Spectral induced polarization (SIP) measurements were collected at the Lapires talus slope, a long-term permafrost monitoring site located in the western Swiss Alps, to assess the potential of the frequency dependence (within the frequency range of 0.1–225 Hz) of the electrical polarization response of frozen rocks for an improved permafrost characterization. The aim of our investigation was to (a) find a field protocol that provides SIP imaging data sets less affected by electromagnetic coupling and easy to deploy in rough terrains, (b) cover the spatial extent of the local permafrost distribution, and (c) evaluate the potential of the spectral data to discriminate between different substrates and spatial variations in the volumetric ice content within the talus slope. To qualitatively assess data uncertainty, we analyse the misfit between normal and reciprocal (N&R) measurements collected for all profiles and frequencies. A comparison between different cable setups reveals the lowest N&R misfits for coaxial cables and the possibility of collecting high-quality SIP data in the range between 0.1–75 Hz. We observe an overall smaller spatial extent of the ice-rich permafrost body compared to its assumed distribution from previous studies. Our results further suggest that SIP data help to improve the discrimination between ice-rich permafrost and unfrozen bedrock in ambiguous cases based on their characteristic spectral behaviour, with ice-rich areas showing a stronger polarization towards higher frequencies in agreement with the well-known spectral response of ice.
Mountain permafrost regions are highly sensitive to climate changes, with significant implications for the hydrological regimes. Water reservoirs and sources in many mountain ranges in the world are threatened by changes of the cryosphere; and thus, knowledge of the ground ice and water content in permafrost regions is critical for the estimation of water storage capacities and future water supplies (e.g. Arenson and Jakob, 2010; Halla et al., 2021; Harrington et al., 2018; Langston et al., 2011; Rangecroft et al., 2016; Schrott, 1998). Monitoring of the thermal state of permafrost has become an essential task in mountain regions in order to better understand the dynamics of mountain permafrost, for instance through borehole ground temperature networks on a global (Global Terrestrial Network of Permafrost, GTNP; Biskaborn et al., 2019) and regional (Swiss Permafrost Monitoring Network; PERMOS, 2021) scale. However, from borehole temperature monitoring alone we cannot differentiate between unfrozen and frozen water content, as we can observe water in the liquid phase even at negative temperatures (e.g. Harris et al., 1988). Additionally, the ground ice content is difficult to assess quantitatively and depends on many parameters such as the permafrost landform and substrate as well as past climate evolution and local topoclimatic effects (e.g. Kenner et al., 2019). Ex situ analysis of ice cores recovered from the drilling of boreholes (e.g. Haeberli et al., 1988; Krainer et al., 2014; Wang et al., 2018) and nuclear well logging can help to quantify porosity and ice content at specific borehole locations (e.g. Scapozza et al., 2015; Vonder Mühll and Holub 1992). However, boreholes are costly and difficult to install at high-mountain permafrost sites, and the information obtained is limited to discrete locations.
Geophysical methods have emerged as important techniques in alpine permafrost investigations, as they provide quasi-continuous information about subsurface properties and heterogeneities (e.g. Hauck et al., 2011; Hilbich et al., 2008; Mollaret et al., 2019; Steiner et al., 2021; Wagner et al., 2019). Hence, geophysical information supports and interconnects spatially sparse borehole data and can provide essential information about the temporal evolution of subsurface permafrost characteristics (e.g. Hauck, 2013; Scott et al., 1990). In particular, electrical resistivity tomography (ERT) has become a routine tool for the monitoring of active-layer dynamics and the internal structure of permafrost landforms, taking into account the controls of temperature on electrical resistivity (e.g. Coperey et al., 2019; Hauck, 2002; Hauck et al., 2011; Hilbich et al., 2008, 2009; Keuschnig et al., 2017; Krautblatter et al., 2010; Mollaret et al., 2019; Parkhomenko, 1982; Supper et al., 2014). The discrimination between unfrozen and frozen water content could be improved with the help of ERT, especially in monitoring applications although uncertainties remain (e.g. Hauck, 2002; Hauck and Kneisel, 2008; Oldenborger and LeBlanc, 2018). In the case of unfrozen materials, low resistivity values are observed due to electrolytic conduction taking place along the water-interconnected pores and along the electrical double layers (EDLs) formed at the interface between water and mineral surfaces (e.g. Leroy et al., 2008; Revil and Glover, 1998; Ward, 1990; Waxman and Smits, 1968). Upon freezing, the mobility of the ions is reduced, and conductive pathways break down, increasing the electrical resistivity for frozen soils and rocks (e.g. Hauck, 2002).
In many practical applications, the interpretation of the subsurface electrical resistivity is difficult, since air, rock matrix and ice can result in similar resistivity values. Refraction seismic tomography (RST) is commonly used as an additional method to improve the quantification of the ice content within the subsurface, as the acoustic velocity of air and ice differs by an order of magnitude (Hausmann et al., 2007; Hilbich, 2010). Within the so-called four-phase model (4PM, Hauck et al., 2011), electrical resistivity and P-wave velocity data sets are combined to estimate ice, water and air contents from petrophysical relations. Recently, Wagner et al. (2019) implemented a joint inversion algorithm that iteratively solves for the petrophysical parameters from ERT and RST data sets based on the 4PM. This algorithm has demonstrated an improved ability to estimate relevant parameters (such as water and ice content) for a variety of permafrost sites (Mollaret et al., 2019) and for time-lapse monitoring applications (Steiner et al., 2021). However, the interpretation of geophysical signatures of air, ice and rock matrix is still open to discussion.
The induced polarization (IP) method has emerged as a promising method in hydrogeological studies due to its sensitivity to pore-space geometrical characteristics (e.g. Binley et al., 2015; Binley and Slater, 2020; Kemna et al., 2012; Revil, 2012; Weller et al., 2013). While the resistivity method measures the medium's ability to conduct electric current (transport of charges) in terms of transfer resistances, the (frequency domain) IP method also measures the ability of the medium to electrically polarize (local separation of charges and thus electrical energy storage) in terms of electrical impedances (e.g. Binley et al., 2005; Kemna et al., 2012; Revil and Skold, 2011; Sumner, 1976). The build-up of charge concentration gradients responsible for the polarization effects measured in IP takes place in the vicinity of EDLs at grain–fluid interfaces as well as pore constrictions (e.g. Bücker et al., 2019; Leroy et al., 2008; Revil, 2012; Revil and Florsch, 2010; Schwarz, 1962). IP measurements can be performed at different frequencies in the megahertz–kilohertz range in the so-called spectral IP (SIP) method to quantify and model the frequency dependence of the subsurface electrical properties and link them to lithological, textural, hydraulic or geochemical properties of the ground materials (for further details, see Binley et al., 2015; Kemna et al., 2012; Revil et al., 2012; Weigand et al., 2017).
Laboratory studies have demonstrated the sensitivity of SIP measurements in
soils and rocks to changes in temperature above the freezing point
(e.g. Binley et al., 2010; Zisser et
al., 2010) and under freezing conditions
(e.g. Coperey et al., 2019; Kemna et al.,
2014a; Olhoeft, 1977; Revil et al., 2019; Stillman et al., 2010; Wu et al.,
2017). In the context of permafrost,
Duvillard et al. (2018) and
Coperey et al. (2019) investigated
in the laboratory the effect of temperature (between
The main challenge regarding the conduction of field SIP measurements corresponds to the contamination of the data at frequencies above 1 Hz by electromagnetic (EM) coupling (e.g. Flores Orozco et al., 2021; Pelton et al., 1978; Zimmermann et al., 2019). EM coupling may result in self-induction of the near-subsurface materials, cross-talking between cables, and the capacitive coupling in the cable–electrode and electrode–ground contacts (e.g. Flores Orozco et al., 2021; Zhao et al., 2013; Zimmermann et al., 2008, 2019). Hence, IP field surveys at higher frequencies are commonly based on the use of separated cables connecting voltage and current electrodes (e.g. Dahlin et al., 2002) to minimize cross-talking, leading to longer field procedures than for single-cable layouts. The challenges in the data acquisition have limited the application of the SIP method in periglacial environments (Bazin et al., 2019; Doetsch et al., 2015; Duvillard et al., 2021, 2018; Grimm and Stillman, 2015), and, to our knowledge, no study has investigated to date the influence of EM coupling and the reliability of frequency domain SIP imaging data sets in high-mountain permafrost environments. Nonetheless, such investigations are critical to evaluate the applicability of the SIP method on permafrost terrain and to extend the capabilities of current permafrost monitoring systems based on the resistivity method.
In this study, we aim at investigating the frequency dependence in SIP imaging results for measurements conducted at the Lapires field site, a high-alpine talus slope in the Swiss Alps. The talus slope represents a typical mountain permafrost landform with a coarse blocky surface and high, heterogeneously distributed ground ice contents. The selected study area is a well-characterized site with extensive information available for the interpretation of the SIP results (e.g. Delaloye, 2004; Hilbich, 2010; Mollaret et al., 2019; Scapozza et al., 2015). Particular emphasis in our study is on the analysis of the quality of the SIP data and an efficient field procedure that provides robust and high-quality SIP imaging data sets less affected by EM coupling while being easy to deploy in rough terrains. To achieve this, we compare data collected with different cables (multicore and coaxial) and different cable layouts. We propose procedures for the collection and processing of SIP data and discuss the spatial extent of the ice-rich permafrost at the site as resolved by means of ERT and SIP imaging. Additionally, we investigate the frequency dependence of the observed field SIP signatures and compare it with SIP laboratory measurements on rock samples from the site and data available in the literature. We hypothesize that the use of coaxial cables improves the SIP data quality and that the SIP method helps to differentiate between different subsurface substrates and thermal conditions at the investigated site.
The frequency domain IP method, also known as the complex resistivity (CR) or
complex conductivity (CC) method, uses four-electrode arrays to measure the
electrical impedance (
There is no fundamental reason and no loss of generality in choosing
In the presence of (liquid) pore water in a metal-free porous rock, polarization effects for frequencies below 1 kHz are generally related to ionic polarization in the EDL at the pore water–solid matrix interface (e.g. Kemna et al., 2012). Polarization mechanisms have been expressed in terms of the polarization of the Stern layer, i.e. the inner part of the EDL (e.g. Leroy et al., 2008; Revil, 2012); the diffuse layer, i.e. the outer part of the EDL (e.g. Dukhin et al., 1974); and the membrane polarization (e.g. Hördt et al., 2016; Marshall and Madden, 1959; Vinegar and Waxman, 1984). The study of Bücker et al. (2019) demonstrates that such models of diffuse layer and membrane polarization are equivalent and quantitatively describe the same response.
Below the freezing point, during the phase change from liquid water (further
referred to as simply “water”) to ice, the salinity of the liquid pore
water phase is expected to increase as saline water begins to crystallize
only below the eutectic temperature (
The study site Lapires is located in the Valais Alps (western Swiss Alps;
46
The composition of the talus slope was derived from four boreholes drilled between 1998 and 2008 (Scapozza, 2013), geophysical measurements (Delaloye, 2004; Hilbich, 2010; Lambiel, 2006; Mollaret et al., 2019), and ground temperature (GT) records (Staub et al., 2015). According to borehole data, the ice-rich permafrost body reaches a thickness of up to 15 m and is overlain by a 5.2 m thick active layer (active-layer thickness of the year 2019) (Scapozza et al., 2015; Staub et al., 2015). None of these boreholes reached the depth to the bedrock reported by Scapozza et al. (2010). A permanent ERT monitoring profile was installed in 2006 (Hilbich, 2010) to observe spatiotemporal dynamics of the freezing and thawing processes; the corresponding ERT results over more than a decade are described in Mollaret et al. (2019). Hilbich (2010) further compared seasonal changes in electrical resistivities with corresponding seismic travel times and borehole data.
Earlier results from the Lapires talus slope by Delaloye (2004), Lambiel (2006) and Staub et al. (2015) suggest that the spatial extent of ice-rich permafrost is most probable in a polygon-shaped zone, which is delineated in Fig. 1 and which we are referring to within this paper (cf. Fig. 1). Using borehole geophysics, Scapozza et al. (2015) estimated the apparent porosity within the permafrost layer between 40 % and 80 %, as well as a volumetric ice content between 20 % and 60 %, with parts completely saturated with ice. Additionally, at the borehole locations, Marmy et al. (2016) (by thermal modelling) and Mollaret et al. (2020) (by geophysical joint inversion) estimated the porosity to be around 40 % to 60 % and an ice content in the range of the mean borehole geophysical estimates.
In our study, we present data collected in the frequency domain using the eight-channel DAS-1 system (from MPT-IRIS Inc.) along five parallel horizontal profiles with a roughly east–west direction and two vertical profiles (as depicted in Fig. 1). For consistency, we use the same profile notation as PERMOS with profiles H1 and V1 (not shown in this study) representing the long-term ERT monitoring profiles (Permos, 2019). The geophysical data presented in this study were acquired in two campaigns: (a) an initial survey conducted at the beginning of September 2018 to test different cable settings and (b) a second survey at the end of August 2019 to map the extension of the permafrost. Both surveys were conducted during periods corresponding to well-developed thaw layers. Borehole temperature data were used for validation of the geophysical results, including the temperature profiles of three boreholes where permafrost has been observed (BH-1108, BH-1208 and BH-0198) and one borehole where no permafrost was found during drilling (BH-1308) (see Fig. 1b).
An important focus of our study aimed at finding the field procedure that provides high-quality SIP imaging data sets with minimum disturbance by EM coupling yet that is robust and easy to deploy in rough terrains, such as high-alpine permafrost landforms. To this end, we conducted SIP measurements using two different cable types, multicore (mc) and coaxial cable (cc), as well as two different cable layouts, a single-cable thread and separated cables. The latter corresponds to the use of two cables for each electrode position to minimize cross-talking between the cables, with one cable used to inject current and the second for voltage measurements. In particular, four different settings were compared and are described in more detail in Table 1: (a) permanently installed single multicore cables along profile H1 (4 m electrode separation, 43 electrodes, 168 m profile length), (b) single coaxial cables along profile H2 (32 electrodes with 5 m separation resulting in a profile length of 155 m), (c) separated multicore and (d) separated coaxial cables (24 electrodes, 5 m separation, 115 m profile length) along a part of profile H2 (first electrode corresponds to the twelfth electrode of profile H2; cf. Fig. 1). The single coaxial cable and the separated cable setups were placed at a different locations (H2) to avoid noise in the data due to the presence of the permanently installed electrodes and cables from profile H1. The deployed coaxial cable consists of a bundle of independent coaxial cables with the shield of all wires attached at the end connector to permit grounding through the measuring device (for further details see Flores Orozco et al., 2021). The ERT monitoring multicore cable was permanently installed in 2008 in the context of the PERMOS ERT network using common wires with no specific isolation between wires or other preventative methods for EM coupling, as this cable is only used for ERT monitoring. Multicore cables used in this study correspond to standard cables supplied by IRIS Instruments. Data quality was evaluated by means of normal and reciprocal (N&R) analysis, with a reciprocal reading referring to a repetition of the measurement after interchanging current and potential dipoles. Accordingly, N&R data were collected for each profile (cf. Table 1). Analyses of the misfit between N&R readings were used for the identification of outliers in the data (related to high discrepancies between N&R readings) and the quantification of data error (corresponding to small fluctuations between N&R readings), as described in previous studies (e.g. LaBrecque et al., 1996; Flores Orozco et al., 2012; Slater et al., 2000).
In August 2019, we collected SIP data along four additional profiles: H3,
H4, V2 and V3 using 32 electrodes with a separation of 10 m between them,
resulting in a profile length of 310 m (Fig. 1). The position of the
profiles was selected to cover ice-rich and ice-poor areas as well as
different substrates (e.g. fine-grained, blocky areas and bedrock). Contact
resistances were measured before each data acquisition with observed values
between 5 and 60 k
Overview of the SIP measurement setup deployed along seven profiles to evaluate the data quality for different cable types and setups and for mapping purposes.
The N&R analysis is based on the concept that normal and reciprocal
readings should be identical, with small variations typically indicating the
influence of random noise, while large changes point to readings affected by
systematic errors, for instance due to a poor galvanic contact in one of the
electrodes or polarization of electrodes
(e.g. Binley et al., 1995; Flores Orozco et al., 2021; Huisman et al., 2016;
Zimmermann et al., 2019). Accordingly, for each normal and reciprocal pair,
we can compute the average impedance magnitude
For the quantification of data error in the impedance phase readings, we
applied a constant-error model (i.e. no dependence on the impedance
magnitude or phase values), obtained as
For the inversion of the SIP data, we used the finite-element
smoothness-constraint inversion code CRTomo (complex resistivity tomography code; Kemna, 2000), which uses
impedance magnitude and phase values to compute the distribution of the
complex resistivity in the subsurface for every profile and frequency
separately. This algorithm allows us to control the inversion of the data to
a confidence interval defined by the data error estimates described by the
error models in Eqs. (7) and (8) (Kemna, 2000; Flores Orozco et al., 2012). The code allows us to terminate the inversion when a
root mean square of 1 is reached, which means the model is fitted to the data
considering the interval of confidence quantified by means of the error
parameters. As demonstrated in several studies, this approach minimizes the
risk of overfitting the data in the inversion and the generation of
artefacts. We blanked those areas in the inverted images associated with
cumulated sensitivity values 2 orders of magnitude smaller than the
highest cumulated (absolute) sensitivity (normalized cumulative,
error-weighted sensitivities), as described by
Weigand et al. (2017). We used the same
error parameters (
Figure 2 shows a modified version of the pseudosection, where we present both normal and reciprocal readings, in terms of the impedance magnitude and phase, after the removal of outliers following the procedure described above. Pseudosections allow for an easy visualization of the spatial consistency in the readings and the position of the removed quadrupoles. In Fig. 2 we compare the filtered pseudosections for data collected with single multicore cables (Fig. 2a), separated multicore cables (Fig. 2b), separated coaxial cables (Fig. 2c) and single coaxial cables (Fig. 2d). Pseudosections are presented for impedance magnitude measurements at 0.5 Hz, as we observed no frequency dependence for the impedance magnitude (data not shown), while impedance phase readings are presented at four frequencies in the range between 0.5 and 75 Hz.
In general, the comparison of the four settings indicates that (a) measurements with coaxial cables show a higher data quality (i.e. a lower
standard deviation of
Pseudosections for normal and reciprocal data at four different
frequencies (0.5, 7.5, 25 and 75 Hz) collected at the Lapires site
In Fig. 3, we present a statistical analysis of the misfit of normal and
reciprocal phase
Misfits in phase values between normal and reciprocal phase and
resistance readings collected at different frequencies (0.5, 7.5, 25 and 75 Hz)
and with different cable settings:
We present in Fig. 4 resistivity imaging results for data collected along
profiles H2, H3, H4, V2 and V3, which clearly reveal two main units, i.e. a
low- and a high-resistivity unit. These resistivity variations coincide with
the temperature records in the four boreholes; i.e. frozen conditions are
represented by high resistivities and vice versa. The borehole positions are
indicated in the resistivity images including thaw depth and permafrost base
at the date of the measurement. By extracting specific resistivity values
from the inversion result for all profiles at close proximity to a borehole
at the depth of the permafrost base, a mean value for the boundary between
ice-rich and unfrozen talus of 10 000
Figure 4b shows the model parameters extracted at the intersection of two
crossing profiles, revealing a consistent vertical distribution of electrical resistivity values. The active layer is partly visible for H2 due to the
smaller electrode spacing of 5 m but is still hard to distinguish from the
ice-rich permafrost because of similar electrical resistivity values for
air- and ice-filled talus. In general, all profiles reveal resistivity
values in the range of 10 to 100 k
The right-hand part of profile H3 is characterized by the transition from
the talus slope into a bedrock slope with a thin veneer of vegetated
sediment cover (250–310 m horizontal distance). The observed resistivity
range of the bedrock slope is with 10–29 k
Before discussing the induced polarization imaging results, it is
recommended to look at the frequency dependence in the electrical
impedances, expressed in terms of the apparent resistivity (
Visualization of the frequency dependence in the electrical
impedance measurements collected along profile V2. Impedance magnitude
values are converted to apparent resistivity
To investigate variations in the polarization response, we present in Fig. 6
exemplary imaging results expressed in terms of the phase (
Range of complex resistivity values observed in the inversion results of all profiles for different subsurface materials.
The first 120 m of profile H3 (Fig. 6a) reveal in general low values for all
parameters (e.g. Table 2) at 0.5 and 75 Hz related to the fine-grained,
unfrozen material. The middle part of H3 shows much higher values than the
unfrozen area for both 0.5 and 75 Hz, clearly delineating lateral variations
in the subsurface, which we interpret as the blocky, ice-rich material of
the talus slope. The right part of profile H3 covers the bedrock slope
(
Complex resistivity inversion results in terms of real and
imaginary components and phase at 75 and 0.5 Hz for profiles
Profile V3 in Fig. 6b also demonstrates the improved interpretation of
subsurface properties by means of induced polarization (
To investigate in detail the frequency dependence of the electrical
properties, we show in Fig. 7 CR values extracted from a virtual borehole in
(a) the unfrozen part of profile H4 and (b) the ice-rich permafrost zone of
profile V2. The values were extracted between adjacent electrodes along the
vertical black lines (a pixel width of 10 m) for inversion results
independently obtained at each frequency (0.5–75 Hz). The different
spectral behaviour allows for a clear distinction between frozen and unfrozen
conditions. For the unfrozen part in profile H4 we observe low real and
absolute imaginary resistivities (
Extracted complex resistivity values (real and imaginary
components) in a virtual borehole in
In complex resistivity imaging data, EM coupling is known as an important
source of error affecting
Based on the use of single coaxial cables, our analysis demonstrates the possibility of collecting data with a high reciprocity in the range between 0.5 and 75 Hz, with a higher reciprocity in the higher frequencies compared to the study of Flores Orozco et al. (2021). This is likely due to the high resistivity of the substrate which shifts inductive coupling to higher frequencies. Accordingly, our data reveal poor reciprocity for readings collected above 100 Hz, resulting in just a small number of quadrupoles remaining after filtering. Thus, we reduced our interpretation of the imaging results to data collected at 75 Hz and below. Although several quadrupoles had to be discarded above 100 Hz, some of the measurements collected with small separations between current and potential dipoles show a high SNR and smooth impedance phase spectra for the entire frequency range as observed in Fig. 5. Only by looking at the frequency dependence of the electrical impedance, a distinction between frozen and unfrozen conditions can be found that is consistent with nearby borehole temperature data (cf. Fig. 1). In well-controlled conditions in a permafrost tunnel of frozen silts, Grimm and Stillman (2015) collected data with the SIP Fuchs III instrument (from Radic Research) with a 20 kHz bandwidth, which permits the digitalization of the data in remote units directly connected with the electrode, effectively minimizing EM coupling at frequencies below 100 Hz (e.g. Martin et al., 2020) and inductive coupling at frequencies up to 20 kHz (e.g. Grimm and Stillman, 2015). However, the deployment of such a system dramatically increases the fieldwork in comparison to the laying of a single cable. Thus, for our study and further investigations in alpine permafrost, we believe that the use of a single coaxial cable might be the best compromise considering the improved data quality (i.e. reciprocity) and simple procedures for field surveys.
The consistent analysis of the SIP data collected in different profiles and at multiple frequencies revealed the possibility of quantitatively correlating spatial variations in the complex resistivity with variations in the ice content and geological units (Fig. 8). As discussed in Kemna (2000) and Flores Orozco et al. (2011, 2012), the use of error models in the inversion of the data and a careful quantification of the data error permit fitting the different data sets to adequate confidence intervals and to correctly retrieving the frequency dependence of the electrical parameters during the inversion. Grimm and Stillman (2015) used the time-lapse feature of Res2DInv (2D RESISTIVITY & IP INVERSION software, Aarhus GeoSoftware; Loke and Barker, 1996) to invert the entire frequency spectrum, which applies a regularization across successive measurements but without adequate error parametrization in the inversion. In our analysis, we took special care in the quantification of the data error but performed an independent inversion of the data sets for all frequencies, accounting only for spatial regularization across each imaging plane. An alternative approach (e.g. Günther and Martin, 2016; Kemna et al., 2014b; Son et al., 2007) relies on a simultaneous inversion of SIP data measured over a range of frequencies. Although multifrequency inversion may improve the consistency between results and its interpretation, previous studies have demonstrated that adequate error quantification also permits a quantitative interpretation of SIP imaging results even without any spectral regularization (e.g. Flores Orozco et al., 2013). The consistency between imaging results obtained for different profiles (cf. Fig. 4b) at different frequencies and with borehole data demonstrates the possibility of relying on this approach.
With this measurement setup for alpine permafrost and based on the proposed methodology to process and invert the SIP data sets, we present in Fig. 8 a synopsis of all profiles for a characterization of the spatial extent of permafrost at the Lapires test site. The complex resistivity at 5 Hz is shown in terms of the real (Fig. 8a) and imaginary (Fig. 8b) components with additional spectra depicted at selected locations (Fig. 8c). The values are shown as an arithmetic mean at a depth of 10 m at each electrode position. The interpreted permafrost extent using the thresholds defined in the Results section is indicated for three different depths (7, 10 and 15 m). A spline function was fitted to obtain three polygons, which can be compared to the assumed permafrost distribution from previous studies. When comparing the polygons delineating the permafrost extent at different depths for the real and imaginary components, we observe a reduction in the size with depth (for the measurements conducted in 2019) and an overall smaller spatial extent of permafrost mapped by Staub et al. (2015) (cf. Fig. 1). The outline of the permafrost extent in Fig. 1 was established by Delaloye (2004) between 1998 and 2004 using bottom temperature of snow cover (BTS), universal temperature logger (UTL), vertical electrical sounding (VES) and borehole temperature measurements. Thus, caution must be taken when comparing our results to the study of Delaloye (2004), as we used a different methodology, equipment and resolution. Nevertheless, the reduction in permafrost extent that is suggested by the results of this study is consistent with the findings of Mollaret et al. (2019), who also report a strong and spatially consistent resistivity decrease over the whole monitoring profile H1 and hence a decrease in ice content at the Lapires talus slope (based on long-term resistivity changes over 1 decade from 2006 to 2017). They showed that the most significant resistivity decrease at LAH (horizontal profile in Lapires; profile H1) is below the ice-rich body due to air circulation. Mollaret et al. (2019) state as well that amongst all ERT-monitored permafrost sites in the Swiss Alps, the Lapires talus slope shows one of the most severe increases in permafrost temperature, which had been confirmed later by Permos (2021). A thorough analysis as to whether the observed reduction in permafrost extent within our study compared to the estimate by Delaloye (2004) is a result of permafrost degradation or if it is solely based on methodological differences is, however, beyond the scope of this study.
Real and imaginary resistivity at 0.5 Hz yield similar results for the
extent of permafrost with slightly smaller polygons delineated for
Characterization of the spatial extent of permafrost of the
Lapires talus slope for the complex resistivity. The complex resistivity
values are expressed as real
In Fig. 8c, we depict the spectra of the complex resistivity for different
substrates and thermal conditions: unfrozen, fine-grained talus; frozen,
blocky talus; and bedrock. Here, pixel values represent the mean of
As already depicted in the imaging results of Fig. 6 and observed in other
permafrost studies using only electrical resistivity tomography (e.g. Mollaret et al., 2020;
Steiner et al., 2021), the interpretation of
Within our study, we showed that we can discriminate between different substrates and ice contents, and other studies demonstrate that the induced polarization method is also applicable for morphologically different mountain (bedrock, coarse blocks) (e.g. Maierhofer et al., 2021) and arctic (unconsolidated sediments) (e.g. Doetsch et al., 2015) permafrost sites. However, the frequency dependence of the polarization response of ice-rich and ice-poor sites with different geologies needs to be analysed in more detail in future investigations.
If complex resistivity values are markedly different for laterally varying
unfrozen and frozen subsurface conditions as demonstrated above, they should
show the same effect in vertical direction regarding the transition from the
unfrozen active layer to the permafrost body. In Fig. 9 we present (a) the
borehole temperatures at BH-1108 at the time of the SIP survey with the
resistivity profile at 0.5 Hz in close proximity to the borehole and (b) the
spectral response for pixel values extracted from the inversion results of
profile H2 close to borehole BH-1108, where the 5 m electrode spacing allows
us to investigate shallow structures. The electrode spacing of 5 m was
chosen to improve the resolution close to the surface and delineate the
contact between the active layer and the permafrost body better. Hilbich et
al. (2009) applied numerical modelling and analysed the depth-of-investigation (DOI) index (introduced by Oldenburg and Li, 1994) and the
resolution matrix (e.g. Menke, 1984) to identify unreliable model regions
in ERT data collected at a coarse blocky and ice-rich permafrost site. They
found that the determination of the transition from the active layer to the
permafrost table with electrical methods is limited by its vertical
resolution which is dependent on the electrode spacing. Thus, from numerical
modelling (not shown) we found that a separation of 5 m with dipole lengths
of 5 and 20 m were small enough to delineate the transition between the
thawed active layer and the ice-rich permafrost. The pixel values of Fig. 9
represent the mean values for a pixel width of 5 m for two different depth
ranges: 0–5.6 m (thawed active layer) and 5.6–19.5 m (permafrost).
Previous geophysical investigations in close proximity to BH-1108 report low
seismic P-wave velocities of 500–1500 m s
Coperey et al. (2019) recently
presented complex conductivity spectra for data collected in the laboratory
in a broad temperature range (between
However, a comparison of these studies with our results is not straight
forward, as they investigated the SIP response of different materials
ranging from saline permafrost to sandstone and granite samples which are
hardly comparable to the SIP response of a talus slope consisting of big
blocks and voids filled with ice and air (where mixing models would be
needed to upscale the electrical response from the sample scale to the scale
resolved by electrical imaging). Additionally, the various permafrost
studies use different parameters to describe the frequency dependence of the
polarization; thus care has to be taken in the comparison of the results.
Within the frequency range investigated in our analysis, we are not able to
capture the ice relaxation peak (ranging from 1 to 100 kHz for relevant
permafrost temperatures); hence, in this study we cannot apply the approach
of Grimm and Stillman (2015) to quantify
ice content. Nevertheless, the increase in polarization magnitude of the
ice-rich talus material observed in Fig. 8 is consistent with the observed
decrease in temperature and increasing ice content. Given the lack of
high-frequency data, this study does not address the distribution of
spectral (e.g. Cole–Cole) parameters and their correlation with
spatiotemporal changes in the subsurface. However, further studies should
consider such analyses together with laboratory measurements in samples to
improve the quantification of ice content in alpine permafrost. Concerning
the improvement in the 4PM, our results suggest that SIP data may help in
the differentiation between air-filled and ice-rich, blocky material and
also between frozen and unfrozen bedrock, since air has no polarization
response and unfrozen bedrock can be identified based on the local maximum
at low frequencies in both
In this study, we presented SIP imaging data collected in the frequency domain from 0.1 to 225 Hz using a dipole–dipole measurement protocol. We compared data acquired using single multicore, separated multicore, single coaxial and separated coaxial cables to find a field protocol that provides SIP imaging data sets less affected by EM coupling. Results demonstrate that single coaxial cables yield a high reciprocity in the range between 0.5 and 75 Hz, leading to an improvement in SNR compared to the other cable setups.
Using this measurement setup we characterized the spatial extent of
permafrost at the Lapires talus slope based on the real and imaginary
components of the complex resistivity at 0.5 Hz. We observe an overall
smaller spatial extent of permafrost compared to the assumed distribution
from previous studies and a slight decrease in the spatial extent of
permafrost with depth. The complex resistivity images reveal clear
variations in the electrical values between frozen and unfrozen states and
between different substrates but more pronounced variations in the pattern
of the frequency dependence of
We conclude that with appropriate measurement and processing procedures, the characteristic dependence of the SIP response of frozen rocks on temperature, and thus ice content, can be utilized in field surveys for an improved assessment of thermal state and ice content at permafrost sites. Future research should be particularly conducted on the combination of field studies with laboratory analyses for an ice content quantification that would rely on SIP data. Further studies should concentrate on the time-lapse analysis of the polarization response in permafrost environments and the application of SIP for different permafrost landforms (e.g. rock glaciers, bedrock permafrost).
The borehole temperature data from the PERMOS network are available in
PERMOS (2019) at
AFO, CHa, CHi and TM designed the experimental setup. TM and AFO collected and processed the geophysical data. AFO, CHa, CHi and TM interpreted the geophysical signatures, and AFO, CHa, CHi, AK and TM discussed the results. TM led the preparation of the draft, for which AFO, CHa, CHi and AK contributed equally.
At least one of the (co-)authors is a member of the editorial board of
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We are thankful to the PERMOS office for providing the borehole temperature data and to the cable car company Télénendaz S.A. for the logistical support to our research activities at the Lapires field site. We are thankful to Martin Mayr, Philipp Zehetgruber and Guy Ramsden for their help in the collection of the geophysical data. We gratefully thank the reviewer Jacopo Boaga, a second anonymous reviewer and the editor Peter Morse for their helpful comments and suggestions that substantially improved the quality of the paper.
This research has been supported by the Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung (grant no. 200021L_178823) and the Deutsche Forschungsgemeinschaft (grant no. 403089687).
This paper was edited by Peter Morse and reviewed by Jacopo Boaga and one anonymous referee.