Pseudo 3-D P wave refraction seismic monitoring of permafrost in steep unstable bedrock

Authors

  • Michael Krautblatter,

    Corresponding author
    1. Landslide Research, Faculty of Civil Geo and Environmental Engineering, Technische Universität München, Munich, Germany
    • Corresponding author: M. Krautblatter, Landslide Research, Faculty of Civil Geo and Environmental Engineering, Technische Universität München, Arcisstrasse 21, DE-80333 Munich, Germany. (m.krautblatter@tum.de)

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  • Daniel Draebing

    1. Department of Geography, University of Bonn, Bonn, Germany
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Abstract

[1] Degrading permafrost in steep rock walls can cause hazardous rock creep and rock slope failure. Spatial and temporal patterns of permafrost degradation that operate at the scale of instability are complex and poorly understood. For the first time, we used P wave seismic refraction tomography (SRT) to monitor the degradation of permafrost in steep rock walls. A 2.5-D survey with five 80 m long parallel transects was installed across an unstable steep NE-SW facing crestline in the Matter Valley, Switzerland. P wave velocity was calibrated in the laboratory for water-saturated low-porosity paragneiss samples between 20°C and −5°C and increases significantly along and perpendicular to the cleavage by 0.55–0.66 km/s (10–13%) and 2.4–2.7 km/s (>100%), respectively, when freezing. Seismic refraction is, thus, technically feasible to detect permafrost in low-porosity rocks that constitute steep rock walls. Ray densities up to 100 and more delimit the boundary between unfrozen and frozen bedrock and facilitate accurate active layer positioning. SRT shows monthly (August and September 2006) and annual active layer dynamics (August 2006 and 2007) and reveals a contiguous permafrost body below the NE face with annual changes of active layer depth from 2 to 10 m. Large ice-filled fractures, lateral onfreezing of glacierets, and a persistent snow cornice cause previously unreported permafrost patterns close to the surface and along the crestline which correspond to active seasonal rock displacements up to several mm/a. SRT provides a geometrically highly resolved subsurface monitoring of active layer dynamics in steep permafrost rocks at the scale of instability.

1 Introduction

[2] Degrading permafrost in rock walls is a major hazard due to both rockfall activity and slow rock deformation that endanger infrastructure and can cause casualties [Bommer et al., 2010; Harris et al., 2009]. Enhanced tourism-related use [Messerli, 2006] and the revival of hydropower generation and storage in high-topography Alpine settings require an enhanced assessment of the rockfall hazard from permafrost rock walls, as much of the infrastructure was designed at a time when thawing permafrost was not taken into consideration [Haeberli et al., 2010]. Rock permafrost is not synonymous with perennially frozen rock as intact rock often only freezes significantly below the datum freezing point T0 (0°C) due to the effects of solutes, pressure, pore diameter, and pore material [Krautblatter et al., 2010; Lock, 2005]. However, below 0°C, ice develops in cavities such as fractures and fissures in the rock mass [Hallet et al., 1991], and thus, the perennial presence of ice has serious implications on the thermal, hydraulic, and mechanical properties of the system. Two lines of evidence support the hypothesis of increasing instability in thawing permafrost rock walls: Rockfall inventories point toward an increasing frequency and magnitude of rockfalls from permafrost-affected rock walls [Noetzli et al., 2003; Ravanel and Deline, 2008; Schoeneich et al., 2004] and, from a geotechnical point of view, mechanical properties of water-saturated rock and ice are highly susceptible to temperature changes close to the thawing point [Krautblatter et al., 2013]. Slope instability in thawing permafrost bedrock is affected by (i) temperature change, (ii) altered hydrostatic pressure, (iii) ice segregation, and (iv) loading. (i) Temperature changes control ice mechanical properties [Davies et al., 2000; Guenzel, 2008] and rock-mechanical properties [Inada and Yokota, 1984; Krautblatter et al., 2013; Mellor, 1973] of permafrost rocks. (ii) Permafrost can influence the hydrostatic pressure in rock walls due to water seepage from decaying permafrost and due to perched water levels in rock masses with ice-sealed rock [Fischer et al., 2007; Harris and Murton, 2005; Pogrebiskiy and Chernyshev, 1977]. Elevated hydrostatic pressure promotes the creep of ice [Weertman, 1973], increases lateral shear stress on the rock mass, and reduces friction by lowered effective normal stress. (iii) Ice segregation acts to prepare and enlarge existing planes of weakness and to abolish the effects of surface roughness along these [Gruber and Haeberli, 2007; Murton et al., 2006]. (iv) Temperature cycles can lead to cyclic loading due to the volumetric expansion of warming ice [Davies et al., 2000]. These destabilization processes occur below the active layer in several to tens of meters depth and cannot be observed at the surface. Subsurface methods to temporally and spatially monitor stability-relevant parameters in permafrost rocks are crucial to understand involved processes at relevant depths and will gain increasing importance in the foreseeable future.

[3] Hauck and Kneisel [2008] provide an overview of geophysical methods for permafrost monitoring in loose materials and underlying bedrock in high-mountain environments. Hereby, tomographies are a common geophysical display tool for imaging spatial changes in physical parameters such as P wave velocity, electrical resistivity, and others in 2-D and 3-D sections. Tomographies are solved as an inverse problem based on systematic spatial measurements of electrical, seismic, and other properties like, for instance, electrical resistance and seismic wave traveltimes. Significant freezing-induced changes in these physical properties have been observed in laboratory studies, and these support the interpretation of tomographies in terms of permafrost occurrence and change. The use of repeated electrical resistivity and seismic refraction tomography for active layer monitoring along fixed transects in unconsolidated permafrost materials has been shown by several authors [Hilbich, 2010; Hilbich et al., 2011, 2008; Kneisel et al., 2008]. However, few geophysical studies exist on the applicability of geophysical methods in steep low-porosity bedrock. Sass [1998] showed that electrical resistivity tomography (ERT) is capable of measuring temporal and spatial variations of the freezing front on a centimeter- to decimeter-scale in solid rock faces. Krautblatter and Hauck [2007] extended this method to a decameter scale and applied it to the investigation of active layer processes in steep permafrost rock walls. A first attempt for the quantitative application of ERT in rock walls, in particular to image the temperature distribution inside rock walls, has been demonstrated by Krautblatter et al. [2010]. However, the resolution of ERT is limited to the detection of bulk resistivity properties of usually decimeter- to meter-thick layers and their change with increasing investigation depth, whereas seismic methods are predestined to resolve sharp boundaries and discontinuities with higher geometric accuracy. Seismic refraction tomography (SRT) and ground-penetrating radar have been applied to determine 2-D and 3-D rock mass properties and potential instabilities in unfrozen rocks [Heincke et al., 2006a, 2006b]. Significant correlations between P wave velocity and joint spacing were demonstrated in seismic refraction surveys for the upper 25 to 30 m [Barton, 2007; Sjogren, 1984; Sjogren et al., 1979]. The application of SRT in steep permafrost rock walls has not been demonstrated yet, probably due to the challenges in field surveying, laboratory analysis, and the misconception that P wave velocity would not increase significantly upon freezing in low-porosity rocks.

[4] Refraction seismics is based on the interpretation of refracted head waves that indicate the transition of a slower unfrozen top layer to a frozen layer with faster P wave propagation below [King et al., 1988]. McGinnis et al. [1973] explain the relative increase in P wave velocity Δvp (%) of frozen rocks

display math(1)

as a result of porosity p (%). Bedrock with porosities below 3.6% would not cause any P wave acceleration in the laboratory; bedrock with porosities below 5% would cause an acceleration <6%, hardly detectable in field surveys. Timur [1968] suggested a three-phase time-average equation to estimate compressional wave velocities vp

display math(2)

where φ is pore space, and Si is the fraction of pore space occupied by ice, (1−Si) is the pore space filled by water under the assumption that air is absent, and vm, vi, and vl are P wave velocities of the rock matrix, interstitial ice (3.31 km/s), and water (1.57 km/s), respectively. However, both studies rely on Timur's [1968] laboratory testing, where only two samples had less than 10% porosity. These water-saturated shale samples with 3.5 and 9.6% porosity had shown P wave velocity increases of 8 and 36% that significantly exceed estimates of equation (1) and are not explainable with equation ((2)). Thus, for consolidated samples (i.e., bedrock), Carcione and Seriani [1998] introduced the “cementation effect.” For this, they used the Leclaire et al. [1994] model with a logistic growth function of P wave velocity due to freezing but performed slowness averaging of ice and solid phases when computing average moduli. Comparing models that average bulk modulus (Voigt), compressibility (Reuss/Wood), slowness [Wyllie et al., 1956], and two-thirds phase models [Minshull et al., 1994; Zimmerman and King, 1986], Carcione and Seriani [1998] concluded that the considered cementation effect best explains experimental data from high-porosity bedrock samples where the proportion of supercooled unfrozen water in pores controls wave propagation. In low-porosity bedrock, the expansion of rigid rock is restricted and ice pressure controls wave propagation; Draebing and Krautblatter [2012] tested 22 low-porosity and almost fully saturated rock samples and incorporated the results in a modification of Timur's [1968] two-phase equation

display math(3)

where m is the lithology-dependent P wave velocity increase of the rock matrix due to developing ice pressure [Draebing and Krautblatter, 2012]. P wave velocity in low-porosity bedrock types increases by 11–166% when freezing and should be detectable in field surveys.

[5] The present knowledge of permafrost distribution at the meter and decameter scale, at which instability develops, is restricted. This is due to the complex interplay of topographic, hydrologic, climatic, and long-lasting transient thermal influences and due to the lack of appropriate monitoring techniques [Harris et al., 2009]. Coupled glacier-permafrost systems develop complex behaviors due to hydrological interconnectivity between glaciers and permafrost systems, the impact of hanging glaciers, the onfreezing of glacierets, and enhanced heat transfer along ice-filled fractures [Haeberli, 2005; Harris and Murton, 2005; Krautblatter, 2010; Moorman, 2005]. Spatial and temporal effects of snow cover, the onfreezing of glacierets, and ice-filled fractures on steep permafrost rocks have not been monitored yet with sufficient resolution. Snow cover influences permafrost distribution by insulating or cooling the subsurface, altering the albedo and influencing water availability [Gruber, 2005; Gruber and Haeberli, 2007]. Snow warming or cooling effects depend on season, quantity, and thermal characteristics [Ishikawa, 2003; Luetschg et al., 2008; Phillips, 2000]. Climate change scenarios of the Intergovernmental Panel on Climate Change [2007] point toward decreasing snow depth at lower altitudes and a reducing of the snow season [Bavay et al., 2009]. Luetschg et al. [2008] postulate amplified effects of temperature rise for regions with thin snow cover and where the snowmelt is preponed. Ice-filled rock crevices act as efficient semiconductors. Cold thermal impulses propagate instantaneously, as no active layer has to be frozen, and effectively, with the high thermal conductivity of ice of 2.2 W/mK along ice-filled fractures. Warm thermal impulses are buffered by the latent heat capacity of ice. Conduction of cold thermal impulses along ice-filled fractures operates effectively during a much higher number of days compared to snow-free rock surfaces. The reaction of high Alpine permafrost rock walls to climate change will additionally be orchestrated by changes in permafrost-glacier interconnectivity and snow cover depth and duration. Detailed insights into the thermal control exerted by snow cover, onfreezing, and ice in fractures are essential to anticipate the impact of climate change on permafrost rocks.

[6] In this paper, we use laboratory calibration (section 3.1) to establish a P wave velocity versus temperature relation (section 4.2). This helps to accurately interpret permafrost distribution scenarios observed in field measurements (section 4.3). In the field, we appraise data on steep rock faces and process these data (section 3.2), analyze raw data (section 3.3), and use up-to-date inversion methods to create tomographies. We test the sensitivity of the tomographies to initial settings like velocity (section 3.4) and ray propagation (section 3.5). We use a 1-D conduction model (section 3.6) to link seismic results with modeled permafrost development during the year (section 5.4).

[7] This article aims to show (i) that, in contradiction to the McGinnis et al. [1973] hypothesis, low-porosity rocks show significant P wave acceleration when freezing; (ii) that the increase of P wave velocity is accurately detectable in high-resolution field surveys; and (iii) that P wave SRT delivers a geometrically precise delineation of active layer depth in steep unstable permafrost rock walls including complex effects exerted by lateral onfreezing, persistent snow cover, and ice in fractures.

2 Study Area

[8] The study site close to the crestline between Matter and Turtmann Valleys (3070 to 3150 m above sea level (asl), Valais, Switzerland) consists of slaty paragneiss which slightly dips (10–20°) toward the NE slope. Several rock bars dissect the Rothorn-NE-Glacier into small glacierets. The mean annual air temperature inferred from measurements in the Matter Valley from 1962 to 1990 is −3.5°C. Since 2002, climatological data have been recorded close to the study site at a meteorological station at 2770 m asl and were corrected 0.6°C per 100 m.

[9] In 2005, four rock temperature loggers were installed at 10 cm depth and in four aspects according to the design suggested by Gruber et al. [2003]. Mean rock near-surface temperatures in winter 2005/2006 were on average 5.5°C lower than in 2006/2007 (Figure 1b). The relatively cool August 2006 (mean air temperature (MAT) 0.0°C), when seismic monitoring began, interrupted the warmer July and September (MAT 7.0°C and 3.9°C) periods in 2006. In summer 2007, temperatures rose continuously until July/August (MAT 3.3°C). The crestline of the Steintaelli is most of the time covered by a 2–3 m thick and wide snow cornice. In August 2007, the north-facing slope also hosted snow/firn patches and the advancing glacier extended onto Transect 1 and froze onto the rock wall (Figure 2c). Persistent ice also exists in decimeter-wide rock fractures along the crestline that are created by the diverging rock block creep with crack openings of several millimeters per month in late summer [Krautblatter, 2009].

Figure 1.

(a) The study site “Steintaelli” at the crestline between Matter and Turtmann Valleys, Valais, Switzerland; the white lines indicate the five seismic arrays that collate into the 2.5-D tomography displayed in Figure 2a. (b) Monthly air and rock temperatures indicate a several degrees colder winter period in 2005/2006 than in 2006/2007.

Figure 2.

(a) Geometry of the 2.5-D transect consisting of five parallel monitoring transects with 120 geophones and 200 shot positions across the instable Steintaelli crestline. Contour lines in Figure 2a and (b) color scale indicate altitude above 3100 m asl.

3 Methods

3.1 Laboratory Work

[10] P wave velocity at different rock temperatures was measured using two 30 × 20 × 15 cm large cuboid paragneiss samples taken from Steintaelli rock crests. These large rock samples incorporate dozens of cleavages to cope with their natural heterogeneity of schistosity. Porosity ranges between 1.94 ± 0.10% (Sample S4) and 2.40 ± 0.12% (Sample S1). Samples were submerged in low conductive 0.032 (±0.002) S/m water in an undisturbed closed basin to approach their chemical equilibrium. Pore space was fully saturated under atmospheric pressure, as free saturation resembles the field situation more closely than saturation under vacuum conditions [Krus, 1995; Sass, 2005]. Samples were cooled in a range of 20 to −5°C in a Weiss WK 180/40 high-accuracy climate chamber. Ventilation was applied to avoid thermal layering. Samples were loosely coated with plastic film to protect them against drying. Three calibrated 0.03°C accuracy thermometers measured rock temperature at different depths to account for temperature heterogeneity in the sample. The mean deviation of measured temperature heterogeneity in the sample is indicated by error bars in Figure 8. The P wave generator and the receiver were placed on flattened opposite sides of the cuboid samples. The traveltime of the P wave was picked using a Fluke ScopeMeter with an accuracy of 1–2 × 10−6 s. The internal deviation induced by the measurement procedure was assessed by conducting five subsequent traveltime measurements. We measured P wave velocities in the direction of cleavage and perpendicular to the cleavage to quantify anisotropy.

3.2 Data Appraisal

[11] In 2006, five parallel transects with 24 drilled geophone positions each (total 120) were installed across the NE- and SW-facing steep crestline. We applied 2 m geophone spacing along transects, and the five parallel transects are separated by a 4 m spacing. Exact geophone x, y, and z positions were measured using a Leica TCA 1800 L tachymeter with an accuracy of approximately 1 cm (Figure 2).

[12] Forty shot positions with 2 m spacing along each transect start 13 m north of first geophone and end 19 m south of the last geophone. Shot positions were marked for repeated measurements with identical geometries. The resulting pseudo 3-D array comprises 78 × 16 m and consists of 200 shot positions arranged around 120 geophone positions. Enhanced coupling of the geophones was accomplished by firmly fixing geophones in 10 mm holes drilled in the rock face. We recorded seismic data with a 24 channel seismograph (Geode, Geometrics Inc.) with 4.5 Hz geophones in August and September 2006 as well as in August 2007. A 5 kg sledgehammer was used as a source; for signal improvement and noise reduction, multiple shots were stacked. To cope with short traveltimes, the record interval was set to 63 µs which corresponds to a 0.25 m propagation of a 4.0 k m/s P wave. The first arrival was amplified by 36 dB to better show first arrivals of remote shots. We used the software package ReflexW 5.5.2 for processing and interpretation of refraction seismic data. The reconstruction of the subsurface velocities in ReflexW is based on the adaptation of synthetic traveltimes calculated by forward modeling to observed traveltimes. The tomographic algorithm applies the simultaneous iterative construction technique [Sandmeier, 2008], i.e., the iterative process ends if a stopping criterion is fulfilled (for modeling parameter settings and stopping criteria, see Table 1) and displays the best model result. First arrivals of seismic waves are picked manually, and topography is readily implemented in the traveltime analysis.

Table 1. Adjusted Parameters for ReflexW Tomography Modeling
Modeling ParameterValue/Active
Space increment (m)0.5
Maximum number of iterations50
Maximum CPU-time (s)1000
Threshold0.001
Defined data variance0.1
Model change A1
Model change B0.1
Convergence search10
Maximum def. change (%)50
Maximum beam width10
Started curved ray1
Average x2
Average z2
Minimum velocity0
Maximum velocity6000
Statistical criteriumActive
Check no ray areaActive
Curved rayActive
Force first iterationActive

[13] First arrivals of shots are picked at high plot scales (>1500); higher plot scales increase the amplitude without altering the wavelength (Figure 3). This picking mode allows a precise picking with picking errors ranging from 0.25 ms for first arrivals close to the shot and up to 1 ms for first arrivals far from the shot. As a result, the P wave velocity can differ up to ± 300 m/s but typically less.

[14] The quality of tomographies is assessed in terms of root-mean-square (RMS) and total absolute time difference. The latter sums up absolute time differences between calculated and measured travel times independently and evaluates the overall adaptation [Sandmeier, 2008]. For this, we used a position bin size that is a quarter of the model block size of 0.5 m (K.-J. Sandmeier, personal communication, 2011).

3.3 Raw Data Analysis

[15] Mean first arrival traveltimes of August and September 2006 as well as August 2007 are plotted against the mean source-receiver offset of every 5 m source-receiver offset (Figures 3 and 4) [Hausmann et al., 2007; Hilbich, 2010]. The dotted lines indicate velocities above 4.1 km/s and 5.3 km/s, respectively. All transects show existence of low P wave velocities below 3.0 km/s. Mean monthly (2006) and annual (2006/2007) traveltime differences were plotted against the shot position. Negative values indicate a mean traveltime decrease, i.e., a P wave velocity increase. The raw data provides valuable information for the preprocessing of tomography modeling and the evaluation of model quality.

Figure 3.

(top) Picked first arrivals of a shot at 5 m in Transect 1 in September 2006; the plot scale is 60. (bottom) One single first arrival at 8 m with a plot scale of 1866.

Figure 4.

Mean traveltimes are plotted against mean source-receiver offset for every 5 m source-receiver offset and indicate P wave velocities below 3.0 km/s, above 4.1 km/s, and above 5.3 km/s. Mean traveltime differences are plotted against shot position for subsequent measurements (NF = north face, SF = south face, and CR = crestline) and indicate tendency of thawing or cooling as monthly and annual response, respectively.

3.4 Initial Model Optimization and Data Quality

[16] Initial model velocity and gradient influence raypath propagation of seismic waves. Hauck [2001] and Lanz et al. [1998] recommend adjusting initial velocities to representative P wave velocities for the research area if a priori information is available or, alternatively, to overestimate initial velocity gradients to ensure sufficient ray coverage. We tested different start models with initial velocities ranging from 2.0 to 5.5 km/s and gradients of 0, 0.2, and 0.6 km/s; best results in terms of RMS and total absolute time difference were gained without a predefined gradient. We tested initial model velocities between 2.0 and 5.5 km/s using data sets of Transects 1, 5, and 9. Total absolute time difference decreases with increasing initial velocity and reaches a minimum at 4.0 km/s in Transect 1 and at 3.5 km/s in Transects 5 and 9 (Figure 5). The RMS minima in Transects 1, 9, and 5 at initial P wave velocities of 3.5 km/s and 2.5 km/s are only slightly below RMS values at 4.0 km/s.

Figure 5.

Total absolute time difference (solid lines) and RMS (dashed lines) for different initial P wave velocities implemented in ReflexW modeling.

[17] According to RMS error and total absolute time difference, initial velocities of 3.5 and 4.0 km/s show best results (Figure 5). Raw data analysis shows the existence of P wave velocities ≥ 5.3 km/s and ≤ 2.5 km/s, which correspond to laboratory values for paragneiss samples. Initial velocities lower than 4.0 km/s would exclude higher velocities in the final tomographies (Figure 6). Tomographies based on initial velocities faster than 4.5 km/s exclude velocities lower than 3.0 km/s. We decide to choose the initial velocity of 4.0 km/s to combine best fit in terms of RMS error and total absolute time difference with the most appropriate representation of raw data lower than 2.5 km/s and faster than 5.3 km/s in the final tomographies.

Figure 6.

Response of Transects 1, 5, and 9 to different initial velocities (vp) for the inversion modeling process.

3.5 Model Sensitivity

[18] Model resolution and accuracy are influenced by the number of model blocks and should correspond to the density of raypaths [Hauck and Vonder Mühll, 2003]. An increasing number of model blocks enhances model resolution but decreases model accuracy. Ray density and the number of rays crossing a cell generally decrease with increasing depth [Lanz et al., 1998]. Due to the shallow thawing depth, we define 0.5 m as the minimum acceptable resolution. ReflexW displays ray density as the number of rays crossing a model block divided by the total number of rays (Figure 7) [Sandmeier, 2008].

Figure 7.

Ray density in the five transects with n is giving the total number of rays in each transect and ranges between 391 and 733. The maximum ray density of 100% equals the total number of rays n.

[19] Model regions with ray densities close to 25% indicate subparallel movement of up to 100 rays and more and indicate high accuracy, while ray densities close to 0 indicate low accuracy. In the resulting tomographies, we blanked out sections of the tomographies that are not sufficiently covered by rays.

3.6 Thermal Modeling

[20] To justify our interpretations (section 5.4), we try to link seismic data from the different times and years with thermal modeling of 2006. We use the data from NW- and south-exposed temperature loggers (Figure 2) as input data for a thermal underground model. The simplest way to analyze the thermal variation in depth in time is the use of 1-D heat conduction given by a sinusoidal temperature variation

display math(4)

where T is temperature (°C), t is time, z is depth of rock, MART is mean annual rock temperature, Ta is the half amplitude of the sinusoidal variation, ω is the frequency of sinusoid (in our case, 1 year), and κ is the thermal diffusivity [Carslaw and Jaeger, 1986; Williams and Smith, 1989]. In 2006, MART is −3.4°C for NE-Logger and −0.3°C for south-Logger, Ta is 9.3 K and 8.6 K, respectively.

[21] Thermal conductivity of Alpine metamorphic approaches values between 1.5 and 3.5 W m−1 K−1,and specific heat capacity between 0.75 and 0.8 kJ kg−1 K−1 [Vosteen and Schellschmidt, 2003]. We use a thermal conductivity of 2.5 W m−1 K−1, a specific heat capacity of 0.8 kJ kg−1 K−1, and a density of 2600 kg m−3 for slaty paragneiss. The calculated volumetric heat capacity is 2.08 × 106 J m−3 K−1 and thermal diffusivity is 1.2 × 10−6 m2 s−1. The assumed geothermal gradient is 0.05 W m−2. This model is purely conductive and does not account for discontinuities in the rock mass, multidirectional heat flow due to topography [Noetzli et al., 2007], and advective [Hasler et al., 2011a, 2011b] or conductive processes [Hasler et al., 2011a].

4 Results

4.1 Laboratory Results

[22] P wave velocities parallel and perpendicular to the cleavage increase by 10–13% (550–660 m/s) and more than 100% (2400–2700 m/s) subsequent to freezing (Figures 8 and 9).

Figure 8.

P wave velocity of frozen and unfrozen Steintaelli paragneiss samples in the direction of the cleavage and perpendicular to the cleavage.

Figure 9.

Scenario development demonstrated for the measurement of Transect 1 on 5 August 2007 based on laboratory measurements. Scenario 1 (Permafrost at 4.1 km/s; blue area), the maximum permafrost distribution, is based on perpendicular laboratory measurements; Scenario 2 (Permafrost at 5.3 km/s; violet area), the minimum permafrost distribution, is based on measurements parallel to cleavage direction (see text).

[23] Otherwise, P wave velocities parallel to the cleavage direction stay constant above (S1: 5228 ± 25 m/s and S4: 5239 ± 19 m/s) and significantly below freezing point (S1: 5774 ± 21 m/s and S4: 5895 ± 27 m/s) at relevant temperatures of −3°C to −5°C. Correspondingly, P wave velocities perpendicular to the cleavage direction stay constant (S1: 1953 ± 15 m/s and S4: 1667 ± 14 m/s) above the freezing point and respond with a sudden increase below the freezing point to values of 4331 ± 12 m/s (S1) and 4404 ± 36 m/s (S4) between −3°C and −5°C. Supercooled conditions were possibly observed between 0°C and −0.25 ± 0.15°C (S4).

4.2 Raw Data

[24] The raw data show mean traveltimes in the range of frozen P wave velocities perpendicular (≥4.1 km/s) and parallel to the cleavage (≥5.3 km/s) in all transects (Figure 4). Thawing or drying of rocks increases traveltimes, freezing and wetting reduce traveltimes. From August to September 2006, Transect 7 shows a remarkable increase of traveltimes while other transects show diverse traveltime changes. From August 2006 to August 2007, traveltimes predominantly decrease in Transects 1 and 3, while the remaining transects show more differentiated patterns.

4.3 Scenario Building

[25] Laboratory results were used to reference field values. In the field, raypaths combine vertical (perpendicular to cleavage) and horizontal (parallel to cleavage) directions (Figure 7). As we pick first arrivals, faster raypaths along the cleavage will outpace slower raypaths perpendicular to cleavage for longer distances. Seismic waves perpendicular to the cleavage are only recognized near to the surface. For higher depths, the critical distance is exceeded and first arrivals filter fast parallel P waves.

[26] Thus, the laboratory P wave velocity of frozen rock perpendicular to the cleavage (≥ 4.1 km/s) represents the maximum permafrost distribution and Scenario 1 is valid close to the surface (Figure 9). Scenario 2 (≥ 5.3 km/s), based on laboratory measurements parallel to the cleavage, is the minimum scenario for permafrost distribution and is increasingly valid for greater depths but will overestimate the P wave velocity of the complete raypath. Therefore, the reality will be best displayed in a combination of Scenarios 1 and 2. The scenarios are implemented in the tomographies in terms of dotted lines for Scenario 1 (possibly frozen) and continuous lines for Scenario 2 (frozen). P wave velocities in Figures 6 and 10 are classified according to laboratory results as “unfrozen,” “possibly frozen,” and “definitely frozen” with P wave velocities from 1.5 to 4.1 km/s, 4.1 to 5.3 km/s, and 5.3 to 6.0 km/s.

Figure 10.

Seismic refraction tomographies for Steintaelli study site. Tomographies show effects of onfreezing (I), persistent cornice development (C), and ice-filled fractures (f). Areas with low ray densities are blanked out. For the definition of “possibly frozen” and “definitely frozen” see Figure 9.

5 Discussion

5.1 Laboratory

[27] The laboratory calibration of P wave velocities of frozen and unfrozen samples appears to be a necessary and helpful tool for both accurate preprocessing of the tomographic inversion and the interpretation of tomographies. The laboratory values show that (i) low-porosity metamorphic rocks show significant increases in P wave velocity when freezing and (ii) velocities parallel and perpendicular to the cleavage tend to differ by a factor of 2 when unfrozen but assimilate when freezing. Thus, seismic refraction is generally capable of detecting permafrost in low-porosity rocks that constitute steep rock walls. P wave velocities between 1.5 and 4.1 km/s can be defined as definitely unfrozen rock and velocities between 5.3 and 6.0 km/s refer to definitely frozen conditions. However, transitional velocities between 4.2 and 5.2 km/s cannot be assigned to either frozen or unfrozen rock due to the effect of anisotropy. As has been demonstrated in Figure 6, the range of laboratory P wave velocities in combination with raw data analysis is an important quality check for tomographies and helps to choose appropriate initial velocities. This is increasingly true as rock samples show significant anisotropic behavior and mixing laws do not apply well to low-porosity rocks [Draebing and Krautblatter, 2012]. While the P wave velocity of ice (approximately 3.3 km/s) is an important indicator for the occurrence of frozen ice-rich sediment [Hilbich, 2010], this benchmark is not applicable to frozen bedrock. The anisotropic behavior of rocks also requires the use of two scenarios for minimum (≥ 4.1 km/s, freezing velocity perpendicular to cleavage) and maximum extend (≥ 5.3 km/s, frozen velocity parallel to cleavage) of frozen rock in SRT.

5.2 Field Methodology

[28] The field appraisal with small geophone and shot position spacings of 2 m and several offset shot positions appears to deliver appropriate ray coverage for active layer detection [Vonder Mühll et al., 2001]. Short travel distances and high P wave velocities require highly resolved (here 63 µs) recording of traveltimes. As refracted waves travel along boundaries of material with different elastic properties, layer boundaries can be sharply delineated with high accuracy [Hauck and Vonder Mühll, 2003]. Layer boundaries with high velocity differences result from the large seismic velocity contrast between the active layer and the permafrost body [Hauck and Vonder Mühll, 2003] or anisotropies corresponding to macroscopic ice-filled faults and joints [Heincke et al., 2006b]. According to the laboratory results, the transition from frozen to unfrozen bedrock is a good target because of the sharp gradient in P wave velocity and elastic properties. The concentrated travel of seismic rays along the refractor at the transition between unfrozen and frozen rock presumably provides a more accurate detection of depth by SRT in comparison to ERT. In ERT, bulk-apparent resistance measurements with half-space geometries covering volumes of several cubic meters at relevant depths will smooth the transition from unfrozen to frozen bedrock. According to the high ray coverage at the transition layer in SRT and the reduced smoothing of an ERT bulk effect, we assume that SRT can provide a more accurate estimate of active layer depth.

5.3 Raw Data Analysis and Inversion

[29] We introduced several quality criteria for SRT to address the inverse problem: (i) RMS and absolute time difference should be at a reasonably low level, but the lowest level might not necessarily indicate the best model fit. RMS and absolute time difference approach their minima between 2.5–4 km/s and 3.5–4 km/s, while higher initial P wave velocities cause increasing errors. Predefined gradients generally caused higher errors. (ii) The coincidence of laboratory P wave velocity values for paragneiss samples and P wave velocities derived from traveltime analysis provides a quality criterion for tomographies. Tomographies should roughly cover the entire spectrum of P wave velocities from 1.7 (S4, perpendicular) to 5.9 (S1, parallel) km/s. In reality, this means that velocities ≥ 6 km/s are improbable, velocities ≥ 4.1 km/s must be expected for longer raypaths in frozen rocks, and velocities ≤1.7 km/s are only possible for dry rocks at the surface [Sass, 2005]. Mean traveltimes indicating P wave velocities ≥ 5.3 km/s would only occur for a ray movement predominantly parallel to the cleavage over most of the travel distance. Thus, we assume that appropriate SRT would simultaneously (i) indicate low RMS and absolute time differences (valid for initial velocities 3.5–4 km/s) and (ii) cover the spectrum of velocities predefined by laboratory and raw data analysis (valid for initial velocities 4–4.5 km/s), and thus, initial velocities of 4 km/s fulfill both quality criteria.

[30] To avoid misinterpretations of SRT, we blanked out areas that are not determined by seismic waves. Because of subparallel movement of seismic rays resulting from high velocity gradients, ray coverage and ray density provide only partial information about the spatial resolution, and some studies used ray density tensors [Heincke et al., 2006b]. Here we used the ray density to define well-covered and noncovered parts of SRT and displayed only the well-constrained parts in final SRT (Figure 10).

5.4 Permafrost Interpretation

[31] The late summer distribution of definitely frozen rock at depth (i.e., permafrost) is governed by aspect. Permafrost is omnipresent below the NW-facing slope and along the crestline (0–40 m), mostly present at the NW foot of the slope (−13 to 0 m), and virtually absent on the SW-facing rock slope (40 to 65 m). Lateral onfreezing (I) of the glacieret and firn/ice remnants below snow patches at the NW foot (−13 to 0 m) corresponds to definitely frozen rock at the surface and lowest recorded rock temperatures from spring to early summer (Logger E in Figure 1). Surface permafrost is also found below the combination of the virtually persistent snow cornice (C) and decimeter-wide ice-filled fractures (f) (see Figure 10). Active layer depth in undisturbed NW-facing rock slopes approaches 4–10 m in September 2006, after a considerable propagation of the thawing front from August to September. Thermal modeling of the 2006 data assumes an active layer depth of 3.75 m on the NE-facing slope (based on NW-Logger) and 8 to 9.25 m on the SW-facing slope (based on south-Logger). The modeled active layer depth underestimates the active layer depth resulting from lack of anisotropic heat transfer due to discontinuities, advective processes due to percolating meltwater [Hasler et al., 2011b], and possible convective processes [Hasler et al., 2011a]. There is no up-to-date model taking account of these processes and rock mass properties. Active layer depth in August 2007 reaches 2–5 m.

[32] Raw data show remarkable monthly thawing processes on the SW-facing slopes of Transects 1 and 3 and on the NE-facing slope of Transect 7. Shorter traveltimes on the crestline can be interpreted as impacts of onfreezing and cornice development resulting in snow cover isolation [Keller and Gubler, 1993] preventing thawing in 2007 in Transects 1, 3, and 5. The onfreezing in Transects 7 and 9 and cornice in Transect 9 persists and responds with only small traveltime differences.

[33] Linear features like fractures will affect tomographies in different ways. Air-filled fractures at the surface will significantly reduce the bulk P wave velocity of the surrounding rock mass according to fracture density, dimensions, and orientation of fractures [Barton, 2007; Sjogren et al., 1979]. Ice-filled fractures could be either resolved or not resolved according to their size with respect to SRT resolution. They could act as a blind layer or be detected according to their ambient influences on the neighboring rock mass. Assuming that ice-filled fractures only exist in frozen rock, ice in fractures (3.3 km/s) will act as a blind layer. The rock mass surrounding an ice-filled fracture is often cooler than the surrounding due to the high thermal conductivity of ice and its semiconductor performance. In that case, rather the indirect effect on the frozen rock mass is detected. The permafrost distribution at the crestline is obviously heavily influenced by the centimeter- to decimeter-wide ice-filled fractures.

[34] Only few studies have focused on the snow on Alpine permafrost terrain [Hanson and Hoelzle, 2004; Keller and Gubler, 1993; Schmidt, 2010]. Steep rock walls (>45°) in high Alpine terrain tend to have a much thinner and more heterogeneously distributed snow cover than is found in flatter terrain [Lapen and Martz, 1996; Seligman, 1980; Wirz et al., 2011]. Spatial and temporal distribution of snow in structured rock faces are increasingly controlled by wind, local topography, and radiation patterns [Winstral et al., 2002]. The SRTs display surficial frozen bedrock in late summer under snow cornices along the crestline and under persistent snow patches in the north face. Snow cover is among the most important influences on permafrost distribution in Alpine rock walls that yet cannot be sufficiently modeled [Gruber and Haeberli, 2007; Krautblatter et al., 2012]. The SRT technique developed in this paper could, thus, significantly contribute to the understanding of snow, ice, and water influence on local permafrost evolution and the resulting impacts on stability.

6 Conclusion

  1. [35] Refraction seismic in steep permafrost rock walls is a nontrivial task due to high topography, anisotropic seismic behavior of rocks, an unknown range of subsurface velocities, and a curved ray penetration that is difficult to judge.

  2. [36] We have installed a 2.5-D P wave refraction seismic array across the instable Steintaelli crestline, Matter Valley, Switzerland, at 3070–3150 m asl. It comprises 78 × 16 m, consists of 200 shot positions arranged around 120 geophone positions, and was measured repeatedly in 2006 and 2007.

  3. [37] Laboratory measurements of P wave velocity of decimeter-large cuboid water-saturated paragneiss samples was performed at temperatures from 20°C to −5°C at small increments in a laboratory cooling device.

  4. [38] These show that parallel to cleavage velocity increases from 5228 ± 25 m/s (Sample S1) and 5239 ± 19 m/s (S4) to values of 5774 ± 21 m/s (S1) and 5895 ± 27 m/s (S4) upon freezing. Perpendicular to the cleavage, P wave velocity increases from 1953 ± 15 m/s (S1) and 1667 ± 14 m/s (S4) to values of 4331 ± 12 m/s (S1) and 4404 ± 36 m/s (S4), respectively.

  5. [39] We argue that (i) a priori information on P wave velocity behavior from laboratory testing, (ii) traveltime raw data analysis, and (iii) initial model evaluation with different initial velocities and gradients are needed to create reliable seismic refraction tomographies in steep fractured bedrock.

  6. [40] Glacier onfreezing, the position of snow accumulations, and deep-reaching ice-filled fractures seem to have a systemic and locally dominant impact on spatial and temporal permafrost development.

  7. [41] Glacier onfreezing can cause permafrost up to the surface without active layer below the ice; deep ice-filled fractures and persistent snow patches can generate extended permafrost in positions that would otherwise have no permafrost—these features correspond with the highest measured rock displacement activity.

  8. [42] Here we show for the first time that calibrated seismic refraction tomography provides a geometrically highly resolved subsurface detection of active layer and permafrost dynamics in steep permafrost rock walls at the scale of instability.

Acknowledgments

[43] This study was supported by the DFG-Research Training Group “Landform (GRK 437),” by the DFG research project “Sensitivity of rock permafrost to regional climate change scenarios and implications for rock wall instability,” and the DACH (DFG/SNF) project “ISPR Influences of snow cover on thermal and mechanical processes in steep permafrost rock walls.” The authors acknowledge G. Nover and J. Ritter for infrastructural support and S. Verleysdonk, D. Funk, P. Oberender, and S. Wolf for the field work.

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