the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Feb 2025
Integrated approach for characterizing aquifer heterogeneity in alluvial plains
Abstract. This study introduces a robust methodology for characterizing heterogeneity in alluvial aquifers by integrating borehole data, electrical resistivity tomography (ERT) and stochastic modeling. The approach was tested in the Varaždin aquifer to simulate the distribution of four hydrofacies identified from borehole data: gravel (G), gravel, sandy to clayey (Gsc), sand with gravel, clayey to silty (Sgcs), and clay to silt, sandy (CSs). The spatial distribution of hydrofacies was modeled using the combination of geostatistical and stochastic tools. Entropy factor analysis reveals a lack of consistent vertical transition patterns between hydrofacies, highlighting the role of relative proportions in determining their spatial distribution. As the thin Sgcs-CSs layer limited the ERT resolution below 20 m depth, synthetic models were incorporated into the ERT analysis to provide more reliable delineation of hydrofacies at greater depths. The resulting dimensions of the lens-shaped structures revealed horizontal hydrofacies continuity, and were incorporated into horizontal Markov chain models. The 3D Markov chain models were used to generate 10 stochastic realizations of the hydrofacies distribution. The validation results identified the representative hydrofacies model for the Varaždin aquifer with a prediction accuracy of 63 %, which is consistent with findings from similar studies. Results from simulations focused on the Vinokovšćak wellfield area show that the integration of ERT data into the model development improves the hydrofacies prediction accuracy by 0.3 to 5.0 %, depending on the grid resolution. The analysis of different grid resolutions demonstrates that the optimal cell size is closely related to the lens length. While smaller grids fail to capitalize on finer resolution due to oversegmentation, coarser grids provide a simplified hydrofacies model, potentially increasing prediction accuracy but losing spatial resolution. This methodology forms a basis for integrating spatial heterogeneity into groundwater models, serving as a practical tool for sustainable management in alluvial and other sedimentary environments worldwide.
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RC1: 'Comment on egusphere-2025-327', Thomas Hermans, 14 Mar 2025
Dear authors,
I read with interests this paper entitled: “Integrated approach for characterizing aquifer heterogeneity in alluvial plains”. In this article, a methodology is proposed to integrate geophysical data as a constraint for geostatistical simulations meant for generating realistic realizations of alluvial aquifer heterogeneity. The topic is relevant, as these aquifers are amongst the most complex to characterize, while there are often exploited for drinking water production and highly contaminated in and around cities due to industrial activity. I support any effort related to a better characterization of these complex systems. In that sense, the paper is interesting, but from my point of view, the reader is left with a feeling of unfulfilled expectations. My major concerns are described below:
- Geophysical data are not really used as a soft constraint in this study, but merely to estimate correlation lengths. This is a strong limitation of this work since correlation lengths from tomographic methods are known to be biased (Day-Lewis and Lane, 2004). This likely explains the limited added value of ERT for the evaluation criteria compared to other studies that used ERT in a similar context (e.g. Hermans et al., 2015). Actually, looking at your objectives, I see many similarities withy the study by Hermans et al. (2015). They used ERT to constrain hydrofacies simulated by MPS. They also used falsification to deduce the most realistic training image. They further constrained their simulations by hydrogeological data collected during a pumping test. Also see the work by Barfod et al. (2018) for a similar approach. Therefore, I think it is important to better describe the global context of using geophysical data to constrain geological models, and discuss the proposed methodology in that perspective. Ideally, it would be good to also include simulations where the geophysical data are actually used as soft constraints for the detailed area where data is available.
- The introduction should focus more on studies which investigated heterogeneity characterization, which is also the topic of this paper. Here are a few references that are relevant, there are many more (and more recent): Baines et al. 2002; Bowling et al. 2005, 2007; Bersezio, Giudici, and Mele 2007; Mastrocicco et al. 2010; Doetsch et al. 2010, 2012a. Gottshalk et al., 2017.
- The methodology uses thresholds on resistivity to classify the deposits in hydrofacies (L120-122). But with such a low number of validation wells, the uncertainty cannot be captured, does it? See Hermans and Irving (2017) for a study dedicated to uncertainty analysis in a similar context. This paper shows that such a threshold actually does not exist. For any resistivity value, every hydrofacies has a specific probability of occurrence. This comes mostly from the limitation of geophysical inversion which smooths interfaces, but can also results from the heterogeneity within the sediments. This has also been demonstrated by Isunza-Manrique et al. (2023) in another context. To me, this aspect is essential for any study aiming at a robust integration of geophysical data in a stochastic framework. I would also extract 1D resistivity distribution at the location of borehole and show in parallel the hydrofacies (L182). Because of the smoothing effect of inversion, I really doubt that fixed boundaries can be used. It could reveal a lack of co-located data to derive these ranges.
- I find n=10 realizations a very low number to look at uncertainties. In particular, the objective of a stochastic studies should be to deduce posterior probabilities, and not only deduce the most likely model (see line 162). I think more realizations are needed given that 4 facies are considered.
- Some important elements of the methodology are unclear. For example, it is not explained how the correlation lengths are extracted from the geophysical inversion (L169-170). It is crucial to the methodology, and any subjective element or involved parameters should be identified, also considering my other remarks (see point 3 above).
- L197-203. This part is presented as one of the novelty of the paper. However, as explained above, other studies using TI for hydrofacies simulations proposed a more thorough analysis of this (see Hermans et al., 2015 for MPS, and Hermans and Irving, 2017 for synthetic studies and Gottshalk et al. 2017 for indicator simulations). Here, a deterministic approach is first used to derive some correlation lengths that are then integrated in geostatistical simulations, this is not really an integration of ERT into stochastic modelling, which would imply some consideration of the related uncertainty (i.e. probability distributions). Note also that the approach of using synthetic models to validate interpretation is not new. See Caterina et al. 2013 for example. The modelled lenses are very thin. Can they really explain the low resistivity observed, or is it simply a loss of resolution with depth ? How can you be sure only the background profile is found at depth?
Specific comments:
- There are too many technical details for an abstract. It is not understandable what the grid refers to (ERT inversion grid, hydrofacies simulation grid?). I also miss some context. Typically an abstract should be structured as: 1) Global context 2) Specific research gap 3) Proposed methodology 4) Main results 5) Conclusion.
- The resolution of ERT always decreases with depth.
- Not clear what is meant by boundary conditions in this context.
- MPS can also be pixel-based. The original SNESIM algorithm was a pixel-based MPS algorithm (Strebelle, 2002), so is the direct sampling algorithm (MAriethoz et al., 2010).
- “Depending on” rather than “Given”.
- Reference to specific Excel functions is not necessary.
- Reference to an automated python script is not necessary. It is expected that you made the process automatic.
- A resistivity of 4600 Ohm.m seems very high for alluvial sediments. Is this realistic?
- I don't see any sharp boundaries in the figure, which is a result of the smoothness constrained used for inversion. Have you considered other inversion approaches (blocky inversion, minimum gradient support, etc.)?
- Figure 4. You select different values for the different lenses, why? Why is the CSs layer discontinuous? Wouldn't a continuous layer also explain the data?
- What is “the virtual position of the borehole”? Do you mean a projection of the borehole on the profile?
- Table 1 gives mean values and ranges, but it is not mentioned how many lenses are detected to calculate them.
- Figure 8. The number of correct predictions is quite low. What would be the score if the most abundant facies (background?) would be predicted everywhere?
- It is not clear to me what “oversegmentation of the lenses” is. Aren’t you overinterpreting distributions that are not significantly different given the low number of samples (n=10)? Wouldn’t you need many more validation data to analyze the risk of oversegmentation?
- L335-340. Maybe refer to the work of Danish colleagues who developed a scale of “reliability” when building their geological models using hard and soft data (e.g., Enemark et al., 2024 and references therein).
- L342-359. See my main comments related to other studies which proposed more advanced methodologies.
References
Baines D., Smith D.G., Froese D.G., Bauman P. and Nimeck G. 2002. Electrical resistivity ground imaging (ERGI): a new tool for mapping the lithology and geometry of channel-belts and valley-fills. Sedimentology 49(3), 441–449.
Barfod, A.A.S., Vilhelmsen, T.N., Jørgensen, F., Christiansen, A.V., Høyer, A.-S., Straubhaar, J., Møller, I., 2018. Contributions to uncertainty related to hydrostratigraphic modeling using multiple-point statistics. Hydrol. Earth Syst. Sci. 22, 5485–5508. https://doi.org/10.5194/hess-22-5485-2018.
Bersezio R., Giudici M. and Mele M. 2007. Combining sedimentological and geophysical data for high resolution 3D mapping of fluvial architectural elements in the Quaternary Po Plain (Italy). Sedimentary Geology 202, 230–248
Bowling J., Harry D., Rodriguez A. and Zheng C. 2007. Integrated geophysical and geological investigation of a heterogeneous fluvial aquifer in Colombus Mississippi. Journal of Applied Geophysics 65, 58–73
Bowling J., Rodriguez A., Harry D. and Zheng C. 2005. Delineating alluvial aquifer heterogeneity using resistivity and GPR data. Ground Water 43(6), 890–903.
Caterina, D., Beaujean, J., Robert, T., Nguyen, F., 2013. A comparison study of different image appraisal tools for electrical resistivity tomography. Near Surface Geophysics 11, 639–657. https://doi.org/10.3997/1873-0604.2013022
Day-Lewis, F.D., Lane, J.W.Jr., 2004. Assessing the resolution-dependent utility of tomograms for geostatistics. Geophysical Research Letters 31, L07503. https://doi.org/10.1029/2004GL019617
Doetsch J., Linde N., Coscia I., Greenhalgh S.A. and Green A.G. 2010. Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data. Geophysics 75(6), G53G64.
Doetsch J., Linde N., Pessognelli M., Green A.G. and Günther T. 2012a. Constraining 3-D electrical resistance tomography with GPR reflection data for improved aquifer characterization. Journal of Applied Geophysics 78, 68–76.
Enemark, T., R. B. Madsen, T. O. Sonnenborg, L. T. Andersen, P. B. E. Sandersen, J. Kidmose, I. Moller, T. M. Hansen, K. H. Jensen, and A.-S. Hoyer (2024). “Incorporating interpretation uncertainties from deterministic 3D hydrostratigraphic models in groundwater models”. In: Hydrology and Earth System Sciences 28.3, pp. 505–523. doi: 10.5194/hess-28-505-2024. url: https://hess.copernicus.org/articles/28/505/2024/.
Gottschalk, I.P., Hermans, T., Knight, R., Caers, J., Cameron, D.A., Regnery, J., McCray, J.E., 2017. Integrating non-colocated well and geophysical data to capture subsurface heterogeneity at an aquifer recharge and recovery site. Journal of Hydrology 555, 407–419. https://doi.org/10.1016/j.jhydrol.2017.10.028
Hermans, T., Irving, J., 2017. Facies discrimination with ERT using a probabilistic methodology: effect of sensitivity and regularization. Near Surface Geophysics 15, 13–25.
Hermans, T., Nguyen, F., Caers, J., 2015. Uncertainty in training image-based inversion of hydraulic head data constrained to ERT data: Workflow and case study. Water Resources Research 51, 5332–5352. https://doi.org/10.1002/2014WR016460
Isunza Manrique, I., Caterina, D., Nguyen, F., Hermans, T., 2023. Quantitative interpretation of geoelectric inverted data with a robust probabilistic approach. GEOPHYSICS 88, KS73–KS88. https://doi.org/10.1190/geo2022-0133.1
Mariethoz, G., Renard, P., Straubhaar, J., 2010. The Direct Sampling method to perform multiple-point geostatistical simulations. Water Resources Research 46. https://doi.org/10.1029/2008WR007621.
Mastrocicco M., Vignoli G., Colombani N. and Zeid N.A. 2010. Surface electrical resistivity tomography and hydrogeological characterization to constrain groundwater flow modeling in an agricultural field site near Ferrara (Italy). Environmental Earth Sciences 61(2), 311–322.
Strebelle, S., 2002. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Mathematical Geology 34, 1–21.
Citation: https://doi.org/10.5194/egusphere-2025-327-RC1 -
AC1: 'Reply on RC1', Mitja Janža, 03 Jun 2025
We thank the reviewers for their thorough evaluation and valuable suggestions to improve our manuscript. Please find attached our final author responses, which address all comments point by point (reviewer's text underlined).
Sincerely,
The Authors
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RC2: 'Comment on egusphere-2025-327', Anonymous Referee #2, 17 Apr 2025
General comments
Thank you for submitting this manuscript. Personally, I am curious about applying stochastic modelling for the purposes of electrical resistivity response of the subsurface, so I found it an interesting and engaging read. The reasoning, or wider context, behind the research is well formed (in that the aquifer which is the subject matter of the research is critical to the local water supply). The methodology in this manuscript seems competent, though I’m not familiar with the T-PROGS software that underpins the stochastic modelling efforts. I find the results insightful, however, I do have concerns about the statistical significance the stochastic outputs with and without the benefit of geoelectrical information.
Regardless I wish the authors well, and hope my comments are useful to them. Furthermore, I would like to recommend that this manuscript be accepted on the basis of moderate revisions.
Specific comments
Lines 93 – 95: Is it known how K is determined in these boreholes? Are they determined in situ (e.g. falling/rising head tests) or via laboratory investigations on samples.
Lines 198 – 202: As the ERT is sensitive to 20 m below the ground level, I agree that the synthetic modelling should also be limited to 20 m. Although, I’m unsure if the inclusion of synthetic modelling improves the sensitivity of the electrical measurements to various hydrofacies below 20 m depth. If one proposes a tomography model (be it through a smoothness regularised gauss newton approach, as with R2, or via stochastic approaches) the raw data is still fundamentally only sensitive to the upper 20 m in this case. It’s a limitation of where the electrical current flows, as the authors point out (Lines 198-199). Nevertheless, I think the authors could argue here that the synthetic modelling benefits ground model development by incorporating prior knowledge of the geology.
Figure 4: How did the authors build the lens shapes in the mesh? The results are quite exciting. What is the data misfit of the traditional tomography section and synthetic model versus the real data?
Figure 5 b: Referring to Figure 2 (which shows a 3D visualisation of the boreholes) the “Clay to silt, sandy” (CSs) hydrofacies appears to dominate the near surface, furthermore, previous studies (Karlović et al., 2021) suggest that the geology is layered. Yet in this figure (5 b) the CSs hydrofacies distribution has little lateral continuity. Can the authors comment on why that might be?
Line 254: What is not clear to me is which information from the electrical resistivity tomography is included or how it is included into the T-PROGS software. Is it just the lens lengths as stated on line 167?
Figure 7 b: See above comment about Figure 5 b.
Lines 308 – 309: Is an improvement of 0.3 to 5.0 % statistically significant enough to argue that the inclusion of ERT has improved the outcome of stochastic modelling? My experience with Markov chain Monte Carlo methods is that the answer can differ for repeated runs by a few percentage points. If the T-PROGS software is utilising Markov chains as the authors state (Line 136) then the question is whether the results are repeatable.
Technical corrections
None noted.
Citation: https://doi.org/10.5194/egusphere-2025-327-RC2 -
AC2: 'Reply on RC2', Mitja Janža, 03 Jun 2025
We thank the reviewers for their thorough evaluation and valuable suggestions to improve our manuscript. Please find attached our final author responses, which address all comments point by point (reviewer's text underlined).
Sincerely,
The Authors
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AC2: 'Reply on RC2', Mitja Janža, 03 Jun 2025
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CC1: 'Comment on egusphere-2025-327', Lee Slater, 21 Apr 2025
This is an interesting contribution to studies that aim to improve hydrofacies distribution by combining electrical geophysical datasets with discrete borehole logging datasets. The approach is applied to an important study area and addresses issues with nitrate contamination of critical aquifers used for water supply. The comments posted to date identify some key areas for improvement. In particular, I agree with the need to [1] better define this contribution within the scope of previous similar (foundational?) work [2] better recognize the limitations of using smooth electrical resistivity tomography (ERT) inversions for defining discrete hydrofacies boundaries, and [3] reassess the use of the synthetic models to assess the reliability of the estimated hydrofacies models. With respect to the third point, I am not entirely sure what was done. The approach described by the following statement is hard to follow: “This issue has been addressed by introducing synthetic models into the ERT interpretation, based on the assumption that if the ERT imaging from synthetic modeling matches or closely resembles to ERT imaging obtained from field measurements, the interpretations and resulting hydrofacies models are reliable”. As already noted, it is not reasonable to synthetically infer structures at depth beyond the resolution of the acquired field measurements. Perhaps I am misunderstanding the strategy applied. I suggest that the revisions include a better illustration/justification of the approach with a concrete example of the value added.
One additional point to consider in the revisions is that the paper implicitly assumes that variations in grain size primarily control variations in electrical resistivity. Of course, resistivity also depends strongly on porosity, fluid conductivity, and the degree of saturation. Although variations in porosity sensed with resistivity could contribute to improved hydrofacies discrimination, variations in fluid conductivity and degree of saturation would likely complicate the delineation of hydrofacies. Is there any field data available to constrain the magnitude of these variations? Presumably, water tables are available in the wells. Significant variations in fluid conductivity might be expected given the nitrate contamination problem. Perhaps these complicating factors can partly explain why the improvement in the prediction of hydrofacies distribution is modest when ERT is added? Some further discussion of this issue is required.
This paper will make a valuable contribution to the hydrogeophysics literature once the comments provided in the posted discussions are addressed.
Citation: https://doi.org/10.5194/egusphere-2025-327-CC1 -
AC3: 'Reply on CC1', Mitja Janža, 03 Jun 2025
We thank the reviewers for their thorough evaluation and valuable suggestions to improve our manuscript. Please find attached our final author responses, which address all comments point by point (reviewer's text underlined).
Sincerely,
The Authors
-
AC3: 'Reply on CC1', Mitja Janža, 03 Jun 2025
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