The crystal orientation fabric (COF) in ice cores provides detailed information, such as grain size and distribution and the orientation of the crystals in relation to the large-scale glacier flow.
These data are relevant for a profound understanding of the dynamics and deformation history of glaciers and ice sheets.
The intrinsic, mechanical anisotropy of the ice crystals causes an anisotropy of the polycrystalline ice of glaciers and affects the velocity of acoustic waves propagating through the ice.
Here, we employ such acoustic waves to obtain the seismic anisotropy of ice core samples and compare the results with calculated acoustic velocities derived from COF analyses.
These samples originate from an ice core from Rhonegletscher (Rhone Glacier), a temperate glacier in the Swiss Alps.
Point-contact transducers transmit ultrasonic P waves with a dominant frequency of 1
Improved glacier flow models require a profound knowledge on sub- and englacial processes and the properties governing these processes.
The data for studying englacial processes are usually derived either from borehole measurements or from ice core analyses.
These ice core analyses provide useful physical properties, such as elastic parameters, density, electric conductivity, and permittivity
For the analysis of the COF, thin sections of ice (
Important factors to consider when designing a measurement procedure for COF analyses are grain size and shape of the ice samples or the air bubble distribution, which influences the density of the ice.
The grain size and shape differ significantly between cold ice and temperate ice.
Cold ice typically has larger quantities of small (millimetre-sized) grains, whereas temperate ice has significantly fewer grains, but they are larger, with their diameter being up to several centimetres.
Furthermore, the grains in temperate ice are often more irregularly shaped and interlocked and consequently appear as several individual grains within the thin sections.
This often leads to a misinterpretation of the actual COF
Different geophysical methods have been employed to explore the horizontal extension of the major layers of changing COF (e.g.
A direct comparison of the measured and calculated velocities is still limiting as the measured data may be affected by macro-structural features such as crevasses, fractures, changing ice porosity due to air bubbles, or meltwater within the ice matrix.
In order to avoid all these limitations, direct ultrasonic measurements along an ice core, from which the COF is usually derived, could be employed and may provide the best agreement between COF-derived and measured acoustic velocities.
Such a comparison of ultrasonic measurements with COF-derived velocities is the aim of this study.
We obtain seismic velocities from ultrasonic measurements on ice core samples from the temperate Rhonegletscher (Rhone Glacier) in Switzerland.
We already analysed the actual COF of these ice core samples in a recent study
For our velocity investigations we used an ice core drilled on Rhonegletscher, Central Swiss Alps.
The ice core was drilled in August 2017 with a recently developed thermal drilling technique suitable for temperate ice
Immediately after extracting the ice core, it was stored at
The hexagonal crystal structure of an ice monocrystal causes an anisotropy in its elastic parameters and therefore affects the propagation velocity of seismic waves.
As a result of the crystallographic symmetry, the acoustic velocity parallel to the
Due to the symmetry relations
The theoretical framework calculates the effective elasticity tensor and derives the seismic velocities from this tensor.
Then, the velocities are derived by solving the Christoffel equation This approach is based on an earlier study of It then considers the elements of a monocrystal tensor For each ice grain The rotated monocrystal tensors are summed up elementwise as With the known elastic properties, the Christoffel equation provides the link to analytic solutions for acoustic velocities
The calculations for the polycrystalline tensor and acoustic velocities are described in more detail in
The seismic velocities can be calculated from the elasticity tensor or the inverse compliance tensor. Both approaches provide velocity profiles oscillating around an upper (Voigt bound) and lower (Reuss bound) mean velocity
The dominating COF causes an acoustic velocity anisotropy, and this anisotropy can be verified and quantified by direct laboratory measurements. These measurements were conducted in the cold laboratory at WSL Institute for Snow and Avalanche Research (SLF), Davos.
The orientation of each individual ice core segment was marked at the time of drilling based on mechanical onsets and supporting magnetometric measurements.
This ensures a comparison between COF, ultrasonic measurements, and glacier flow at all depths.
The temperature for the ultrasonic measurements was chosen to be at
An ultrasonic point-contact (PC) transducer transmitted an acoustic signal into the ice.
This signal was recorded by a second transducer on the opposite side of the core.
In the current experimental set-up only measurements parallel and perpendicular to the vertical axis of the ice core (colatitude
Figure
The transducers were screwed in an aluminium tube which was held by an aluminium frame with an inner diameter of 90
In addition to the ultrasonic measurements, the porosity (i.e. the volume of air within the ice) was analysed by X-ray micro-computer tomography (CT) scans.
For the scanning and analysis, we followed the same procedures previously adopted for bubbly ice from Dome C
Seven ice core samples, obtained from 2, 22, 33, 45, 52, 65 and 79 m depth, were analysed.
The corresponding COF patterns (presented in Fig.
COF patterns and calculated seismic velocities for all seven analysed ice core samples:
We calculated the acoustic velocities from the COF patterns of all samples.
The resulting velocity distributions (Fig.
The P wave velocity for vertically incident waves (parallel to
Mean values for measured and calculated seismic velocities for
Mean, minimum, and maximum calculated P wave velocities (i.e. derived from the COF pattern and not from ultrasonic experiments, without air correction) and degree of anisotropy for each COF sample.
We measured the acoustic velocities on five of the above-mentioned ice core samples.
The ice core samples were taken from 2, 22, 33, 45, and 65
In a first step, the recorded traces were shifted to correct for zero-time
To ensure data consistency, the reciprocal travel times were compared for quality checks. Rays with opposing azimuths (
Mean measured seismic velocities from ultrasonic experiments (orange curve and red dots) with maximum and minimum values (light red areas) for five ultrasonic samples and the corresponding calculated velocities from the COF distribution (blue curve) from Fig.
All five samples show a set of two maxima surrounded by four minima and two local side maxima. For the samples at 2, 22, and 65
The X-ray CT images provide porosity information in the vicinity of the horizontal ultrasonic measurements (summarised in Table
The individual CT-derived porosity values (Table
Porosity values (
The results for COF-derived velocities and the ultrasonic velocity profiles are compared in Figs.
Azimuthal variations in the horizontal measurements are compared in Fig.
Seismic waves have a band-limited frequency content resulting in a finite range of wavelengths.
As indicated in Sect.
Raw image from fabric analyser, showing a typical grain distribution found in the temperate ice core. The coverage by ultrasonic measurements (dashed lines) and an example for the first Fresnel zone (homogeneous medium approximation) are superimposed: S is the sending transducer, and R is the receiver. The distance between source and receivers is
In contrast to the ultrasonic measurements, the thin sections for the COF-derived velocity profiles only provide limited information in the third dimension.
This is even more important for an estimated guess of the size of such branched and large grains.
Grains close to the thin section but out of plane are invisible for the COF-derived velocity profiles.
Furthermore, a cut through a large branched grain may make this grain appear as several small grains, usually called island grains (see
Therefore, the velocities of COF analysis and the ultrasonic measurements are expected to be different in the presence of large grains.
Conversely, a good match can be expected when a large number of small grains is involved.
To investigate this further, we computed grain size distributions (Fig.
Number of grains over all clusters in the individual samples. The mean grain size
As a result of the previous discussion, we also assume that a larger amount of ultrasonic measurement levels should lead to a better match with the statistically averaged profile from the COF analysis.
Additional ultrasonic measurements are available for the sample of 33
Mean measured seismic velocities from ultrasonic experiments (orange curve and red dots) and the corresponding calculated velocities from the COF distribution (blue curve) for the sample at 33
Comparison of different fabric types and their velocity profiles for different inclination angles:
To conclude, ultrasonic and COF analyses complement each other.
The first is a deterministic approach allowing for a detailed analysis of a particular ice core volume of a few cubic centimetres.
The latter is a statistical approach that provides an integrated COF pattern derived from several centimetre-long (up to 50
In this study, the COF patterns are assumed to be known a priori, and the ultrasonic results could be correlated with this known COF. The question that arises is if ultrasonic measurements are a suitable method to determine unambiguously unknown COF patterns?
To address this question, we consider the sample at 22
To further reduce this ambiguity, adding additional ultrasonic measurements spanning a range of azimuths and inclinations such that the area of the stereoplots would be sampled more regularly would be required. With modern point-contact transducers, it seems to be feasible to implement such an experimental layout with a reasonable expenditure of time when using a multi-channels recording system.
These ambiguities show that COF analyses will also be required in the future, but ultrasonic measurements can support this analysis and bridge the gaps between the discrete COF samples.
Finally, ultrasonic measurements on ice cores and in boreholes provide the link between COF and surface geophysical velocities
Our measurement scheme (Fig.
In addition, the determination of the exact distance between source and receiver should be automated.
A manual measurement of the distances, as performed in our experiments, leads to a higher uncertainty in the derived velocities.
Moreover it is not feasible with several transducers.
These improvements require a more comprehensive measurement device.
Such a device could be employed in a processing line (e.g. in polar ice core drilling projects) with existing devices such as for dielectric profiling (DEP)
We have performed ultrasonic experiments on ice cores from a temperate glacier, and we compared the results with those from a well-established COF analysis method.
The main objectives of this study were (i) to compare the ultrasonic and COF-derived seismic velocities and (ii) to check if ultrasonic measurements have the potential to replace or reduce the labour-intensive and destructive COF analysis.
Our main findings can be summarised as follows:
Ultrasonic and COF-derived seismic velocities are comparable when the grain size of the ice crystals is sufficiently small. However, this condition is generally not met in temperate ice. As a consequence, we recommend applying this method to cold (e.g. polar) ice cores with small grains. In the presence of large grains, we observe a poor correlation between the ultrasonic and COF-derived velocities. The ultrasonic measurements belong to the deterministic approaches. Each measurement samples the actual three-dimensional volumes (Fresnel volumes) and only considers the grains therein. The COF-derived profiles provide a statistical mean value of the velocities for all thin sections. Therefore, the number of measurement levels of ultrasonic measurements needs to be sufficiently large. This is especially relevant for samples from temperate ice cores. In the presence of a significant porosity (i.e. air bubbles), a correction needs to be applied to make ultrasonic and COF-derived velocities comparable. This requires the determination of the porosity. In this study, we have employed a CT scanner for that purpose. In principle, ultrasonic measurements can be employed for determining COF patterns. However, this requires a relatively dense sampling of the ice core, including a broad range of azimuths and inclination angles. Our experimental set-up, including only horizontal and vertical measurements, led to ambiguous results.
On the basis of our findings, we conclude that ultrasonic measurements are not yet an adequate replacement for COF analysis.
However, since the development of ultrasonic transducers is progressing rapidly, we judge it feasible that adequate experimental layouts of ultrasonic experiments can be implemented in the foreseeable future.
This would offer substantial benefits since it would reduce the labour-intensive COF analysis.
Furthermore, the ultrasonic measurements offer the significant advantage of being non-destructive, and the samples of the generally valuable ice cores would remain available for other analyses of physical properties.
This also means that the ultrasonic measurements can continuously be obtained on freshly drilled cores.
Nevertheless, a certain but reduced number of thin sections for a COF analysis can still be used to calibrate the ultrasonic data and to dispose of ambiguities with direct comparisons of the results of both methods from the same ice core samples.
The ice fabric data and the LASM images are published in the open-access database PANGAEA® (
This study was initiated and supervised by HM, AB, and IW. SH, JK, and IW analysed the ice core microstructure to obtain the COF and calculate the seismic velocities. SH, MG, and HL planned and conducted the ultrasonic and CT measurements. Data processing and calculations were made by SH with support from all co-authors. The paper was written by SH, with comments and suggestions for improvements from all co-authors.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The data acquisition for this project has been provided by the Paul-Scherrer Institute, Villingen, the Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, and WSL Institute for Snow and Avalanche Research SLF, Davos. We especially thank Matthias Jaggi, Paul Selvadurai, and Claudio Madonna for their extensive technical and scientific support for the ultrasonic measurements and the equipment provided and Theo Jenk, Margit Schwikowski, and Jan Eichler for their support during ice core drilling and processing. We acknowledge Kenichi Matsuoka for the editorial work and the reviewers Valerie Maupin and Sridhar Anandakrishnan for their helpful comments.
This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant nos. 200021_169329/1 and 200021_169329/2).
This paper was edited by Kenichi Matsuoka and reviewed by Valerie Maupin and Sridhar Anandakrishnan.