10 section 2.3 please introduce here BE = barometric efficiency

This section related to damping could be put into or right after section 2.2.2.

p.12 equation (26) in the denominator, the \theta should be rather a \gamma.

p.14 equations 32-35 are solved using an iterative LS scheme. Why not using a Bayesian inference in particularly to check the correlations between the various parameters?

p.17 line 349 please define MASL (m above sea level)

p.17 last line: “the ~28 days” as the minimum requirement for what? In order to separate M2 and S2 in terms of frequency resolution we would need 57 days. Please precise.

p.18 line 378 Detrending using SciPy function detrend is done by fitting a linear function, not by moving average, please correct this sentence; the moving average enables to low pass filter the data.

p.21 section 3.3 The choice of the post-strain model for the Death Valley site should be discussed since the phase shift of -1 degree is at the limit between pre and post-strain models.

p.24 section 4.2 I do not really understand this long discussion. It should be simplified in order to highlight the major points.

p.24 line 497 typo: stain à strain

p.25 line 533 typo stain à strain

p.28 lines 606-609 these statements have already been claimed before, please remove this repetition.

p.26 section 4.4, discussion on the negative Poisson ratio. What about the influence of ocean loading? Have you quantified its impact on the amplitudes and phases of M2 and S2 for the 4 sites considered in this study? Uncertainties on the M2 and S2 phases should be discussed too since it may influence the values of the Poisson ratios obtained at the end. Correlation between the parameters should be checked too.