Radio-frequency probes of Antarctic ice birefringence at South Pole vs. East Antarctica; evidence for a changing ice fabric by Besson et al. Besson and coauthors studied propagation of radio waves reflected off the internal reflectors at a site at South Pole, as a function of polarization axis in th

Besson and coauthors studied propagation of radio waves reflected off the internal reflectors at a site at South Pole, as a function of polarization axis in the horizontal plane and oblique radio wave scattering. The authors performed various attempts using their own radar system using a kind of monopulse radar that use wide range of frequency spectrum. The authors' main points include (i) findings of several major internal reflectors at timing lower than ~19 uS, (ii) a difference in birefringence between South Pole and Dome Fuji, (iii) orientation dependence of reflection amplitude at some reflectors, and (iv) "most precise determination of the ice thickness at South Pole". The title of the paper reflects the authors main claim ice fabric is different between South Pole and Dome Fuji. According to the authors' affiliations and according to their earlier publications, the authors' main research field include neutrino and neutrino detection.


Introduction
In the current picture, radio frequency scattering is primarily the result of three different 15 mechanisms as one probes from the ice surface down to the bed. In the uppermost portion of the ice sheet, scattering is dominated by layered density variations, followed by so-called "acid", or "conductivity" scattering (sulfates and nitrate layers, e.g. often associated with volcanic activity), followed by "crystal orientation fabric" (COF) scattering due to changes in the crystal orientation in the deeper ice, presumably resulting from 20 a combination of considerable overpressure and the resistance to motion presented by the underlying bedrock. Near the bed is an "echo-free zone" (EFZ), in which the reflection strengths are typically smaller than current instrumental sensitivity (Drews et al., 2009). The three scattering types can be separated on the basis of the magnitude of the radar echoes they produce, as well as the frequency dependence of 25 those radar echoes. The most extensive (and, to a large extent, defining)

Birefringence
The presence of a preferred crystal orientation fabric can lead to an asymmetry in the radio wavespeed with azimuthal polarization; i.e. birefringence. Physically, this corresponds to a difference δ in the real permittivity for propagation along the ordinaryvs. extraordinary-axes. In the simplest picture of two-dimensional ice crystals stacking 5 in the horizontal plane, with the perpendicular (ĉ-axis) correspondingly aligned with the verticalẑ-axis, one would expect radio wave propagation along the vertical from the surface to the bedrock (i.e. with the electric-field polarization axis in the horizontal) to be independent of azimuth, and birefringence to be noticeable as a difference between horizontal vs. vertical signal propagation. Laboratory measurements, in fact, 10 determined an asymmetry of ∼ 3.3 % between these two wave speeds (Fujita et al., 1996). The local horizontal ice flow, however, produces an azimuthal asymmetry in the horizontal plane, and also suggests a "natural" axis which may result in a wavespeed asymmetry.
Although birefringence is now well-established in the ice sheet (Table 1), data on 15 exactly what depths birefringence is physically generated within the ice sheet is still incomplete. Data indicating correlations of birefringent effects with local ice flow are also not entirely concordant; at least one measurement found a lack of alignment between the implied birefringent basis and the surface ice flow direction (Doake, 1981;Woodruff and Doake, 1979). 20 2 Measured azimuthal variation of radar echoes, normal incidence

Set-up
The Martin A. Pomerantz Observatory (MAPO) building, located within 1 km of the geographic South Pole, houses the signal generator and data acquisition system used for these measurements. Two 1. 25 m long, were fed from within MAPO through a conduit at the bottom of the building and out onto the snow. Each cable was then connected to a Transverse ElectroMagnetic (TEM) horn antenna on the snow surface. These antennas, constructed at the Institute of Nuclear Research in Moscow, were also used in our previous measurement of the ice attenuation length at the South Pole (Barwick et al., 2005). As with our previ-5 ous measurement, for in-ice transmission, each horn antenna is placed face-down on the surface looking into the snow. These antennas have reasonably good transmission characteristics, from 60 MHz up to 1300 MHz, as indicated by the Voltage Standing Wave Ratio (VSWR) data in Fig. 1. We note that the measured frequency response shown in Fig. 1 corresponds to the horn antennas in their experimental configuration 10 and therefore should correctly represent the horn characteristics relevant to this measurement. The forward gain of the horns is approximately 10× that of an isotropic emitter (∼ 10 dBi) in air, or ∼ 12-15 dBi in-ice. The co-polarization to cross-polarization isolation ("polarization purity") was measured at South Pole, and also in the lab at the University of Kansas, to exceed 10 dB.

15
Signals were taken from a fast pulse generator inside MAPO through the coaxial cable out to the transmitter horn. Receiver horn signals are high-and low-pass filtered to remove components below 200 MHz and above 1 GHz, notch filtered to suppress the large South Pole background noise at 450 MHz which serves as the station Land Mobile Radio carrier, and finally amplified by +52 dB prior to data acquisition and storage; 20 the total time delay through the associated cables has been measured to be 190 ns. Data acquisition of receiver horn waveforms was performed using a LeCroy 950 Waverunner digital oscilloscope. This scope features adequate bandwidth (1 GHz) and a high maximum digitization speed (16 GigaSamples s −1 -GSa s −1 ). For the measurements described herein, the scope sampling rate was generally set to 2 GSa s −1 . To 25 enhance signal-to-noise, many waveforms (40 000 typically) were averaged. Trigger stability was ensured by splitting the output of the pulse generator, with one copy being sent to the transmitter horn antenna, and the other providing the trigger signal for the LeCroy scope. We note three primary differences between our radio echo sounding (RES) apparatus, which was originally developed for application in Antarctica cosmic ray detection, and that typically employed for RES measurements: 1. We use a nanosecond-scale transmitted pulse, vs. "tone" signals of frequency ∼ 100-200 MHz, having duration of order microseconds. 5 2. Our receiver data acquisition samples at between 1 and 2 GSa s −1 , vs. sampling rates which are comparable to the CW signal being broadcast.
3. Reflections are reconstructed directly by averaging, rather than synthesizing the reflected echogram image using SAR techniques.

Full azimuthal scan
Figures 2 and 3 display the measured voltage as a function of echo time, as the polarization orientation of the transmitter and receiver are rotated. For ease of display, echograms have been vertically offset and alternately displaced by ±100 ns relative to each other. In actuality, the most prominent echoes are observed to be synchronous 15 within one nanosecond of each other, up to 19 µs echo time, and thus excludes the possibility of a birefringent effect in the upper half of the ice sheet, in contrast to the East Antarctica measurements (Fujita et al., 2003(Fujita et al., , 2006. Antennas aligned with MAPO were assigned a zero-degree orientation; for reference, the surface ice flows in a direction corresponding to roughly +153 • in these coordinates. In these figures, the no-20 tation "A × B" designates the azimuthal polarization orientation of transmitter ("A") and receiver ("B"), respectively. "60 × 150" correspondingly indicates a cross-polarization orientation. Several features are immediately evident from Figs. 2 and 3: (a) the presence of several short-duration returns at approximately 6, 9.6, 13.9, 17  received power in the cross-polarization orientation than the co-polarization orientation, (c) in general, the "continuum" received power, away from evident peaks, in the cross-polarization orientation is smaller than the co-polarization power (presumably related to the geometric characteristics of volumetric scattering in the bulk ice), and (d) for the 9.6 µs echo, we observe a sequence of three distinct echoes, separated by ap-5 proximately 0.1 µs. We note that the implied depth of the return at 13.9 µs is consistent with layering identified using a laser dust logger in boreholes drilled for the IceCube experiment (Abassi et al., 2012).

Time domain characteristics of observed returns
We have investigated the temporal and frequency characteristics of our observed 10 echoes. An earlier study concluded that "anisotropic scattering", occuring at depths where the alignment of the ice crystal fabric changes directions, is responsible for many of the echoes observed at intermediate depths. Such scattering, of the COF type, should be independent of frequency, over the interval 60-179 MHz (Matsuoka et al., 2003). COF scattering can thus be distinguished from acid layer scattering, which 15 features amplitude believed to vary inversely as frequency, but not from density layer scattering. Figure 4 compares zooms of the time domain waveforms of the reflections observed at 6, 9.6, 13.9, 17 and 19 µs. We observe that the shallower time-domain returns are, if anything, longer in duration than the deeper returns, indicating higher fractional signal 20 content at lower frequencies. Overall, the similarity of the waveforms suggest that the same scattering mechanism may be responsible for all observed reflections. Note that the waveforms shapes, qualitatively, disfavor a model wherein ice attenuation increases with frequency, as this would tend to reduce the sharpness of the later, rather than earlier returns.

Attenuation length dependence on depth and temperature
The observed echo amplitudes shown in Fig. 4 are largely determined by three factors: the intrinsic reflectivity of each layer, the diminution of signal power P signal with 5 distance, and attenuation of the signal due to continuous ice absorption. For the directional horn antennas used in this experiment, P signal ∝ r −α , with 1 < α < 2. If we assume that the scattering mechanisms for all reflections are the same, and further assume approximately equivalent reflection coefficients for all internal layers, we can determine a "local" amplitude attenuation length between the first three, and last three layers, as 10 shown in Table 2, by direct application of the Friis equation (Balanis, 1997). For this calculation, we take α = 2; assuming a cylindrical-flux tube with no transverse spreading (α = 1) gives values approximately 20 % smaller than those presented in Table 2. Our estimates, showing a general trend of shorter attenuation lengths closer to the bed, are consistent with the expected warming of the ice sheet from below, and the corre-15 sponding reduction in attenuation length with increasing temperature. We note that the temperature dependence of conductivity scattering would lead to a reduction in reflection coefficient with depth and could therefore also account for some of the variation observed; in Table 2, we neglect the 6 • K difference in layer temperature between the depth implied for the 13.9 µs reflection vs. the 19.6 µs reflection. For this translation, we 20 use a temperature-weighted average EM wave velocity of 169 ± 0.3 m µs −1 below the firn (Dowdeswell and Evans, 2004); through the firn, we use direct measurements of radio propagation wavespeed (Kravchenko et al., 2005).

Variation in return amplitude with azimuth
A comparison of the maximum amplitudes observed for the 5 primary reflections is 25 presented in Table 3; asterisks indicate that the reflection at that depth and orientation angle was insufficiently distinct from noise. Figure 7 displays the peak amplitude voltages vs. co-polarization orientation angle. For three of these layers, we observe an apparent co-sinusoidal variation which is roughly in phase with the ice flow direction (153 • , shown as the blue arrow in the figure); no obvious correlation is apparent for the 6 µs and 19 µs reflections. We emphasize that the azimuthal variation observed in this 5 experiment is otherwise unrelated to the azimuthal variation reported in East Antarctica (Fujita et al., 2006); in particular, those variations were attributed to destructive interference between projections of the radio-frequency electric field vector propagating along two orthogonal axes. In our case, there is no (obvious) operative interference mechanism. I.e. the synchronousness (to within 1 nanosecond) of the reflections, at all 10 polarizations, rules out the possibility that the observed azimuthal amplitude variation is the result of birefringence-induced interference effects; the mechanism responsible for our observed variation is therefore different than the mechanism responsible for the variations in amplitude observed at Dome Fuji, which were attributed to birefringence, and also exhibited a faster phase variation than we observe.

15
A previous paper (Besson et al., 2010) investigated the basal echo times at South Pole as a function of polarization. That study demonstrated that reflections through the full ice sheet, off the bedrock, do exhibit the azimuthal dependence of echo times and voltages characteristic of birefringence. Specifically, for polarizations aligned parallel to the putative ordinary axis, only one return is observed, with a voltage V max fast and a nega-20 tive echo time offset relative to that observed for polarizations aligned with the putative extraordinary axis, presumably rotated by π/2 radians. If we designate the voltage observed for alignments parallel to the ordinary axis as V max fast , then, for polarizations at π/4 radians relative to each axis, two returns should be observed, each with amplitude 1/ √ 2 as large as the co-aligned case; i.e. V fast (π/4)/V slow (π/4) = 1. Additionally, for Besson et al., 2010) shows measurements consistent with these expectations, and thus, a correlation consistent with ice flow direction defining the extraordinary axis.

Oblique radio wave scattering
The problem of securing power sources for both transmitters and receivers at remote field sites presents an obstacle to performing radar measurements at non-zero inclination angles. Nevertheless, such measurements are the most obvious method of probing the three-dimensional characteristics of birefringence, rather than merely investigating 5 effects exclusively in the horizontal plane. In our picture, a ray having an electric-field polarization vector E incident on a medium (in our case, ice) is characterized by three principal orthogonal axes x, y and z, which we associate with the ice-flow direction (y-), the vertical (z-) and a corresponding x-axis given by the cross-product of y-and z-unit vectors. For our geometry, 10 y-is approximately grid south, and x-is approximately grid east.
In the general case of three-dimensional birefringence, we associate the three coordinate axes with corresponding refractive-indices n x , n y and n z . Using the angles θ and φ as the conventional polar and azimuthal angles, the amplitudes of the projected components are then given by the standard expressions: A x = |E| sin θ cos φ, 15 A y = |E| sin θ sin φ, and A z = |E| cos θ. At South Pole, such measurements were performed in December 2011, both along and transverse to the horizontal ice-flow direction ( Fig. 9). Both transmitter and receiver were propped up approximately 1 m above the ice surface, at a 45-degree angle relative to the surface, thus broadcasting both a direct signal through the air, as well as a signal broadcast into, and received after re-20 flection from the intervening ice. The ray geometry for typical measurements are shown in Fig. 10.
A simple trigger, based on reception of the direct through-air signal broadcast at the receiver was employed -a more sophisticated trigger, which would have synched the received signal to a simultaneously-broadcast, narrow-band transmitter signal as 25 was done in the past (Barwick et al., 2005), was, unfortunately, not available for these measurements. At each transmitter location, both horizontally polarized ("HPol") and also vertically polarized ("VPol") data were collected. An additional data point was taken approximately 60 degrees relative to the ice flow direction (i.e. 30 degrees relative to a perpendicular to the ice flow direction and labeled "Tx3" in the figure) at a transmitterreceiver separation of 400 m as a cross-check.
Our primary results are shown in Figs. 11 and 12. A cross-correlation analysis determines the time staggers between the two signal onsets to be 49.2 ns and 50.1 ns 5 in Figs. 11 and 12, very consistent with the 50.0 ns time offset previously reported for the birefringent propagation time asymmetry measured in vertical propagation (Besson et al., 2010), as expected from Fig. 10. As a cross-check, propagation from "Tx3" also yields an echo time difference consistent with 50 ns (Fig. 13).
In principle, the VPol signals can be projected separately into the horizontal and 10 vertical planes. However, the amplitude of the VPol component, given the relatively short horizontal baselines, is immeasurably small in our data sample. Clearly, what is needed to make this measurement more compelling is to broadcast over larger horizontal distances, and thereby probe a more vertical VPol propagation vector. Such a measurement will require a revised trigger scheme, such as that used previously at

Ice depth measurement
The times of the received bedrock echoes relative to the through-air trigger, for each polarization, are directly given by the average index-of-refraction and the depth of the intervening ice.  Fig. 14. The ice thickness difference, at those locations, as a function of the numerical separation (in meters) between the CRESIS vs. the BEDMAP sampling points, is shown in Fig. 15. Although the depth difference distribution clusters at zero, we observe large deviations from zero depth difference; the rms of the distribution is approximately 115 m.

5
We can estimate the ice thickness depth at South Pole from our data, obtained using a considerably faster pulse, using the following procedure. Since the index-of-refraction of refraction varies through the firn, we calculate an "average" value based on the measured radiofrequency light speed to a depth of 200 m (Kravchenko et al., 2005), and assuming a constant value of n = 1.782 at greater depths; this procedure yields a depth-10 averaged index-of-refraction value of 1.773. We can then calculate the ice depth, independent of any system delays, by comparing the measured through-ice transit time, relative to the through-air trigger signal, against the calculated through-ice transit time, knowing the horizontal spacing between transmitter and receiver at each source point, and leaving the depth as a free parameter. Results are shown in Fig. 16. We find rela-15 tively good agreement between the average of our three measurements (2841 ± 15 m) with a previous estimate of 2850 m for the ice thickness at South Pole (Besson et al., 2010). Note that the errors are comparable to the expected depth difference due to bedrock slope. By comparison, we note that the BEDMAP (The BEDMAP Collaboration, 2012) collaboration have tabulated the ice sheet depths at latitude 89.975 • S, in 20 increments of 0.36 degrees of longitude. Those depths are shown in polar form, with an offset of 2700 m, in Fig. 17. Our value is bracketed by the tabulated BEDMAP depths, albeit with smaller error bars.

Future work using embedded transmitters
Owing to the difficulty of embedding transmitters at depth within the ice sheet itself, 25 virtually all of the radar data that has been collected thus far has been collected along a vertical chord. In January 2011, three high-power (5 kV amplitude, 100 ps rise time) radio pulsers were deployed as part of the Askaryan Radio Array (ARA, Allison, 2011) 4706 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | deployment during that austral season. Two have been frozen in at depths of 1450 m (offset horizontally by approx. 200 m); the third has been frozen in at a depth of 2400 m. These pulsers are locally slaved to a high-precision Rubidium oscillator, also deployed in-ice at the location of the transmitters themselves, to permit waveform averaging of received signals by either embedded, or surface receivers. Those transmitters should 5 afford an unprecedented opportunity to measure the complex permittivity of ice, in the radio frequency range, and provide a new suite of measurements, not only for the ARA particle astrophysics experiment, but the radioglaciological community as well. In particular, those transmitters will allow high-precision, long-baseline probes of the ice along a horizontal chord for the first time.

Conclusions
We have observed azimuthal correlations of echo returns with ice flow direction at South Pole, which we summarize as follows: -As with previous work around Dome Fuji, we also observe a correlation of surface iceflow direction with echo amplitude for internal reflections at echo times up 15 to 20 µs. However, we note several differences between our measurements and those previous probes of the ice sheet in East Antarctica (Fujita et al., 2006): -Although reflections at ∼ 1 km depth in East Antarctica were explained as due to transitions between layers with different COF alignments, we find no evidence for the expected concommitant birefringent effect due to COF align-20 ment. This implies that the ice fabric is not monolithic across the Antarctic continental surface.
-For some alignments, we observe cross-polarized signal strength that exceeds the co-polarized signal strength, in contrast to the expectation (Fujita et al., 2003) that the co-polarized signal sets a physical limit on the observed of successively rotated diffraction gratings in optics, and suggests that such a mechanism may be operative within the ice, as well, with layers functioning as gratings.
-A separate data sample taken in December 2011, with transmitter and receiver separated horizontally by ≈ 0.5 km affirms the quantitative results of our previous 5 measurements for the total birefringent asymmetry through a vertical chord of the ice, using co-located transmitter and receiver. Our measurements also permit a precise measurement of the thickness of the ice sheet at Pole (2841 ± 15 m), where the quoted error is based on the observed spread in our individual trials.
-In the "standard" picture, if the c-axis is exactly vertical, and the wavespeed asym-10 metry is different only for propagation perpendicular (i.e. along z) vs. perpendicular (horizontal) to the crystal stacking axis (i.e.ĉ), then the wavespeed is uniform for all directions in the horizontal plane and there is no expected birefringence as a function of azimuthal orientation. However, our results imply an asymmetry for azimuthal propagation along vs. perpendicular to the ice flow direction, in 15 contrast to the laboratory measurements for single crystals, which would have implied azimuthal symmetry. Our results are consistent with a vertical girdle average orientation at depths greater than ∼ 1200 m, although ice core analysis indicates that the ice should be increasingly uniaxial at these depths.
Two additional inputs could significantly clarify the association between Radar Echo 20 Sounding measurements and ice chemistry, either: (1) an ice core taken at South Pole, preferably retaining the azimuthal information of the extracted core itself, or (2) nsduration probes of the Antarctic ice sheet at a location where a core has already been taken (Vostok, or WAIS, e.g.). Such data will hopefully be available at some point in the near future. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | for very helpful discussions, as well as our colleagues on the RICE and ANITA experiments. We also thank Andy Bricker of Lawrence High School (Lawrence, KS) for his assistance working with Lawrence High School students who performed essential antenna calibrations. This work was supported by the National Science Foundation's Office of Polar Programs (grant OPP-0826747) and QuarkNet programs. Any opinions, findings, and conclusions or recom-    note that the measured frequency response shown in Figure 1 corresponds to the horn antennas in their experimental configuration and therefore should correctly represent the horn   Fig. 3. Ensemble of echo amplitudes observed as a function of azimuthal orientation, for both co-polarized and cross-polarized broadcast signals, for echo times between 13 µs and 20 µs. In addition to vertical offset, alternate waveforms are also offset by ±100 ns along horizontal.       for the 9.6 µs return compared to the 6 µs reflection, con-225 sistent with the qualitative conclusion drawn from the time domain waveforms shown in Figure 4. alcure of r the indiwas peak s * than the mechanism responsible for the variations in amplitude observed at Dome Fuji, which were attributed to birefringence, and also exhibited a faster phase variation than we observe.  Besson, D. and others, 2010)) shows measurements consistent with these expectations, and thus, a correlation consistent with ice flow direction defining the extraordinary axis. 3 Oblique Radio Wave Scattering 305 ments are shown in Figure 10 A simple trigger, based on 335 air signal broadcast at the re sophisticated trigger, which w signal to a simultaneously-br ter signal as was done in th 2005), was, unfortunately, n 340 ments. At each transmitter larized ("HPol") and also ve were collected. An addition imately 60 degrees relative t degrees relative to a perpend 345 and labeled "Tx3" in the Figu aration of 400 meters as a cro Our primary results are sh cross-correlation analysis de tween the two signal onsets t 350 11 and 12, very consistent w viously reported for the biref metry measured in vertical p ers, 2010), as expected from propagation from "Tx3" also 355 consistent with 50 ns (Fig. 1 In principle, the VPol sign into the horizontal and vertic tude of the VPol component    Fig. 10. Schematic of signal propagation geometry for antenna configuration parallel to the ice-flow axis; in this case, the transmitter used corresponds to "Tx1", as denoted in the previous Figure. Vertical axis is defined as "+z"; the polar angle between the VPol propagation vector and the z-axis is defined as θ. Geometries for the other two transmitter positions ("Tx2" and "Tx3" in the previous Figure) are not shown.  Fig. 10. Schematic of signal propagation geometry for antenna configuration parallel to the iceflow axis; in this case, the transmitter used corresponds to "Tx1", as denoted in the previous figure. Vertical axis is defined as "+z"; the polar angle between the VPol propagation vector and the z-axis is defined as θ. Geometries for the other two transmitter positions ("Tx2" and "Tx3" in the previous figure) are not shown.  Fig. 11. Reflection echoes observed for HPol and VPol propagation; transmitter (at "Tx1") and receiver separated by ∼800 m and radio propagation aligned with the local ice-flow direction at South Pole. Note the suppressed zero along the x-axis, corresponding to the trigger time. We can estimate the ice t from our data, obtained using ing the following procedure. of refraction varies through erage" value based on the m 395 speed to a depth of 200 m(K and assuming a constant value this procedure yields a depth Fig. 11. Reflection echoes observed for HPol and VPol propagation; transmitter (at "Tx1") and receiver separated by ∼ 800 m and radio propagation aligned with the local ice-flow direction at South Pole. Note the suppressed zero along the x-axis, corresponding to the trigger time.  Fig. 13. Reflection echoes observed for HPol and VPol propagation; transmitter (at "Tx3") and receiver separated by ∼400 m and radio propagation at 60 degrees relative to the local ice-flow direction at South Pole.
numerical separation (in meters) between the CRESIS vs. the