the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 May 2025
Detecting ground ice in warm permafrost with the dielectric relaxation time from SIP observations
Abstract. The melting of ground ice poses significant hazards in permafrost regions, making effective detection methods essential. Conventional geophysical techniques like electrical resistivity, seismic surveys, or ground-penetrating radar alone often produce ambiguous results due to the overlap of material characteristics between frozen and unfrozen ground. This study addresses these limitations by using the dielectric relaxation time of ice as a unique indicator of ground ice. We developed a method to quantify relaxation time from Spectral Induced Polarization (SIP) data measured by the FUCHS III device. The method's effectiveness was demonstrated through synthetic data and two field surveys. SIP field measurements, ranging from 1.46 Hz to 40 kHz, were conducted on a retrogressive thaw slump and a pingo in Yukon, Canada. The extracted relaxation times were mapped to pseudo-depths obtained from single-frequency inversion. This study proposes a relaxation time range from 10 to 400 µs for ground ice, and the results demonstrate that this range can detect ground ice spectra in field studies. Comparison with observations in a borehole and an exposure of permafrost indicate that relaxation time is less ambiguous in detecting ground ice in warm permafrost than conventional methods such as electrical resistivity tomography.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-1801', Anonymous Referee #1, 16 Jun 2025
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RC2: 'Comment on egusphere-2025-1801', Anonymous Referee #2, 11 Aug 2025
In their preprint submitted to EGUsphere, “Detecting ground ice in warm permafrost with the dielectric relaxation time from SIP observations”, Fereydooni et al. (2025) introduce the Apparent Relaxation Time (ART) approach for detecting ground ice within warm and highly conductive permafrost by leveraging dielectric relaxation time derived from spectral induced polarization (SIP) measurements.
This is a complement approach to use SIP measurements for ground ice detection (without quantification or thermal characterization) in field scale. In addition, the authors present a great dataset of high-frequency SIP measurements of frozen ground, which is of high scientific interest by its own, demonstrate the field applicability of the ART approach for delineating subsurface zones containing ground ice, and compare the results to other established SIP data analysis frameworks.
Nevertheless, fundamental improvements and corrections are required before this draft is suitable for publication in The Cryosphere.
- Correct usage of terminologies, symbols and equations:
Please use the terms “impedance”, “apparent complex resistivity”, and “complex resistivity” correctly (see e.g. Binley and Slater, 2020. Resistivity and Induced Polarization, DOI: 10.1017/9781108685955). Instead of “apparent impedance” use “apparent complex resistivity”.
Use correct notation of complex symbols and indicate all complex valued parameters with $^*$. To indicate real and imaginary part, you can use $^{\prime}$ and $^{\prime\prime}$ instead of subscripts.
Note, that relaxation times from different model definitions are not equivalent (e.g. Limbrock and Kemna, 2024. Relationship between Cole–Cole model parameters in permittivity and conductivity formulation, DOI: 10.1093/gji/ggae300). In this study, a resistivity-based model is used to estimate relaxation times while reverence values for ice a given for a permittivity-based model. As exact relaxation time values are not used for further analysis (e.g. temperature estimates), this is not a big issue but should be mentioned.
Please use short subscripts for parameters and in equations. E.g. “app” or “a” ($\rho_a$) instead of “apparent”, “meas” or “m” instead of “measured”, in Eq. 10: “m” for “measured” or “d” for “data”, and “f” for forward response instead of “predicted”. Also, make sure that you follow the official Copernicus guidelines for mathematical notations and terminology (https://publications.copernicus.org/for_authors/manuscript_preparation.html#math).
- Structure of Section 2 (Background):
Please reorganize this section and rename the subsections. Subsections 2.1 and 2.3 referrer to special media while 2.2 also is about ice polarization and 2.4 about interpretation depending on type of ground media.
- Improve figures:
Make sure that all labels and tick marks are big enough to read. Some figures are very crowdy and messy (mainly Figs. 2 and 6). Maybe you can use some additional subplot (e.g. for real and imaginary part) or different symbols and color-coding to improve readability. Also, avoid having multiple legends within a single subplot.
- Referencing style:
Use consistent referencing style for figures. Sometimes you used “Figure 12b” (e.g. line 303) and sometimes “Figure 10(b)” (e.g. line 270)
Additional inline comments:
L2: “electrical resistivity” is not a method. There is, e.g. “electrical resistivity tomography”.
L20: Olhoeft (1977) is not about ERT but about electrical properties in general and dielectric properties in particular.
L27: Huisman et al. (2016) is not about SIP application to frozen environments.
L29ff: There are also some approaches for spectral data analysis for ice content quantification, e.g. Mudler et al., 2022 or Zorin and Ageev, 2017 (DOI: 10.3997/1873-0604.2017043). An additional approach is the phase-frequency-effect after Maierhofer et al. (2024, DOI: 10.5194/tc-18-3383-2024).
L36: There are tools for full tomographic inversion for sEIT data, e.g. ResIPy or pyGIMLi.
L53: Impedance combines resistance R (instead of resistivity) and reactance X.
Eq. (1) and L56: Voltage and currant are also complex valued parameters here.
L61 and Eq. (3): This is the Debye-model and not the Cole-Cole model. Please cite with Debye, 1929: Polar molecules.
L67 and Eq. (6): This is the Pelton model (Pelton et al., 1978). When formulated for Z*, R_0 must be used instead of \rho_0. Alternatively, you have to use the formulation for \rho^*. Including the Cole-Cole exponent, it is based on the Cole-Cole model and not the Debye-Model.
L73 and L83: The following reference should be used for temperature-dependent relaxation time of ice: Auty and Cole (1952, DOI: 10.1063/1.1700726) or Evans (1965, DOI: 10.3189/S0022143000018840)
L121ff: Is this a realistic scenario, that frozen and unfrozen soil only differ in main relaxation time but have the same \rho_0 and m?
L126f: Please use the equation environment instead of inline equation. Introduce all parameters used (R1, C1, …).
L137: Use the $\pm$-symbol.
L137: Which standard deviation and which mean? Of all values of one spectrum? What is the "unit" of "3"? Or is it just a factor of three?
L138: What is excluded? A single data point from the spectrum at this frequency? Is a data point only excluded from the real or imaginary spectrum, where it exceeded the threshold or is a complex data point (real and imaginary part) also removed if it exceeds only the threshold value for the real or the imaginary part?
Eq. (9): Usually, the total response is the sum of the individual responses. Thus, a “+”-sign is missing.
L154 and Eq. (10): Is this RMSE also used for minimization within the least square method? Or is this a different RMSE?
L158f: Please give more details: Is the same factor applied to both, real and imaginary part? How big is this weighting? How is it defined/chosen?
L161: Accuracy of which results? The spectral fits?
Eq. (10): $i$ is already introduced as imaginary number $i=\sqrt{-1}$
Eq. (10) and following lines: Z* or \rho* are complex valued parameters. Why is only the magnitude used to calculate an RMSE?
Fig. 3: Dots do not represent measured data, but synthetic data to test the spectral inversion code. To my opinion, this figure is not needed and can be removed.
L191ff: This paragraph has many redundant sentences. Reduce it to a single sentence.
Fig. 4a: Scale in (a) way to small.
L244: “result” = Impedance Magnitude from Fig. 7a?
Fig. 7: Why different grid/mesh resolutions between (a) and (b)/(c)?
L268ff and Fig. 10: It looks like there is ground ice more or less everywhere in this figure. Is that realistic?
Fig. 11: Which data are shown here? From the field measurement presented in this study or from measurements at the core or borehole samples?
L294ff: Maierhofer et al. (2022) is looking into full spectral responses. Here you refer to Maierhofer et al. (2024). I think the reason why this is not perfectly differentiate ground ice from other materials is the fact that even the high frequency used in that study (75 Hz) is not within the range of ice polarization relaxation. But not that only single frequencies are used.
Figs. 7, 9, 12 and 13: Why are you using a frequency of 40 kHz as reference? From your spectral responses (e.g. Fig. 6), it would be more convenient to use the peak frequency of the imaginary part (something between 1 kHz and 3 kHz).
Figs. 12 and 13: Maybe the interpretation can be improved, if for ART three different colors are used to distinguish between relaxation times below and above ice-relaxation.
L312: “0C” -> “0 °C”
L321: Just for clarification: Both are directly extracted from the measured spectra without inversion? Because the imaginary parts shown in the previous figures are data from inversion.
L322: Do not introduce parameters within the equation itself.
L330 and L342: Why these threshold values?
Fig. 14a: Often, conductivity or resistivity values are log-normal distributed (log values instead of linear values). Therefore, you can try this as well to get closer to a normal distribution. Later in Fig (c) a log-distribution is used!
L343f: Do you have an independent validation that provides a "true" distribution of ground ice as reference? Here, it is assumed that the ART results are more reliable. Why?
L348: SIP is not a relatively new method, but not that well established as other methods for ground ice characterization.
L350: The issue of manual layout configurations depends on the device not on the method itself.
L355: The abbreviation “SIP” is already introduced.
L365: There are already tools available to properly invert SIP data as mentioned before.
Citation: https://doi.org/10.5194/egusphere-2025-1801-RC2
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