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Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.

Antarctic firn presents an exotic seismological environment in which the behaviors of propagating waves can be significantly at odds with those in other Earth media. We present a condensed view of the nascent field of ambient noise seismology in Antarctic firn-covered media, and highlight multiple unusual and information-rich observations framed through the lens of the firn's important role as a buffer for air temperature anomalies and a complex contributor to ice mass balance. We summarize key results from several recent papers depicting novel wind-excited firn resonances and point to the plethora of ways these observations could facilitate imaging and monitoring of glacial systems at single, isolated seismometers. Finally, we propose significant instrumental and computational objectives necessary to constrain resonance excitation mechanisms and broadly apply these observations as useful monitoring tools in Antarctica. [ABSTRACT FROM AUTHOR]

Distributed Acoustic Sensing (DAS) is increasingly recognised as a valuable tool for glaciological seismic applications, although analysing the large data volumes generated in acquisitions poses computational challenges. We show the potential of active-source DAS to image and characterise subglacial sediment beneath a fast-flowing Greenlandic outlet glacier, estimating the thickness of sediment layers to be 20–30 m. However, the lack of subglacial velocity constraint limits the accuracy of this estimate. Constraint could be provided by analysing cryoseismic events in a counterpart 3-day record of passive seismicity through, for example, seismic tomography, but locating them within the 9 TB data volume is computationally inefficient. We describe experiments with data compression using the frequency-wavenumber (f-k) transform ahead of training a convolutional neural network, that provides a ~300-fold improvement in efficiency. In combining active and passive-source and our machine learning framework, the potential of large DAS datasets could be unlocked for a range of future applications. [ABSTRACT FROM AUTHOR]

Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice. [ABSTRACT FROM AUTHOR]

Antarctic firn presents an exotic seismological environment in which the behaviors of propagating waves can be significantly at odds with those in other Earth media. We present a condensed view of the nascent field of ambient noise seismology in Antarctic firn-covered media, and highlight multiple unusual and information-rich observations framed through the lens of the firn's important role as a buffer for air temperature anomalies and a complex contributor to ice mass balance. We summarize key results from several recent papers depicting novel wind-excited firn resonances and point to the plethora of ways these observations could facilitate imaging and monitoring of glacial systems at single, isolated seismometers. Finally, we propose significant instrumental and computational objectives necessary to constrain resonance excitation mechanisms and broadly apply these observations as useful monitoring tools in Antarctica.

Distributed Acoustic Sensing (DAS) is increasingly recognised as a valuable tool for glaciological seismic applications, although analysing the large data volumes generated in acquisitions poses computational challenges. We show the potential of active-source DAS to image and characterise subglacial sediment beneath a fast-flowing Greenlandic outlet glacier, estimating the thickness of sediment layers to be 20–30 m. However, the lack of subglacial velocity constraint limits the accuracy of this estimate. Constraint could be provided by analysing cryoseismic events in a counterpart 3-day record of passive seismicity through, for example, seismic tomography, but locating them within the 9 TB data volume is computationally inefficient. We describe experiments with data compression using the frequency-wavenumber (f-k) transform ahead of training a convolutional neural network, that provides a ~300-fold improvement in efficiency. In combining active and passive-source and our machine learning framework, the potential of large DAS datasets could be unlocked for a range of future applications.

During the past 20 years, multi-channel radar emerged as a key tool for deciphering an ice sheet's internal architecture. To assign ages to radar reflections and connect them over large areas in the ice sheet, the layer genesis has to be understood on a microphysical scale. Synthetic radar trace modelling based on the dielectric profile of ice cores allows for the assignation of observed physical properties’ variations on the decimetre scale to radar reflectors extending from the coring site to a regional or even whole-ice-sheet scale. In this paper we rely on the available dielectric profiling data of the northern Greenland deep ice cores: NGRIP, NEEM and EGRIP. The three records are well suited for assigning an age model to the stratigraphic radar-mapped layers, and linking up the reflector properties to observations in the cores. Our modelling results show that the internal reflections are mainly due to conductivity changes. Furthermore, we deduce fabric characteristics at the EGRIP drill site from two-way-travel-time differences of along and across-flow polarized radarwave reflections of selected horizons (below 980 m). These indicate in deeper parts of the ice column an across-flow concentrated c-axis fabric.

Microstructures, including crystallographic fabric, within the margin of streaming ice can exert strong control on flow dynamics. To characterize a natural setting, we retrieved three cores, two of which reached bed, from the flank of Jarvis Glacier, eastern Alaska Range, Alaska. The core sites lie ~1 km downstream of the source, with abundant water present in the extracted cores and at the base of the glacier. All cores exhibit dipping layers, a combination of debris bands and bubble-free domains. Grain sizes coarsen on average approaching the lateral margin. Crystallographic orientations are more clustered and with c-axes closer to horizontal nearer the lateral margin. The measured fabric is sufficiently weak to induce little mechanical anisotropy, but the data suggest that despite the challenging conditions of warm ice, abundant water and a short flow distance, many aspects of the microstructure, including measurable crystallographic fabric, evolved in systematic ways.

Antarctic firn presents an exotic seismological environment in which the behaviors of propagating waves can be significantly at odds with those in other Earth media. We present a condensed view of the nascent field of ambient noise seismology in Antarctic firn-covered media, and highlight multiple unusual and information-rich observations framed through the lens of the firn's important role as a buffer for air temperature anomalies and a complex contributor to ice mass balance. We summarize key results from several recent papers depicting novel wind-excited firn resonances and point to the plethora of ways these observations could facilitate imaging and monitoring of glacial systems at single, isolated seismometers. Finally, we propose significant instrumental and computational objectives necessary to constrain resonance excitation mechanisms and broadly apply these observations as useful monitoring tools in Antarctica. [ABSTRACT FROM AUTHOR]

Distributed Acoustic Sensing (DAS) is increasingly recognised as a valuable tool for glaciological seismic applications, although analysing the large data volumes generated in acquisitions poses computational challenges. We show the potential of active-source DAS to image and characterise subglacial sediment beneath a fast-flowing Greenlandic outlet glacier, estimating the thickness of sediment layers to be 20–30 m. However, the lack of subglacial velocity constraint limits the accuracy of this estimate. Constraint could be provided by analysing cryoseismic events in a counterpart 3-day record of passive seismicity through, for example, seismic tomography, but locating them within the 9 TB data volume is computationally inefficient. We describe experiments with data compression using the frequency-wavenumber (f-k) transform ahead of training a convolutional neural network, that provides a ~300-fold improvement in efficiency. In combining active and passive-source and our machine learning framework, the potential of large DAS datasets could be unlocked for a range of future applications. [ABSTRACT FROM AUTHOR]

During the past 20 years, multi-channel radar emerged as a key tool for deciphering an ice sheet's internal architecture. To assign ages to radar reflections and connect them over large areas in the ice sheet, the layer genesis has to be understood on a microphysical scale. Synthetic radar trace modelling based on the dielectric profile of ice cores allows for the assignation of observed physical properties' variations on the decimetre scale to radar reflectors extending from the coring site to a regional or even whole-ice-sheet scale. In this paper we rely on the available dielectric profiling data of the northern Greenland deep ice cores: NGRIP, NEEM and EGRIP. The three records are well suited for assigning an age model to the stratigraphic radar-mapped layers, and linking up the reflector properties to observations in the cores. Our modelling results show that the internal reflections are mainly due to conductivity changes. Furthermore, we deduce fabric characteristics at the EGRIP drill site from two-way-travel-time differences of along and across-flow polarized radarwave reflections of selected horizons (below 980 m). These indicate in deeper parts of the ice column an across-flow concentrated c-axis fabric. [ABSTRACT FROM AUTHOR]

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling.

We use polarimetric radar sounding to investigate ice crystal orientation fabric and its impact on ice viscosity within the near surface of Rutford Ice Stream, West Antarctica. The technique retrieves lateral and depth variations in the horizontal components of ice fabric but no direct information on the vertical fabric component. In the shallowest ice (depths 40–100 m), the fabric is consistent with flow‐induced development and correlates with the surface compression direction. Notably, toward the ice‐stream margin, the horizontal compression angle and azimuthal fabric orientation tend toward 45° relative to ice flow which is consistent with the early stages of flow‐induced fabric under simple shear. The fabric orientation in deeper ice (depths 100–300 m) is, in places, significantly misaligned with shallower ice and the surface compression direction due to sharp depth transitions in orientation. We then use a rheological model to bound effective anisotropic viscosities (directional hardness) of ice that are consistent with the radar measurements. Toward the shear margin, we show that the shallow‐ice fabric does not appreciably soften the ice to lateral shear although this may happen in deeper ice. In the center of the ice stream, we show that lateral and depth variations in the fabric alignment relative to ice flow result in corresponding changes in uniaxial ice viscosities relative to ice flow. Our results indicate that spatial variability in the fabric translates to variability in viscosity that widely used isotropic ice‐flow models are unable to consider. Plain Language Summary: The viscosity of glacier ice is dependent on the direction in which ice crystals are pointing relative to an applied load. This ice crystal orientation fabric also contains information about past ice flow. Compared with the interior of ice sheets, the relationships between fabric, viscosity, and ice flow are relatively unexplored in the ice streams and outlet glaciers which drain the Antarctic Ice Sheet. We use a ground‐based geophysical method to investigate how ice fabric varies spatially within Rutford Ice Stream (West Antarctica) and then calculate the relative viscosity of ice for deformation in different directions. Our results reveal rapidly varying fabric properties within the flow unit. In the shallowest ice, the fabric is consistent with what would be expected from the surface deformation, whereas in deeper ice, this is not always true. We then show that spatial variation in ice fabric translates to lateral and depth variations in directional ice viscosity. This poses challenges for using ice‐flow models to derive glacier bed conditions as they do not generally account for directional viscosity. Key Points: Pronounced spatial variability of ice crystal orientation fabric is inferred from radar sounding in the near surface of Rutford Ice StreamIn the shallowest ice, the fabric is generally aligned with surface compression whereas in deeper ice this is not always the caseThe fabric results in lateral and depth variations of anisotropic ice viscosity within the flow unit including sharp depth transitions [ABSTRACT FROM AUTHOR]

We introduce a transfer matrix model for radio‐wave propagation through layered anisotropic ice that permits an arbitrary dielectric permittivity tensor in each layer. The model is used to investigate how crystal orientation fabrics without a vertical principal direction affect polarimetric radar returns over glaciers and ice sheets. By expanding the c‐axis orientation distribution in terms of a spherical harmonic series, we find that radar returns from synthetic fabric profiles are relatively insensitive to the harmonic mode responsible for a nonvertical principal direction; however, only for normally incident waves. Consequently, the strength of this mode might be relatively difficult to infer in glaciers and ice sheets, which in turn has implications for the ability to determine the full second‐order structure tensor, needed to infer the local flow regime, flow history, or to represent the directional viscosity structure of glacier ice for ice‐flow modeling. Plain Language Summary: The orientation of ice crystals in glacier ice locally co‐evolve with and can enhance the flow of ice. Methods that allow inferring the crystal structure inside glaciers and ice sheets are, therefore, essential for improving the accuracy and realism of ice‐flow models, and have broad implications for understanding past and present flow regimes. In this work, we introduce a new radio‐wave model and use it to investigate the extent to which radar surveys over glaciers and ice sheets can reveal the orientation information necessary to improve such ice‐flow models and construct a proxy for past flow. We show that conventional polarimetric radar surveys, which look straight down, might be poorly suited for the task; a specific but important component of the grain orientation structure cannot be seen with such surveys. We find, however, that radio waves transmitted at an angle to the surface might overcome this crucial limitation and allow the full crystal structure to be inferred. Key Points: Radar returns over glacier ice are, for normal incidence, insensitive to whether or not a vertical principal fabric direction existsThe harmonic mode responsible for a nonvertical principal fabric direction might be determined from oblique radar soundingAssuming a vertical principal fabric direction when there is none can substantially affect inferred directional viscosities of glacier ice [ABSTRACT FROM AUTHOR]

Here we use polarimetric measurements from an Autonomous phase-sensitive Radio-Echo Sounder (ApRES) to investigate ice fabric within Whillans Ice Stream, West Antarctica. The survey traverse is bounded at one end by the suture zone with the Mercer Ice Stream and at the other end by a basal ‘sticky spot’. Our data analysis employs a phase-based polarimetric coherence method to estimate horizontal ice fabric properties: the fabric orientation and the magnitude of the horizontal fabric asymmetry. We infer an azimuthal rotation in the prevailing horizontal c-axis between the near-surface (z ≈ 10–50 m) and deeper ice (z ≈ 170–360 m), with the near-surface orientated closer to perpendicular to flow and deeper ice closer to parallel. In the near-surface, the fabric asymmetry increases toward the center of Whillans Ice Stream which is consistent with the surface compression direction. By contrast, the fabric orientation in deeper ice is not aligned with the surface compression direction but is consistent with englacial ice reacting to longitudinal compression associated with basal resistance from the nearby sticky spot.

The Askaryan Radio Array (ARA) experiment at the South Pole is designed to detect high-energy neutrinos which, via in-ice interactions, produce coherent radiation at frequencies up to 1000 MHz. Characterization of ice birefringence, and its effect upon wave polarization, is proposed to enable range estimation to a neutrino interaction and hence aid in neutrino energy reconstruction. Using radio transmitter calibration sources, the ARA collaboration recently measured polarization-dependent time delay variations and reported significant time delays for trajectories perpendicular to ice flow, but not parallel. To explain these observations, and assess the capability for range estimation, we use fabric data from the SPICE ice core to model ice birefringence and construct a bounding radio propagation model that predicts polarization time delays. We compare the model with new data from December 2018 and demonstrate that the measurements are consistent with the prevailing horizontal crystallographic axis aligned near-perpendicular to ice flow. The study supports the notion that range estimation can be performed for near flow-perpendicular trajectories, although tighter constraints on fabric orientation are desirable for improving the accuracy of estimates.

Microstructures, including crystallographic fabric, within the margin of streaming ice can exert strong control on flow dynamics. To characterize a natural setting, we retrieved three cores, two of which reached bed, from the flank of Jarvis Glacier, eastern Alaska Range, Alaska. The core sites lie ~1 km downstream of the source, with abundant water present in the extracted cores and at the base of the glacier. All cores exhibit dipping layers, a combination of debris bands and bubble-free domains. Grain sizes coarsen on average approaching the lateral margin. Crystallographic orientations are more clustered and with c-axes closer to horizontal nearer the lateral margin. The measured fabric is sufficiently weak to induce little mechanical anisotropy, but the data suggest that despite the challenging conditions of warm ice, abundant water and a short flow distance, many aspects of the microstructure, including measurable crystallographic fabric, evolved in systematic ways. [ABSTRACT FROM AUTHOR]

Crevasses and englacial fracture networks route meltwater from a glacier's surface to the subglacial drainage system and thus influence glacial hydraulics. However, rapid fracture growth may also lead to sudden and potentially hazardous structural failure of unstable glaciers and ice dams, rifting of ice shelves, or iceberg calving. Here, we use passive seismic recordings to investigate the englacial fracture network on Glacier de la Plaine Morte, Switzerland. Glacier dynamics and the drainage of an ice-marginal lake give rise to numerous icequakes, the majority of which generate dispersed, high-frequency Rayleigh waves. A wide distribution of events allows us to study azimuthal anisotropy between 10 and 30 Hz in order to extract englacial seismic velocities in regions of preferentially oriented crevasses. Beamforming applied to a 100-m-aperture array reveals azimuthal anisotropy of Rayleigh-wave phase velocities reaching a strength of 8% at high frequencies. In addition, we find that the fast direction of wave propagation coincides with the observed surface strike of the narrow crevasses. Forward modeling and inversion of dispersion curves suggest that the azimuthal anisotropy is induced by a 40-m-thick crevassed layer at the surface of the glacier with 8% anisotropy in shear-wave velocity.

We compared elastic moduli in polar firn derived from diving wave refraction seismic velocity analysis, firn-core density measurements and microstructure modelling based on firn-core data. The seismic data were obtained with a small electrodynamic vibrator source near Kohnen Station, East Antarctica. The analysis of diving waves resulted in velocity–depth profiles for different wave types (P-, SH- and SV-waves). Dynamic elastic moduli of firn were derived by combining P- and S-wave velocities and densities obtained from firn-core measurements. The structural finite-element method (FEM) was used to calculate the components of the elastic tensor from firn microstructure derived from X-ray tomography of firn-core samples at depths of 10, 42, 71 and 99 m, providing static elastic moduli. Shear and bulk moduli range from 0.39 to 2.42 GPa and 0.68 to 2.42 GPa, respectively. The elastic moduli from seismic observations and the structural FEM agree within 8.5% for the deepest achieved values at a depth of 71 m, and are within the uncertainty range. Our observations demonstrate that the elastic moduli of the firn can be consistently obtained from two independent methods which are based on dynamic (seismic) and static (tomography and FEM) observations, respectively, for deeper layers in the firn below ~10 m depth.

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling. [ABSTRACT FROM AUTHOR]

The Askaryan Radio Array (ARA) experiment at the South Pole is designed to detect high-energy neutrinos which, via in-ice interactions, produce coherent radiation at frequencies up to 1000 MHz. Characterization of ice birefringence, and its effect upon wave polarization, is proposed to enable range estimation to a neutrino interaction and hence aid in neutrino energy reconstruction. Using radio transmitter calibration sources, the ARA collaboration recently measured polarization-dependent time delay variations and reported significant time delays for trajectories perpendicular to ice flow, but not parallel. To explain these observations, and assess the capability for range estimation, we use fabric data from the SPICE ice core to model ice birefringence and construct a bounding radio propagation model that predicts polarization time delays. We compare the model with new data from December 2018 and demonstrate that the measurements are consistent with the prevailing horizontal crystallographic axis aligned near-perpendicular to ice flow. The study supports the notion that range estimation can be performed for near flow-perpendicular trajectories, although tighter constraints on fabric orientation are desirable for improving the accuracy of estimates. [ABSTRACT FROM AUTHOR]

Here we use polarimetric measurements from an Autonomous phase-sensitive Radio-Echo Sounder (ApRES) to investigate ice fabric within Whillans Ice Stream, West Antarctica. The survey traverse is bounded at one end by the suture zone with the Mercer Ice Stream and at the other end by a basal 'sticky spot'. Our data analysis employs a phase-based polarimetric coherence method to estimate horizontal ice fabric properties: the fabric orientation and the magnitude of the horizontal fabric asymmetry. We infer an azimuthal rotation in the prevailing horizontal c-axis between the near-surface (z ≈ 10–50 m) and deeper ice (z ≈ 170–360 m), with the near-surface orientated closer to perpendicular to flow and deeper ice closer to parallel. In the near-surface, the fabric asymmetry increases toward the center of Whillans Ice Stream which is consistent with the surface compression direction. By contrast, the fabric orientation in deeper ice is not aligned with the surface compression direction but is consistent with englacial ice reacting to longitudinal compression associated with basal resistance from the nearby sticky spot. [ABSTRACT FROM AUTHOR]

The observable microstructures in ice are the result of many dynamic and competing processes. These processes are influenced by climate variables in the firn. Layers deposited in different climate regimes may show variations in fabric which can persist deep into the ice sheet; fabric may 'remember' these past climate regimes. We model the evolution of fabric variations below the firn-ice transition and show that the addition of shear to compressive-stress regimes preserves the modeled fabric variations longer than compression-only regimes, because shear drives a positive feedback between crystal rotation and deformation. Even without shear, the modeled ice retains memory of the fabric variation for ∼200 ka in typical polar ice-sheet conditions. Our model shows that temperature affects how long the fabric variation is preserved, but only affects the strain-integrated fabric evolution profile when comparing results straddling the thermal-activation-energy threshold (∼-10°C). Even at high temperatures, migration recrystallization does not eliminate the modeled fabric's memory under most conditions. High levels of nearest-neighbor interactions will, however, eliminate the modeled fabric's memory more quickly than low levels of nearest-neighbor interactions. Ultimately, our model predicts that fabrics will retain memory of past climatic variations when subject to a wide variety of conditions found in polar ice sheets. [ABSTRACT FROM AUTHOR]

In 2010 a reflection seismic survey was carried out on the Alpine glacier Colle Gnifetti. The processed and depth-converted data could be compared to a nearby ice core, drilled almost to the bed. Comparisons showed that the depth of the P-wave bed reflection was too shallow, while the depth of the SH-wave bed reflection fitted the ice-core length well. We are now able to explain the major part of these differences using the existing crystal orientations of the ice at Colle Gnifetti. We calculate anisotropic velocities for P- and SH-waves that are usually picked for stacking and compare them with zero-offset velocities needed for the depth conversion. Here we take the firn pack at Colle Gnifetti into account for P- and S-wave analysis. To incorporate the S-wave analysis we first derive a new equation for the relationship between density and S-wave velocity from diving waves. We show that anisotropic fabrics observed at Colle Gnifetti introduce a difference of only 1% between stacking and depthconversion velocities for the SH-wave, but 7% for the P-wave. We suggest that this difference in stacking and depth-conversion velocity for the P-wave can be used to derive information about the existing anisotropy by combining our seismic data with, for example, radar data. [ABSTRACT FROM AUTHOR]