Permittivity of ice at radio frequencies: Part II. Artificial and natural polycrystalline ice

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Abstract

Precise knowledge of the absolute value and frequency dependence of the dielectric permittivity of ice is the basis for interpretation of radio echo sounding data on glaciers and ice sheets. However, in the range of radio-frequencies, data from direct measurements of the permittivity are sparse, and partially lacking uncertainty estimates. Here, we present new results for artificial and natural ice samples obtained by means of frequency-dependent measurements from 10 MHz to 1.5 GHz with a coaxial transmission line cell. Measurements on eight artificial ice samples grown from ultra-pure water within the cell yield a mean value for the real part of the relative permittivity of 3.18 ± 0.01 at − 20 °C. Sole evidence for dispersion is detected for frequencies below 10 MHz, possibly attributed to the Debye-type relaxation behavior. Investigation of the crystal orientation of the artificial ice samples reveals the c-axes to be predominantly parallel to the electric field inside the cell and allows to calculate a value representative for isotropic crystal orientation of 3.16 ± 0.01. Measurements on acid-doped artificial ice show a linear dependence of the real part with acidity with a gradient of (21.1 ± 3.9) [1/M]. The real part of the relative permittivity of natural firn and ice samples from a high Alpine glacier range from 2.02 at a density of 0.515 g/cm3 to 3.08 at 0.875 g/cm3. Quasi-continuous measurements with the present setup on an alpine firn core are now possible, with resolution depending on the coaxial cell's length, for direct comparison with the established dielectric profiling method.

Highlights

► The real part of the permittivity of ice is measured at 1% uncertainty between 10 MHz and 1.5 GHz. ► The results show no signs of dispersion between 10 MHz and 1.5 GHz. ► In this range, measurements yield a mean value for the real part of isotropic ice of 3.16 +/− 0.01. ► Acid-doped ice and natural firn and ice samples were measured successfully.

Introduction

Radio echo sounding (RES) is a widely used technique for exploring the terrestrial cryosphere as well as extraterrestrial ice bodies. In glaciological applications, RES has become a standard tool for investigating thickness and internal structure of glaciers and ice sheets. Interpretation of RES data requires detailed knowledge of the relative complex dielectric permittivity1 (εr = εr  r) of pure and natural ice. In the frequency range where RES typically operates (≈ 1 MHz–1 GHz) the permittivity of ice is characterised by its real part being almost independent of frequency around εr  3.17 and its imaginary part being very small—in the order of ≈ 10 2—with a minimum around 1 GHz (Evans, 1965, Fujita et al., 2000, Warren, 1984). These dielectric characteristics of ice are explained by the picture of a transition between the Debye-type relaxation behavior (with the relaxation frequency in the kHz-range) and the far-infrared absorption due to lattice vibrations (Bogorodsky et al., 1985, Petrenko and Whitworth, 1999). However, this knowledge relies on only few measurements of the permittivity of ice directly at MHz-frequencies, e.g. Johari and Charette (1975) and Johari (1976). Regarding frequencies between 100 MHz and 1 GHz, measurements by Westphal were published in Evans (1965), however without further details on the used setup and associated uncertainties. Hence, the current demand of accuracy for interpreting geophysical measurements entails the need for additional laboratory measurements on ice at MHz-frequencies. This especially concerns investigating permittivity changes associated with internal reflections in glaciers and ice sheets, which mainly go back to variations in density, acidity and crystal orientation fabric (Fujita et al., 2000).

The influence of density variations on the real part εr of firn and ice has been studied in detail theoretically and empirically (Glen and Paren, 1975, Kovacs et al., 1995, Wilhelms, 2005). Acid-doped ice was investigated in laboratory measurements over different frequency intervals by Matsuoka et al. (1996) (1 kHz–30 MHz), Matsuoka et al. (1997a) at 5 GHz, Fujita et al. (1992) at 9.7 GHz and between 100 and 600 MHz in Fujita et al. (2000). These studies report a linear relation between εr and acidity, where the gradient depends on temperature and frequency. The permittivity of mono crystalline ice in its prevalent state “Ih” (only ice Ih, as it occurs on earth as well as on several other solar bodies, will be considered here) shows a small anisotropy Δεr=εε, with ε and ε being the relative permittivity measured with the electric field oriented parallel and perpendicular, respectively, to the c-axis of the hexagonal ice crystals. Matsuoka et al. (1997b) concluded from their measurements at 1 MHz and 39 GHz that a frequency-independent anisotropy Δεr of a little more than 1% exists—in agreement with an earlier study at 9.7 GHz by Fujita et al. (1993).

In this present study, we obtain new results from permittivity measurements of natural and artificial ice samples in the MHz-range using a coaxial transmission line setup. Since waveguide methods may not be able to precisely determine the small-valued imaginary part at radio frequencies (Fujita et al., 2000), we put the main focus on the real part of the permittivity. A detailed description of the coaxial cell setup and the deployed permittivity computation algorithms is given in part I of this two-part companion paper. In the present part II, sample characteristics and the results from measuring εr of pure ice in the MHz-range are discussed. Results from an investigation of the influence of acidity are also included. Measurements of natural ice sample are aimed at investigating as to what extent the results obtained from artificial samples may be representative for real glacier ice, as well as at measuring firn and ice samples of different densities. For this purpose, natural samples of firn and ice are used, originally retrieved from Colle Gnifetti and Grenzgletscher (Monte Rosa massif, Swiss-Italian Alps), respectively. Within the range of the uncertainty of the presented results, εr of pure artificial and natural ice sample reveal no frequency dependence above 10 MHz. This lack of dispersion is highlighted because it is of central interest for the application of RES in glaciological research.

Section snippets

Determining ice permittivity with the coaxial transmission line cell method

Measurements are performed using a large-volume coaxial transmission line setup. Outer diameter of the inner, inner diameter of the outer conductor and sample holder length are 26, 60 and 200 mm respectively, giving a total volume of 459.3 cm3. The dielectric sample is inserted between the inner and outer conductor of the sample holder. Reflection and transmission due to the resulting impedance jump in the coaxial line are measured as scattering parameters (S-parameters) with an Agilent ET8714

Sample preparation

Artificial ice samples are prepared to fit the coaxial geometry by freezing water inside the cell: The sample holder can be sealed watertight and is then filled with degassed, ultra-pure water and left in the cold room (− 20 °C) standing upright. The freezing process of the water inside the cell progresses from the outer conductor towards the centre cylindrical axis. This method yields very homogenous clear ice with no cracks and only few thin radially oriented air inclusions remaining. The

Pure, artificial ice samples

Over 30 different artificial samples were measured and their permittivities calculated from the S-parameters with the Debye-model optimisation and the BJI-method. A total of eight different pure3 artificial ice samples could be measured at highest possible accuracy with the coaxial probe inside an insulating styrofoam box stabilizing the ambient temperature around (− 20 ± 2) °C. Since the measured frequency interval does only cover the high

Permittivity of artificial, pure ice

The value of εr measured on artificial, pure ice samples can be regarded as a mixture of ε and ε. Based on the crystal orientation distribution of the ice sample the relative contributions of ε and ε can be calculated, as well as a value representative for isotropic ice εiso.

Conclusion

We measured the frequency-dependent properties of artificial and natural ice samples with a coaxial transmission line setup. Within 10 MHz to 1.5 GHz uncertainty for the real part εr is about 1%. The only evidence for frequency dependence in εr is detected below 10 MHz, possibly the high-frequency tail of the Debye-type relaxation behavior. For the frequency range between 10 MHz and 1.5 GHz, eight artificial ice samples reveal a frequency-independent real part with a mean value of εr = 3.18 ± 0.01

Acknowledgements

We would like to thank S. Kipfstuhl for providing for the crystal orientation analysis, B. Oswald for the Debye-based optimisation, and S. Fujita, K. Roth, D. Wagenbach and F. Wilhelms for valuable comments and discussions. Financial support for this study was provided by a completion grant of the University of Heidelberg Graduate Academy to P. Bohleber, the Emmy Noether-program of the Deutsche Forschungsgemeinschaft grant EI 672/5-1 to O. Eisen and Project Wa 2112/2-1 of the Deutsche

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