Electrical resistivity tomography monitoring of permafrost in solid rock walls

Authors


Abstract

[1] This article describes the first attempt to conduct electrical resistivity tomography (ERT) in solid permafrost-affected rock faces. Electrode design, instrument settings, and processing routines capable of measuring under relevant conditions were developed. Four transects, with NW, NE, east (E) and south (S) aspects, were installed in solid rock faces between Matter Valley and Turtmann Valley, Switzerland, at 3070–3150 m above sea level. DC resistivity in the transects was measured repeatedly during the summer and compared by applying a time-lapse inversion routine. Resistivity values were calibrated using observed rock surface conditions of thawed, damp rocks (1–8 kΩ m), deeply frozen rocks (18–80 kΩ m), and the transition from damp thawed to frozen rocks (8–18 kΩ m). Mean surface layer resistivities of transects respond to air temperatures below 0°C with a rapid increase by a factor of 1.4 to 2.9 from values of 12–15 kΩ m to values of 22–31 kΩ m. Rock layers at depths of 2–6 m display a general trend of resistivity decrease in summer, corresponding to a persistent thawing process. Their response to anomalously cool August temperatures occurs with a time lag of 2 to 4 weeks. Only transects E, NE and NW display persistent, high-resistivity permafrost bodies (>50 kΩ m) mostly at depths of 6–10 m. The maximum thaw depth of a continuous thawing front above permafrost is 6 m. However, the ERT results emphasize the role of heat transfer by deep-reaching cleft water systems. Thus permafrost occurs in lenses rather than layers. ERT provides rapid detection of ice and water distribution in permafrost-affected bedrock.

1. Introduction

[2] Numerous rockfall events involving permafrost-affected rock walls have been observed over the course of the last century. Noetzli et al. [2003] reported 19 cliff falls (104–106 m3) and bergsturz (>106 m3) events since the beginning of the 20th century in the European Alps. Recent observations indicate that the frequency of rockfalls originating from permafrost rock walls has increased. Gruber et al. [2004a] described and modeled the effects of the hot 2003 summer on rock wall permafrost in the Alps, with implications mainly for mid- and high-magnitude rockfalls. Sass [2005b] measured elevated levels of small-scale rockfall in rock walls with degrading permafrost in the German Alps. While small-magnitude rockfalls on average cause more casualties than high-magnitude rockfalls [Hungr et al., 1999], single high-magnitude rockfalls can cause catastrophic damages, such as the Huascarán ice and rock avalanche in 1970, which was detached from a permafrost rock area and buried two villages with 20,000 inhabitants [Erismann and Abele, 2001]. Although the effects of global warming on rock wall permafrost are not yet fully understood, predictions point toward rapid degradation of permafrost in rock walls in the next few decades [Salzmann et al., 2007] contributing to elevated levels of permafrost-related hazards.

[3] At present, information about the spatial distribution of permafrost in rock walls is derived from two sources. Several boreholes drilled in permafrost rocks provide information on thermal profiles up to a hundred meters depth [Gruber et al., 2004c; Harris et al., 2003]. This information is supplemented with data sets from temperature loggers that record surface rock temperatures, usually in small holes of several centimeters depth. These data sets are then used to create energy balance models that calculate the spatial distribution of rock temperatures even in geometrically complex rock walls [Gruber et al., 2004a, 2004b; Noetzli et al., 2007; Peter, 2003]. Two problems associated with this approach are that temperature loggers and boreholes provide only point measurements with unknown spatial representativeness, and that validation of the models at depth is difficult to achieve.

[4] Systematic comparison of different geophysical methods for monitoring permafrost in high-mountain environments has been published by Hauck [2001]. From the large variety of geophysical methods, electrical resistivity tomography (ERT, also named DC resistivity tomography), was considered well suited for a number of permafrost-related problems. The major advantage in applying resistivity measurements to assess mountain permafrost lies in the fact that freezing and thawing of most materials is associated with a resistivity change of several orders of magnitude, which, in turn, is easily detectable with geoelectrical instruments. The installation of permanent electrodes and modeling of subsequent resistivity data sets within the same inversion routine (so-called time-lapse inversion) allows direct monitoring of the spatial and temporal permafrost variability in loose materials and rock masses beneath loose debris covers [Hauck, 2002; Hauck and Vonder Mühll, 2003]. The first attempt to derive spatial information from solid rock faces by ERT was conducted by Sass [2003]. In subsequent studies, Sass provided further evidence that ERT measurements are capable of measuring the degree of rock moisture [Sass, 2005a] and temporal and spatial variations of freeze and thaw limits [Sass, 2004] in solid rock faces. These ERT measurements were confined to the upper weathering crust (centimeter- to decimeter-scale) of rock faces with electrode spacing of only several centimeters.

[5] This study extended ERT to solid permafrost rock walls and monitored depths up to 10 m by enlarging electrode spacing to the meter scale. The scope of the electrical resistivity profiles includes subsurface information from depths in which permafrost in high-altitude rock walls is presumed by modeling and determined through borehole measurements [Gruber et al., 2004b]. Possible applications include spatialization of point information obtained from surface temperature and borehole measurements to two-dimensional information and validation of rock wall temperature models. When calibrated sufficiently for different environmental conditions, the technique could provide a fast method to derive the spatial distribution of frozen and thawed rock sections for rockfall hazard evaluation, and possibly for prediction.

[6] Four questions are addressed in this study: (1) Is ERT capable of measuring and monitoring permafrost in solid rock faces? (2) What technical equipment, instrument settings, and processing routines create reliable results? (3) What seasonal and short-term changes of rock freezing can be monitored with ERT? (4) What conclusions can be drawn for the spatial distribution of permafrost in rock walls?

2. Theory

2.1. Factors Influencing Short-Term Resistivity Changes in Rocks

[7] Rocks in the study area can be envisaged as semiconductors, in which electric current propagates by electrolytic conduction. Rock conductivity reflects the amount of pore space, its spatial distribution, the water saturation of pores and the resistivity of pore water, including the ion content. Archie [1942] developed an empirical formula for the resistivity of damp rocks (ρe) from the porosity (Φ), pore space occupied by liquid water (S), and resistivity of pore water (ρw),

equation image

where n, m, and a are constants. Assuming that porosity remains constant over brief intervals, changes in rock mass resistivity must result from changes in pore water resistivity or saturation of pore space with water. The decrease of rock temperatures above the freezing point results in a decrease of the mobility of ions, and this corresponds to a linear reduction of resistivity values. Thus resistivity (ρ) can be calculated as a linear decrease with temperature difference (TT0) from the resistivity value (ρ0) at a reference temperature (T0):

equation image

The constant α approaches values of 0.025 K−1 for most electrolytes [Keller and Frischknecht, 1966]. For temperatures below the freezing point, resistivity depends mainly on unfrozen water content until most of the pore water is frozen. For the range of temperatures encountered in Alpine environments, resistivity can be calculated as an exponential response to the temperature below the freezing point (Tf) according to McGinnis et al. [1973]:

equation image

[8] The factor b in equation (3) determines the rate of resistivity increase and can be derived empirically [Hauck, 2001, 2002]. Resistivity changes along a monitoring transect can be attributed to changes in pore water content and temperature, while changes in porosity and water chemistry can be neglected over daily to monthly measurement intervals in low-porosity rocks.

2.2. Error sources

[9] Distortions of measurements could derive from the electrokinetic potential created by water percolating in rock clefts. Streaming potential is usually restricted to values below 100 mV [Telford et al., 1990, p. 293], and is at least 1–2 orders of magnitude lower than the voltages applied during DC resistivity measurements. Moreover, standard geoelectric instruments reverse currency direction with a frequency of 1–2 Hz, eliminating the effect of steady potentials.

[10] Additional distortions could derive from large resistivity contrasts at the boundary of suspected permafrost bodies, which are usually orientated parallel to the surface. This may result in slight overestimation or underestimation of the depth of the transition layer. The same is true for measurements taken when the rock surface was frozen and therefore included high-resistivity sections. Finally, it is inevitable that certain topographic distortions are included when measurements are taken on a structured rock face. Resistivity values tend to be slightly overestimated in prominent rock spurs and underestimated in rock niches [Holcombe and Jiracek, 1984]. However, the deviation of the transects normal to the strike of the four transects presented here, in relation to transect length, was smaller than in previous studies [Sass, 2003, 2004, 2005a].

[11] It is important to consider that all distortions mentioned above, except electrokinetic potentials, do not influence the comparability of subsequent resistivity measurements, as they remain constant through time. In addition, it is not clear to what degree changes in water chemistry influence measurements. Because of the low permeability of intact gneissic rocks (10−10–10−13 m s−1) [Prinz, 1997], pore water resistivity is probably relatively stable. Solute rejection and the formation of brines in a “pore” scale [Hall et al., 2002; Murton et al., 2000] should be addressed in detail if this method is extended to more porous rock media. However, the permeability of fissured gneiss along discontinuities can be significantly higher (up to 10−3–10−4 m s−1) [Terrana et al., 2005] and solute rejection along discontinuities could cause changes in cleft water conductivity in the microscale.

3. Study Area and Methods

3.1. Study Area

[12] The study area “Steintälli” is located at the crest line between Matter and Turtmann Valleys in Valais, Switzerland, at an altitudinal range of 3070 to 3150 m above sea level (asl) adjacent to the Rothorn summit (Figure 1). Lithology in the study area is dominated by slaty paragneisses with homogeneous structure. The warming tendency after the Little Ice Age resulted in the retreat of the Rothorn NE Glacier, which lost more than 300 m of its maximum length. Presently, the Rothorn NE Glacier is dissected by newly exposed rock bars in several small ice relics, which are subject to further melting.

Figure 1.

Position of the DC resistivity monitoring transects in the study area Steintälli. The transects were named according to their dominant aspect.

[13] The annual average air temperature of the Steintälli approached values of −3.5°C according to measurements taken in the Matter Valley between 1962 and 1990. The permafrost study conducted by Gruber and Hoelzle [2001] in the Matter Valley ranked the whole Steintälli as a “likely permafrost area.” Climatological data have been recorded since July 2002 at a meteorological station located at a horizontal distance of 900 m and at an altitudinal difference of 330 m from the study site (average 3100 m asl). Temperature data were corrected by −1.98°C (0.6°C per 100 m) for the altitudinal difference. The average annual temperature of 2004 at the study site was −3.7°C, which is in accordance with the long-term average value. Although no complete data set was recorded for 2003, existing data from April until August indicate an air temperature several degrees higher than in 2004 and 2005 (Figure 2). August 2005, when geoelectric monitoring was initiated, was anomalously cool after two summer months with average temperatures (Figures 3 and 4) . As all rock bars in the study area are surrounded by ice, local air temperatures can be significantly lower than those measured at the meteorological station. The glacier relics also perform hydrological heat transfer with the rock bars, which is especially evident in the monitoring transect NE, due to the topographic position under an ice relic. The other transects only have lateral contact with glacier remnants (Figure 1).

Figure 2.

Mean monthly temperatures measured at the study site during the thaw periods 2003 to 2005.

Figure 3.

Daily air temperatures and moving average of air temperature in 2005.

Figure 4.

Test measurement of frozen rock surface resistivity values at the NE transect (15 August 2005).

3.2. Data Acquisition

[14] Four rock wall sections in the study area were chosen according to following criteria: (1) Rock walls should represent different aspects (NW, NE, S, E); (2) lithology and discontinuity patterns should be homogeneous within the rock face exposure and at the depth covered by ERT measurements; (3) in accordance with criteria established for the positioning of rock wall temperature loggers by the University of Zurich [Peter, 2003], the central part of the measurement transects should represent a free rock face steeper than 60°, in which electrodes were positioned a few meters above the ground to avoid snow covering them in winter; and (4) planar rock walls were preferred in order to reduce the topography included in the ERT inversion process. As a trade-off between depth information of ERT and the availability of suitable planar rock faces, 60 m long monitoring transects with electrode spacing of 1.5 m were installed in August 2005. To achieve optimal electrical contact with the rock mass, we used 10 mm thick and 10 cm long stainless steel screws as electrodes that were placed firmly in holes drilled in the rock face. The screws remained in the rock wall and were used for all subsequent ERT measurements.

[15] In the south and NE resistivity transects, we measured the topography of the electrode line three-dimensionally using a tachymeter with accuracy of 5 cm. The same method was applied for 20–30 electrodes visible from accessible viewpoints in the east and NW transects. Missing electrode positions were interpolated using information derived from ruler measurements. As deviations normal to the strike cause significant distortions in the two-dimensional analysis [Holcombe and Jiracek, 1984; Telford et al., 1990; H. Maurer, personal communication, 2006], deviations in the z direction of a linear function were calculated from the tachymeter data sets and implemented in the topographic modeling of the inversion software RES2DInv [Loke and Barker, 1996].

[16] We applied an ABEM SAS 300C Terrameter multielectrode resistivity instrument, designed for 41 electrodes. All measurements were conducted with the same current strength settings. In the rare case that resistance variability greater than 1% for a single datum point was observed, additional values were measured automatically. All measurements were conducted using a Wenner array with 190 different electrode combinations, as this array yields the highest signal-to-noise ratios for mountain permafrost environments [Hauck and Vonder Mühll, 2003]. The contact resistance of each electrode was tested before the measurement. As the electrode contact with the ground is difficult in frozen and ice-coated rock faces, even with the electrode design described above, we excluded up to three electrodes if the contact resistance was too high or not constant with time. If more than three electrodes indicated contact problems, the measurement was not included in the time-lapse inversion.

3.3. Data Processing

[17] Subsequent resistivity measurements in the four transects were inverted using the time-lapse inversion routine of the software RES2Dinv [Loke and Barker, 1996]. Use of time-lapse inversion guarantees that all subsequent measurements over a certain transect are processed with the same inversion model used for the first measurement in this transect [Hauck and Vonder Mühll, 2003]. Settings of RES2DInv were adapted to the special conditions present in rock faces. We inverted the data with half electrode spacing of 0.75 m and used a finer mesh size, to cope with high-resistivity contrasts. Robust inversion was applied to avoid smoothing of the resistivity gradients expected in the data sets [Sass, 2004]. Finally, we chose a model with an increase of 10% in layer thickness per layer, as this option provided more stable inversion results.

[18] When applying time-lapse inversions in partially frozen rock walls, it is difficult to obtain resistivity models with a root-mean-square (RMS) error between modeled and observed data of less than 10%. This is partly due to the fact that one to three of the 41 fixed electrodes had insufficient electrical contact and that only the datum points obtained in the first time-lapse measurement can be used for subsequent measurements. A conventional, nontime-lapse inversion of the later measurements gives smaller RMS errors (e.g., 6% for time series 2, 3, and 4 of the NW transect) but produces similar resistivity tomograms. Thus the resistivity tomograms show low susceptibility to the datum points that were removed from the data set due to the time-lapse inversion process. Measurements taken on dewed rock surfaces generally resulted in lower RMS errors (e.g., transect NE 13 August, RMS = 6.1%), while measurements on freshly ice-coated rock faces lead to inversion models with insufficient data fit (e.g., the NE transect, 15 August, RMS > 18%).

4. Results

4.1. Raw Resistivity Data

[19] To assess the quality of the data sets, preliminary analysis of the measured apparent resistivities was performed for each measurement. Apparent resistivity is calculated from the measured ratio between potential difference and injected current (resistance), multiplied with an appropriate geometric factor depending on the electrode spacing. If data quality is sufficient, the apparent resistivity data can be inverted on a two-dimensional grid to yield two-dimensional specific resistivity models (see section 4.2). As can be seen in Figure 5, resistivity measurements with small electrode spacing (1.5 m) indicate high variability in apparent resistivity values. Resistivity changes, measured with larger electrode spacings, occur much slower. This means that the uppermost rock layer (decimeter-scale), which is measured with an electrode spacing of 1.5 m, reacts fast and sensitively to frozen or unfrozen conditions at the rock surface. Subsurface layers (1–10 m depth), which are measured with larger electrode spacing (3–18 m), reacted in a slower and less pronounced manner.

Figure 5.

Apparent resistivity data of transects NE, NW, E, and S.

[20] The apparent resistivity of 40 datum points with electrode spacing of 1.5 m was compared at each measurement position with corresponding environmental conditions. The occurrence of superficially frozen rock surfaces in the north facing transects (NE and NW) was observed to reflect mostly air temperatures and the presence of snow and ice. The rock surface of the east and south transects melts quickly in response to direct solar radiation and therefore often two or three days earlier than north facing transects. The best illustration of this behavior is provided by subsequent measurements on the NW transect on 15 and 16 September. On 15 September, following four partly snowy days with average air temperature of 0.5°C, the NW transect was still frozen and partially ice covered, and yielded a mean apparent resistivity of 24.9 kΩ m for all surface values (electrode spacing of 1.5 m). Being that 15 September was the warmest day in September (7.1°C), the average 1.5 m spacing resistivity declined to 13.6 kΩ m in late afternoon of the following day (16 September, 1630–1830 LT), when the rock face was observed to be mostly ice-free and damp. Transect NE showed mean surface layer resistivity of 15.0 kΩ m on 13 August, subsequent to 4 days with air temperatures ranging from 2.2 to 4.6°C, in contrast to mean values of 21.6 kΩ m on 13 September, following a drop of temperature ranging from −1.6°C to −0.6°C over a 2-day period. Transects E and S thawed in response to intense direct solar radiation on 14 September and showed average 1.5 m electrode spacing resistivities of 12.9 and 11.8 kΩ m, respectively. On 17 August, following a 2-day snow-rich drop in temperature with average temperature of −0.7°C, the same transects had average surface layer resistivities of 30.2 and 30.7 kΩ m. In contrast to the general high temporal variability, rock surface sections that remained permanently damp as a result of cleft water outflow (transects NE, S, NW), yielded low (2–8 kΩ m) and extraordinarily stable apparent resistivity values, which persisted even during phases of intense freezing. The plunge in temperature from 20 to 23 August coincided with a significant redistribution of snow by high wind speeds and therefore yielded a less uniform reaction between different transects. In conclusion, absolute apparent resistivity values of single datum points of the deeply frozen surface rock were observed to range between 18 and 100 kΩ m, while damp rocks typically have values of 2–8 kΩ m, with transitional values ranging from 8 to 18 kΩ m. Average 1.5 m electrode spacing resistivity values, consisting of 40 datum points that reflect transitional freezing in surface bedrock, typically increased from 11–15 kΩ m (unfrozen rock) to 22–31 kΩ m (frozen rock).

[21] Two criteria reveal the subsurface information gathered in the raw data measured with electrode spacing larger than 1.5 m (Figure 5).

[22] 1. Transect NW stands out due to high (average) absolute apparent resistivity values, which are in the range of frozen rock (>18 kΩ m) at all depths. Average values in transects E and NE range between 15 and 23 kΩ m, which corresponds with the transition of thawed to frozen rock. Transect S shows relatively low apparent resistivity values of 12–18 kΩ m.

[23] 2. The change of apparent resistivity values with time is remarkably homogeneous in all transects and at all subsurface depths. All values, measured with electrode spacings larger than 3 m, declined from mid-August to mid-September. The decrease in resistivity with time is more pronounced in the high-resistivity NW transect, with factors up to 1.5. In the lower-resistivity NE, south and east transects, the resistivity decline involves a factor of only 1.05. Only transect NE was recorded before the snowy plunge in temperature at 14–15 August and thus shows a less pronounced decline (Figures 4 and 5). The fact that subsurface apparent resistivity values at the end of August are in a few cases slightly lower than those of mid-August and mid-September can be better explained in combination with the spatial information given in section 4.2.

4.2. ERT Tomographies

[24] Results from the ERT inversions include a range of specific resistivity values between 1 and 120 kΩ m. Spatial patterns of resistivity distribution can be classified according to (1) position; (2) resistivity range; (3) spatial persistence; (4) temporal variability of resistivity; and (5) neighborhood characteristics (see Table 1). As described in section 4.1., the largest part of the surface rock layer down to 2 m depth is characterized by frequent and quick resistivity changes up to a factor of 20 in response to rock surface temperatures. Results presented in this article also relate to specific resistivity measurements of rocks at depths of 2–6 m (“intermediate layer”) and 6–10 m (“bottom layer”).

Table 1. Classification and Characterization of Typical Features in the ERT Transects
PositionResistivity, kΩ mSpatial PersistenceResistivity ChangeExamplesSurface Observation and Subsurface Interpretation of Figures 69a
Surface layer (0–2 m)6–120lowUp to 2000%all transectsFrost susceptible rock surface (f.r.)
Surface layer (0–2 m)2–8high< ± 60%NE, NW, EPermanent cleft water outflow from water-saturated clefts (c.o.)
Intermediate layer (2–6 m)10–30Steady retreatNegative, −20% to −100%Widespread in all transectsSeasonal retreat of frozen rock sections
Intermediate layer (2–6 m)20–80highTemporary reduction (0 to −80%)EIntermediate layer permafrost body (i.p.)
Intermediate layer (2–6 m)2–8high< ± 60%NE, EUnfrozen rock next to water-filled cleft (u.r.)
Intermediate layer (2–6 m)10–23low (weeks)Temporary reduction 0 to −60%S, NWLagged response (thawing) of intermediate layer to warm June/July temperatures (l.r.)
Intermediate layer (2–6 m)15–25Transient phenomenon< ± 60%E, S, NEFreezing corridor between different frozen sections (f.c.)
Bottom layer (6–10 m)20–80highPositive, 0–140%NW, NE, EDeep-seated permafrost bodies (d.p.)
Bottom layer (6–10 m)3–14high< ± 60%EUnfrozen rock next to water-filled cleft (u.r.)
Bottom layer (6–10 m)18–30Transient phenomenon< ± 100%STemporary local frost lense (t.f.)

[25] Three types of resistivity zones can be observed in the bottom layer.

[26] 1. Highly resistive “lenses” with an extent of several meters, high spatial persistence, and a remarkable increase in resistivity up to 140% during the summer period (d.p., deep-seated permafrost).

[27] 2. A low-resistivity body in the bottom layer is only visible in the tomographies of transect E (Figure 6). However, because of its position under a high-resistivity zone it is difficult to judge to what degree its values are influenced by the inversion routine.

Figure 6.

Time-lapse ERT inversion models of transect E with approximate freezing/thawing front (dashed line). Note the response of the frost-susceptible surface layer (f.r.) to the cool second half of August. The freezing corridor (f.c.) extends between intermediate layer and bottom layer permafrost bodies (i.p., d.p.); deep-reaching unfrozen rock (u.r.) is apparent next to permanently water-filled clefts.

[28] 3. Spatially nonpersistent bodies in transect S, which have resistivity values ranging from 18 to 30 kΩ m (t.f., temporary frost lenses, in Figure 7).

Figure 7.

Time-lapse ERT inversion models of transect S illustrating damp unfrozen rock (u.r.) next to water-filled clefts that feed cleft water outflows (c.o.). Note the lagged response (l.r.) of the intermediate layer to warm June/July temperatures and deep-seated transient frost lenses (t.f.).

[29] 1. A typical feature in the intermediate layer is the decline in resistivity values ranging from −20 to −80% in comparison to the first mid-August measurement. This is the most wide-spread phenomenon and can be observed in all tomographies (Figures 69). In all transects that include a measurement at the end of August, the minimum resistivity values in the intermediate layer are apparent at this time (l.r., lagged response, in Figures 6, 7, and 8), while resistivities increase from the end of August until mid-September.

Figure 8.

Time-lapse ERT inversion models of transect NW with approximate freezing/thawing front (dashed line) influenced by frost-susceptible surface rock (f.r.), the lagged response (l.r.) of the intermediate layer to warm June/July temperatures and a deep-seated permafrost body.

Figure 9.

Time-lapse ERT inversion models of transect NE showing unfrozen bedrock (u.r.) in the intermediate and bottom layer next to water-filled clefts that feed permanent cleft water outflows (c.o.). A freezing corridor (f.c.) is developed between frozen bodies in the surface (overhang position) and bottom section.

[30] 2. In some cases the high-resistivity zones of the surface and the bottom layer are connected by corridors with resistivity values between 15 and 25 kΩ m (f.c., freezing corridors, in Figures 6 and 9).

[31] 3. Persistent cleft water outflows (c.o., in Figures 7 and 9) observed at the rock face often correspond to low-resistivity zones extending to depths of 6 m (u.r., unfrozen rock, Figures 6, 7, and 9) and thus into the intermediate layer. Similar to the surface cleft water zones, these patches experience relatively small temporal resistivity changes.

5. Discussion

[32] The electrode design, measurement settings, and inversion parameters applied in our ERT transects resemble those recommended by Sass [2003] for ERT measurement in rocks. Sass applied steel nails or screws, 5 mm in diameter, driven 10 mm into boreholes. We used stainless screws, 10 mm in diameter, driven 100 mm into boreholes to achieve optimum contact in frozen rock. The GeoTom-2D system applied by Sass and our ABEM SAS300 system have different strategies to cope with high resistivities. While the GeoTom system, as modified by Sass, can measure amperages as low as 0.005 mA in response to voltages up to 0.24 V, the ABEM system is capable of applying high voltages up to 160 V to create a stable current of 0.2 mA. Thus the maximum resistance that can be measured by the ABEM device is 800 kΩ (GeoTom modified by Sass 48 kΩ). This restricts the range of measurable resistivities to 1200 kΩ m for an electrode spacing of 1.5 m or 2400 kΩ m for an electrode spacing of 3 m and so on. All measured resistivities, including those of frozen rock, were significantly smaller than the 1200 kΩ m resistivity limitation of the measurement device for the minimum electrode spacing of 1.5 m. One advantage of the ABEM device is that the noise of possible distortions, such as electrokinetic potentials, is reduced when applying voltages 2–3 orders of magnitude higher than these potentials. The settings of the inversion routines such as fine mesh, robust inversion, four nodes, and topography modeling resemble those recommended by Sass [2003]. The advantages of applying time-lapse inversion for data derived from fixed monitoring transect were investigated extensively by Hauck [2002].

[33] Several outcomes support the hypothesis that the monitored rock transects reflect frozen and thawed rock conditions. The transition of thawed to frozen rock conditions observed at the rock surface coincides with a sudden increase of surface resistivity values by a factor of 1.4–2.9 in all transects. Mean values of thawed surface rock indicated values of 12–15 kΩ m, while frozen rock surface conditions typically yield values of 22–31 kΩ m. Because of the fact that the mean apparent resistivity value includes 40 data points with electrode spacing of 1.5 m for every measurement at every transect, this assumption compares the average signal of a few hundred data points and is highly significant. The effect of cooling on the resistivity of nonfrozen rock typically causes resistivity gradients of 0.4 per 10°C temperature change and cannot therefore be responsible for this phenomenon [Hauck, 2001, 2002; Keller and Frischknecht, 1966; Telford et al., 1990]. The laboratory measurements conducted by Hauck [2001] showed that an exponential increase of resistivity with declining temperature in dry and saturated materials occurs only at or below the freezing point [McGinnis et al., 1973]. Comparison with field data taken at the Schilthorn, Switzerland, yielded evidence that this relation is also true for natural conditions. Moreover, similar gradients for the transition of thawed rock to frozen rock were observed by Sass [2004]. Thus there is little doubt that the range of resistivity values from 15 to 22 kΩ m marks the transition between thawed and frozen rock. Completely dry rocks are virtually absent in this system due to the steady presence of snow, ice, and cleft water on the rock surface. According to these results, an approximate 0°C isoline is drawn at 18 kΩ m in transects E and NE (Figures 6 and 8) where continuous freezing/thawing fronts are developed. The uncertainty is given in Figures 69 as the “transition zone” reaching from 14 to 23 kΩ m (brown and orange). It is derived from the 15.0–21.6 kΩ m range plus approximately 10% for additional distortions.

[34] The measurements provide relatively well-calibrated values for different surface rock conditions. Because of reduced physical weathering activity with distance from the rock surface [Lautridou, 1988; Matsuoka, 1990, 2001; Sass, 1998; Viles, 2001], slightly smaller rock porosities with increasing depth could result in reduced maximum resistivity values in frozen rocks. However, previous studies suggest that this effect does not influence resistivity values significantly [Sass, 2003, 2004]. It is therefore a straightforward approach to assume that the resistivity values of surface and subsurface layers of rocks react similarly to freezing.

[35] The distinction between temporarily frozen rock and permafrost occurrences is a difficult task and must rely on characteristics such as (1) the spatial persistence of frozen rock sections; (2) high resistivities that indicate a deeply frozen body capable of resisting a phase of seasonal heat transfer; and (3) a low ambient resistivity decline next to the central permafrost body. High-resistivity bodies that fulfill these criteria can be found at depths of 6 to 10 m in the NE transect below electrode position 6 and in the NW transect below electrode position −6. Transect E stands out because it shows a high-resistivity lens in the bottom layer below −6 m, and an even more pronounced high-resistivity lens reaching into the intermediate layer from −4 m to −8 m. All those bodies in the bottom layer are branded by persistent resistivities exceeding values of 40 kΩ m in the center of the lens, combined with a trend of increasing resistivities during the summer that can exceed 200%. The resistivity of the intermediate layer high-resistivity body in transect E (Figure 6) declines to values of 30–40 kΩ m at the end of August but soon recovers to values exceeding 50 kΩ m. Considering, that ERT based on Wenner arrays tend to underestimate subsurface maximum resistivities [Hauck and Vonder Mühll, 2003] it is virtually certain that these bodies consist of a permanently deep frozen bedrock capable of surviving even warm summers without disappearing. These permafrost bodies show the same inverse temperature trend with surface temperature documented by the 7.3 m deep thermistor in the Stockhorn borehole [Gruber et al., 2004c]. In contrast to the other three profiles, transect S does not display a stable high-resistivity body. Moreover, high-resistivity zones in the bottom layer do not exceed resistivities of 30 kΩ m. Thus the high-resistivity bodies in the bottom layer of transect S could be better interpreted as a unique transient or seasonal event that could result from a reversed temperature trend in the bottom layer, or from other transient cooling effects. However, interpretation of unstable phenomena based on such a short time series should be treated with caution.

[36] Comparison of subsurface information from ERT with modeling approaches based on measurements from rock surface temperature loggers can yield further insights. According to a modeling approach by Gruber et al. [2004a], the expected mean annual rock surface temperature for the NE and NW transects is ∼0°C and, respectively, 2°C and 4°C for transects E and S. In fact, transects NE and NW provide evidence for permafrost bodies, while transect S only shows transient frost lenses. The permafrost body in transect E could be explained by local rock wall topography (perpendicular rock face) (Figure 6) and microclimatic features (ambient chilling by glacier relict). According to this model, thaw depth for the NE and NW transects would range between 5 and 7 m. In fact, the continuously developed thawing lines in the east and NW transects indicate thaw depths of 4–5 m and 6–7 m, respectively.

[37] There is some evidence that the thawing line already retreats in September and that late August tomographies display the annual maximum of thaw depth in 2005. The apparent resistivity data presented in section 4.1. show a uniform decreasing trend of subsurface resistivity values from mid-August to mid-September. The reduction of resistivity generally indicates warming and melting. This reduction is also demonstrated in the tomographies that illustrate resistivity changes (Figures 69). The intermediate layer (2–6 m) of all transects is dominated by a decreasing trend of resistivities with a range up to −80%. Nevertheless, the reduction of resistivity shows high spatial variability. Transect NW (Figure 8) provides the best data set for deriving average thaw depth. When observing the transition between brown and orange colors at 18 kΩ m, a value that approximately marks the transition to deeply frozen rock, it appears that the average freezing line in the central part retreated from 2 to 2.5 m in mid-August to 6 m at the end of August and moved back to approximately 4 m by mid-September. A similar continuous appearance of the thawing line can be detected in transect E. Here, the frost line penetrated 3–4 m into the rock face in mid-August, disappeared by the end of August, and readvanced to 3–4 m in mid-September. In contrast to this, transects NE and S display an inhomogeneous appearance of frozen and unfrozen rock sections without persistent layers.

[38] All transects recorded at least three times provide information on thermal conduction from the rock surface to the intermediate layer (2–6 m). In transects E, NW, and S, maximum thaw depths were reached on 24–25 August, while transects recorded on 14–15 September already indicate readvance of the frost line. The difference between the intensively frozen rock surface and the deeply thawed intermediate layer at the end of August is clearly visible in these transects. The effects include thawing of temporarily frozen sections to more than 6 m depth (l.r., lagged response, in Figures 6 and 8) and warming of intermediate layer permafrost bodies (i.p., in Figure 6, 25 August). Keeping in mind the cool period extending from 2 to 23 August (average air temperature 1.1°C), followed by an extended warmer period (average air temperature 4.1°C) from 24 August to 10 September, the temperature signal in the intermediate layer is delayed by approximately two to four weeks. The propagation of the “August” freezing front is best illustrated in the tomographies showing temporal resistivity changes of transect E (24 August/17 August, 14 September/17 August, in Figure 6). The formation of freezing corridors (f.c., in Figures 6 and 7) between two frozen rock sections in transects S and E coincides with readvance of the freezing front in September and can be interpreted as bilateral chilling that initiates a rapid cooling process. Propagation of heat occurs several times faster than expected from theoretical heat conduction modeling [see, e.g., Yershov, 2004]. This is, however, in accordance with empirical results for heat propagation at the Stockhorn borehole [Gruber et al., 2004c], obtained for comparable conditions at depths of 0.3, 1.3, 1.8, 2.3, 3.3, 7.3, and 13.3 m. The cool September and warm October anomalies of 2002 are visible in the thermal profile at 2.3 m depth with a time lag of 1–2 weeks, in accordance with our observations. However, in the Stockhorn data set this signal disappears at about 3.3 m depth, while our tomographies illustrate monthly signal propagation up to 6–7 m depth (Figures 7 and 8). The Stockhorn borehole is located at 3400 m asl, 300 m higher than our study site. It experiences lower average temperatures and is insulated by a decimeter- to meter-thick debris cover and more latent and sensible heat transfer is therefore necessary for freeze-thaw transitions than at our study site. The time lag is expected to be smaller in our measurements and monthly events can propagate to greater depths. These results match with the time lag observed for rockfalls in the hot summer 2003 [Gruber et al., 2004a]. The discrepancy between theoretical calculations and empirical values (borehole temperatures, ERT, rockfalls) of heat propagation underlines the need for further research, especially on latent and convective heat transfer in these systems.

[39] According to ER tomographies, heat transfer by cleft water is an important determinant of the overall distribution of frozen and thawed rock. This is especially apparent for the low-resistivity zone below the permanent cleft water outflows (c.o.) in transect NE (Figure 9). Movement of cleft water in transect NE is probably a result of the glacier relic above the rock bar (see Figure 1) that feeds water into the cleft system. Smaller outflows of water were observed in transects E and S and also match persistent low-resistivity zones in the tomographies. In transects NE, S, and E, heat transfer by these cleft water systems plays a key role for the development of frozen rock sections at the surface and in the subsurface. Wegmann [1998] noted the importance of percolating cleft water in the thermal regime of rock permafrost, the thickness of the active rock layer, and the mechanical properties and deformation of rock based on laboratory measurements and observations in two boreholes adjacent to the Jungfrau Peak at 3700 m asl. However, present understanding of the latent and sensible heat transfer between percolating water in clefts and permafrost rocks remains poor. This topic could profit enormously from further ERT monitoring transects, especially when combined with other geophysical techniques and “traditional” permafrost temperature measurements and models.

6. Conclusion

[40] ERT is applicable in permafrost rock walls if several technical requirements are considered. These requirements include a special electrode design and certain instrument settings, such as the usage of high voltages and low electrical currents. Time-lapse measurements with fixed electrodes can delimit frozen and thawed rock sections and their temporal evolution. Resistivity values measured under observed conditions at the rock surface indicate values below 15 kΩ m for thawed rocks and greater than 22 kΩ m for frozen rock, with the intermediate range corresponding to the transition between thawed and frozen rocks. Permafrost bodies were found in transects NE and NW, in accordance to rock permafrost models but also in transect E, possibly favored by microclimatic and microtopographic conditions. Continuous thawing fronts above permafrost (transects E and NW) reached a maximum depth of 4–7 m in late August. Rock layers at 2–6 m depth respond to the temporary interruption of summer heat conduction caused by cool August temperatures, with a delay of approximately two to four weeks. The speed of heat transfer is in the range of values reported from borehole measurements at comparable permafrost sites nearby, but much higher than expected from theoretical heat conduction models. Microscale features, such as overhangs and clefts with percolating water, have a high impact and result in a distribution of permafrost in lenses rather than layers. ERT can detect the spatial distribution of frozen and thawed rocks rapidly, but requires careful assessment and calibration according to local environmental conditions. Future improvements of this method should address the error sources described in section 2.2. Additional laboratory and complementary geophysical measurements and improved inversion modeling techniques will increase the reliability of ERT measurements in permafrost-affected bedrock.

Acknowledgments

[41] This study was supported by the Research Training Group Landform, funded by the German Research Foundation. Special thanks to R. Dikau and J.-C. Otto, who supported this study in all stages, and to all those who participated in the field work. The authors gratefully acknowledge the very constructive comments by J. Murton, R. Anderson, S. Gruber, D. Friend, and Associate Editor F. E. Nelson.

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