Accessing the potentially habitable subsurface waters of Ocean Worlds requires a robotic ice probe (or "cryobot") to traverse tens of kilometers of ice with temperatures ranging from ~100 to 273 K. Designing and planning such a mission requires understanding ice probe behavior as a function of the local environment and design parameters. We present experimental results of two laboratory melt probes in cryogenic (79 K) and warm (253 K) ice. The melt probe tested in warm ice had multiple adjustable heaters, enabling optimization of the system's efficiency. The melt probes tested in cryogenic ice operated in vacuum and had internal tether spools, allowing for experimental confirmation of hole closure and the creation of a pressurized pocket with liquid water around the probe. These melt probes were tested at power levels ranging from 120 to 1135 W, achieving descent speeds between 5.3 and 59 cm hr^-1. By analyzing the relationship between power and speed using analytical and high-fidelity numerical models, we demonstrate progress in understanding melt probe performance. We distinguish between the previously confounding terms of probe operational inefficiency and analytical model inaccuracy, allowing us to understand the range of applicability of the analytical models and demonstrate the importance of controlling heat distribution in cryobot design. The validated models show that while numerical models may be required to describe the behavior of short probes descending in limited-size laboratory test beds, the performance of efficient cryobots designed for operation on Ocean Worlds can be predicted by analytical models within 5% error.

Water-filled boreholes in cold ice refreeze in hours to days, and prior attempts to keep them open with antifreeze resulted in a plug of slush effectively freezing the hole even faster. Thus, antifreeze as a method to stabilize hot-water boreholes has largely been abandoned. In the hot-point drilling case, no external water is added to the hole during drilling, so earlier antifreeze injection is possible while the drill continues melting downward. Here, we use a cylindrical Stefan model to explore slush formation within the parameter space representative of hot-point drilling. We find that earlier injection timing creates an opportunity to avoid slush entirely by injecting sufficient antifreeze to dissolve the hole past the drilled radius. As in the case of hot-water drilling, the alternative is to force mixing in the hole after antifreeze injection to ensure that ice refreezes onto the borehole wall instead of within the solution as slush.

We describe the application of the discrete wavelet transform (DWT) in extracting the characteristic absorption signatures of materials from terahertz reflection spectra. We compare the performance of different mother wavelets, including Daubechies, least asymmetric (LA), and Coiflet, based on their phase and gain functions and filter lengths. We show that the phase functions of the wavelet and scaling filters result in spectral shifts to the absorption lines in the wavelet domain. We provide a solution by calculating advancement coefficients necessary to achieve effective zero-phase-function DWT. We demonstrate the utility of this signal processing technique using α-lactose monohydrate/polyethylene samples with different levels of rough surface scattering. In all cases, the DWT-based algorithm successfully extracts resonant signatures at 0.53 and 1.38 THz, even when they are obscured by the rough surface scattering effects. The DWT analysis with accompanying phase corrections can be utilized as a robust technique for material identification in nondestructive evaluation using terahertz spectroscopy.

We have developed a terahertz time-domain polarimetry (THz-TDP) system by applying frequency modulation to electro-optic sampling detection in a nonlinear crystal. We characterized the precision of this system in determining the polarization angles to be 1.3° for fixed time delay, and 0.5° for complete time-domain waveform. Furthermore, we calculated the Jones matrix of the optical components used for beam propagation to calibrate the induced systematic error. The advantages of employing this calibration approach are demonstrated on a sapphire crystal investigated at different sample test positions in transmission configuration, and using high resistivity Si, AlN and quartz in reflection geometry. The new THz-TDP technique has the advantage of not using any external polarizers, and therefore is not constrained by their optical performance limitations, such as restricted bandwidths and frequency-dependent extinction ratio. Finally, the THz-TDP technique can be easily implemented on existing time-domain spectroscopy (TDS) systems.

Over deep Antarctic subglacial lakes, spatially varying ice thickness and the pressure‐dependent melting point of ice result in distinct areas of melting and freeze‐on at the ice‐water interface, that is, at the lake lid. These ice mass fluxes drive lake circulation and, because basal Antarctic ice contains air clathrate, affect the input of oxygen to the lake, with implications for subglacial life. Inferences of rates of melting and freeze‐on, that is, accretion rates, from radar layer tracking and geodesy are limited in spatial coverage and resolution. Here we develop a new method to estimate accretion rate, and the resulting oxygen input at a lake lid, using airborne radar data over Lake Vostok together with ice‐temperature and chemistry data from the Vostok ice core. Because the lake lid is a coherent reflector of known reflectivity (at our radar frequency), we can infer depth‐averaged radio wave attenuation in the ice, with a spatial resolution of ~1 km along flight lines. Spatial variation in attenuation depends mostly on variation in ice temperature near the lid, which in turn varies strongly with ice mass flux at the lid. We model ice temperature versus depth with ice mass flux as a parameter, thus linking that flux to observed depth‐averaged attenuation. The resulting map of melt and accretion rates independently reproduces features known from earlier studies but now covers the entire lid. We find that freeze‐on is dominant when integrated over the lid, with an ice imbalance of 0.05 to 0.07 km³/year, which is robust against uncertainties.

On Earth and on Mars, ice masses experience changes in precipitation, temperature, and radiation. In a new climate state, flowing ice masses will adjust in length and in thickness, and this response toward a new steady state has a characteristic timescale. However, a flowing ice mass has a predictable shape, which is a function of ice temperature, ice rheology, and surface mass-exchange rate. In addition, the time for surface-shape adjustment is shorter than the characteristic time for significant deformation or displacement of internal layers within a flowing ice mass; as a result, surface topography is more diagnostic of flow than are internal-layer shapes. Because the shape of Gemina Lingula, North Polar Layered Deposits indicates that it flowed at some time in the past, we use its current topography to infer characteristics of those past ice conditions, or past climate conditions, in which ice-flow rates were more significant than today. A plausible range of near-basal ice temperatures and ice-flow enhancement factors can generate the characteristic geometry of an ice mass that has been shaped by flow over reasonable volume-response timescales. All plausible ice-flow scenarios require conditions that are different from present-day Mars, if the basal layers are pure ice.

A diagnosis criterion is proposed for noninvasive grading of burn injuries using terahertz radiation. Experimental results are presented from in vivo terahertz time-domain spectroscopy of second- and third-degree wounds, which are obtained in a 72-hour animal study. During this period, the change in the spectroscopic response of the burned tissue is studied. It is shown that terahertz waves are sensitive not only to the postburn formation of interstitial edema, but also to the density of skin structures derived from image processing analysis of histological sections. Based on these preliminary results, it is suggested that the combination of these two effects, as probed by terahertz spectroscopy of the tissue, may ultimately be used to differentiate partial-thickness burns that will naturally heal from those that will require surgical intervention.

We demonstrate the application of THz-TDS in characterizing the severity of burn injuries in a live animal model. 2nd and 3rd degree burns were studied immediately and 72 hours post-burn. A new diagnosis criterion was verified against histopathology.

Radar-sounding of ice sheets on Earth yields crucial information on ice history and dynamics, including
discoveries of subglacial lakes beneath 3-4 km of ice. Mars Express and the Mars Reconnaissance
Orbiter (MRO) have now demonstrated the corresponding power of orbital radar sounding for planetary exploration, in particular by imaging structures within and beneath kilometers of Martian
water ice. Based on this experience, a sophisticated orbital radar sounder is planned for a flagship mission to Europa, with the aim of imaging stratigraphy, faults, diapirs and other geological structure in the upper few kilometers of the water-ice mantle there, and possibly even detecting the upper surface of the (likely) underlying ocean. Recent modeling of the formation and evolution of volatilerich bodies suggests that oceans or lakes of liquid water occur beneath water-ice mantles in a surprising variety of places, including Ceres in the outer asteroid belt, 3 of the 4 Galilean moons of Jupiter as well as Enceladus and Titan in the Saturnian system, and possibly even Pluto. Thus there is now a wide scope for low-cost missions to bodies of exceptional interest, and for radar sounding of icy mantles to image near-surface structural geology related to underlying water (whether past or present).

As ice streams flow into the Ross Ice Shelf, West Antarctica, their bed coupling transitions from weak to transient to zero as the ice goes afloat. Here we explore the nature of the bed across these crucial grounding zones using ice-penetrating radar. We collected several ground-based 2 MHz radar transects across the grounding zones of Whillans and Kamb Ice Streams and inferred bed-reflectivity changes from in situ measurements of depth-averaged dielectric attenuation, made possible by the observation of both primary and multiple bed echoes. We find no significant change in the bed reflectivity across either grounding zone. Combined with reflectivity modeling, this observation suggests that a persistent layer of subglacial water (>%u223C0.2 m) is widespread several kilometers upstream of the grounding zone. Our results are consistent with previous inferences of gradual grounding zones across this sector of the Ross Ice Shelf from airborne radar and satellite altimetry. Separately, the only clear bed-reflectivity change that we observed occurs %u223C40 km downstream of the Kamb Ice Stream grounding zone, which we attribute to the onset of marine ice accretion onto the base of the ice shelf. This onset is much nearer to the grounding zone than previously predicted.

We present sub-millimeter wave reflectometry of an experimental rat skin burn model obtained by the Terahertz Time-Domain Spectroscopy (THz-TDS) technique. Full thickness burns, as confirmed by histology, were created on rats (n = 4) euthanized immediately prior to the experiments. Statistical analysis shows that the burned tissue exhibits higher reflectivity compared to normal skin over a frequency range between 0.5 and 0.7 THz (p < 0.05), likely due to post-burn formation of interstitial edema. Furthermore, we demonstrate that a double Debye dielectric relaxation model can be used to explain the terahertz response of both normal and less severely burned rat skin. Finally, our data suggest that the degree of conformation between the experimental burn measurements and the model for normal skin can potentially be used to infer the extent of burn severity.

The accuracy rates of the clinical assessment techniques used in grading burn injuries remain significantly low for partial thickness burns. In this paper, we present experimental results from terahertz characterization of 2nd and 3rd degree burn wounds induced on a rat model. Reflection measurements were obtained from the surface of both burned and normal skin using pulsed terahertz spectroscopy. Signal processing techniques are described for interpretation of the acquired terahertz waveform and differentiation of burn wounds. Furthermore, the progression of burn injuries is shown by comparison between acute characterization and 72-hours survival studies. While the water content of healthy and desiccated skin has been considered as a source of terahertz signal contrast, it is demonstrated that other biological effects such as formation of post-burn interstitial edema as well as the density of the discrete scattering structures in the skin (such as hair follicles, sweat glands, etc.) play a significant role in the terahertz response of the burn wounds.

Scattering of terahertz waves by surface roughness can obscure spectral signatures of chemicals at these frequencies. We demonstrate this effect using controlled levels of surface scattering on alpha-lactose monohydrate pellets. Furthermore, we show an implementation of wavelet methods that can retrieve terahertz spectral information from rough surface targets. We use a multiresolution analysis of the rough-surface-scattered signal utilizing the maximal overlap discrete wavelet transform (MODWT) to extract the resonant signature of lactose. We present a periodic extension technique to circumvent the circular boundary conditions of MODWT, which can be robustly used in an automated terahertz stand-off detection device.

Previously, it has been shown that scattering of terahertz waves by surface roughness of a target can alter the terahertz absorption spectrum and thus obscure the detection of some chemicals in both transmission and reflection geometries. In this paper it is demonstrated that by employing Maximal Overlap Discrete Wavelet Transform (MODWT) coefficients, wavelet-based methods can be used to retrieve spectroscopic information from a broadband terahertz signal reflected from a rough surface target. It is concluded that while the commonly used direct frequency domain deconvolution method fails to accurately characterize and detect the resonance in the dielectric constant of rough surface lactose pellets, wavelet techniques were able to successfully identify such features.

Internal layers in ice masses can be detected with ice-penetrating radar. In a flowing ice mass, each horizon represents a past surface that has been subsequently buried by accumulation, and strained by ice flow. These layers retain information about relative spatial patterns of accumulation and ablation (mass balance). Internal layers are necessary to accurately infer mass-balance patterns because the ice-surface shape only weakly reflects spatial variations in mass balance. Additional rate-controlling information, such as the layer age, the ice temperature, or the ice-grain sizes and ice-crystal fabric, can be used to infer the absolute rate of mass balance. To infer mass balance from the shapes of internal layers, we solve an inverse problem. The solution to the inverse problem is the best set or sets of unknown boundary conditions or initial conditions that, when used in our calculation of ice-surface elevation and internal-layer shape, generate appropriate predictions of observations that are available. We also show that internal layers can be used to infer martian paleo-surface topography from a past era of ice flow, even though the topography may have been largely altered by subsequent erosion. We have successfully inferred accumulation rates and surface topography from internal layers in Antarctica. Using synthetic data, we demonstrate the ability of this method to solve the corresponding inverse problem to infer accumulation and ablation rates, as well as the surface topography, for martian ice. If past ice flow has affected the shapes of martian internal layers, this method is necessary to infer the spatial pattern and rate of mass balance.

Accumulation rates and their spatio-temporal variability are important boundary conditions for ice-flow models. The depths of radar-detected internal layers can be used to infer the spatial variability of accumulation rates. Here we infer accumulation rates from three radar layers (26, 35 and 41 ka old) in the Vostok Subglacial Lake region using two methods: (1) the local-layer approximation (LLA) and (2) a combination of steady-state flowband modeling and formal inverse methods. The LLA assumes that the strain-rate history of a particle traveling through the ice sheet can be approximated by the vertical strain-rate profile at the current position of the particle, which we further assume is uniform. The flowband model, however, can account for upstream strain-rate gradients. We use the LLA to map accumulation rates over a 150 km x 350 km area, and we apply the flowband model along four flowbands. The LLA accumulation-rate map shows higher values in the northwestern corner of our study area and lower values near the downstream shoreline of the lake. These features are also present but less distinct in the flowband accumulation-rate profiles. The LLA-inferred accumulation-rate patterns over the three time periods are all similar, suggesting that the regional pattern did not change significantly between the start of the Holocene and the last ~20 ka of the last Glacial Period. However, the accumulation-rate profiles inferred from the flowband model suggest changes during that period of up to 1 cm a^-1 or ~50% of the inferred values.

Measurement of incoherent rough surface scattering powers in terahertz frequency regime by means of time-domain spectroscopy has been for the first time demonstrated. Furthermore, applications of such incoherent measurements in spectroscopy and detection of chemicals are presented.

The existence of unique absorption spectrum patterns for many chemicals at terahertz frequencies has opened an exciting avenue in non-contact safe detection of such materials by terahertz spectroscopy. However, scattering of THz waves, which have wavelengths on the order of material grain sizes, by surface roughness challenges the sensitivity of this detection scheme in practice. In this work, we present terahertz time domain spectroscopy results for materials with rough surfaces. Both reflection from and transmission through lactose, which has sharp absorption peaks in the terahertz regime, are studied and the effect of increasing scattering through controlled surface roughness is investigated. Such electromagnetic scattering can alter the terahertz absorption spectrum and thus obscure the detection of chemicals. Furthermore we examine electro-optic detection of terahertz signals reflected from randomly rough targets with a theoretical electromagnetic system perspective and provide a method to retrieve coherent reflection responses from rough surface targets.

The relative importance of surface mass fluxes and ice flow in shaping the north polar layered deposits (NPLD), now or in the past, remains a fundamental and open question. Motivated by observation of an apparent ice divide on Gemina Lingula (also known as Titania Lobe), we propose a two-stage evolution leading to the present-day topography on that lobe of the NPLD. Ice flow approximately balances surface mass fluxes in the first stage, but in the second stage ice flow has minimal influence and topography is modified predominantly by the formation of troughs. We focus here on evidence for the first stage, by testing the fit of topography between troughs to an ice-flow model.

We find that independent model fits on distinct flow paths closely match inter-trough topography, uniformly over a broad region on Gemina Lingula, with mutually consistent and physically reasonable fitting parameters. However, our model requires ice to occupy and flow in spaces where troughs currently incise the ice. We therefore infer that the troughs (and the distribution of mass balance that caused them) post-date deposition of the inter-trough material and its modification by flow. Because trough formation has apparently altered inter-trough topography very little, we infer that trough formation must have been rapid in comparison to the (still unknown) time-scale of flow since troughs began to form. We view the evidence for past flow as strong, but we do not think that topographic evidence alone can be conclusive. Observations of englacial stratigraphy using orbital sounding radars will yield conclusive tests of our inferred mechanism for the formation of inter-trough topography.

The effects of surface scattering on terahertz reflection spectrum for explosive detection are studied by measuring terahertz reflection pulses from sandpapers with different roughness coated with gold. The experimental results show that the amplitude decrease and pulse broadening of the detected signal caused by the surface scattering result in the width reduction of Gaussian distribution of the specular scattering coefficient spectrum. A simple analytical model is applied to the analysis of experimental results and good agreements are obtained.

Terahertz (THz) imaging is emerging as a potentially powerful method of detecting explosive devices, even in the presence of occluding materials. However, the characteristic spectral signatures of pure explosive materials may be altered or obscured by electromagnetic scattering caused by their granular nature. This paper presents THz transmission measurements of granular systems representative of explosives and presents results from dense media theory that accurately explain the observed scattering response.

The relationship between time series of physical surface temperature and microwave brightness temperature of polar firn depends both on the physical properties of the firn and the surface temperature history. In perennially dry firn this relationship is well characterized by a timescale, referred to as the extinction-diffusion time, which is the ratio of the microwave extinction length squared to the firn thermal diffusivity. The extinction-diffusion time is calculated over Antarctica from 1982 to 1999 by comparing thermal infrared observations of physical surface temperature from the advanced very high resolution radiometer (AVHRR) with passive microwave brightness temperatures measured by the scanning multichannel microwave radiometer (SMMR) and Special Senor Microwave Imager (SSM/I). Independent estimates of accumulation rate are derived both from ice cores and from spatially extensive ground and airborne radar echo sounding lines. The extinction-diffusion time is found to vary linearly with accumulation rate from approximately 10 to 50 cm/yr ice equivalent over a large area in West Antarctica. Although this simple relationship does not appear to hold at very low or very high accumulation rates, these results suggest that the extinction-diffusion time holds promise as a viable proxy for accumulation rate variability on polar ice sheets.

The radar reflectivity of an ice-sheet bed is a primary measurement for discriminating between thawed and frozen beds. Uncertainty in englacial radar attenuation and its spatial variation introduces corresponding uncertainty in estimates of basal reflectivity. Radar attenuation is proportional to ice conductivity, which depends on the concentrations of acid and sea-salt chloride and the temperature of the ice. We synthesize published conductivity measurements to specify an ice-conductivity model and find that some of the dielectric properties of ice at radar frequencies are not yet well constrained. Using depth profiles of ice-core chemistry and borehole temperature and an average of the experimental values for the dielectric properties, we calculate an attenuation rate profile for Siple Dome, West Antarctica. The depth-averaged modeled attenuation rate at Siple Dome (20.0 ± 5.7 dB km^-1) is somewhat lower than the value derived from radar profiles (25.3 ± 1.1 dB km^-1). Pending more experimental data on the dielectric properties of ice, we can match the modeled and radar-derived attenuation rates by an adjustment to the value for the pure ice conductivity that is within the range of reported values. Alternatively, using the pure ice dielectric properties derived from the most extensive single data set, the modeled depth-averaged attenuation rate is 24.0 ± 2.2 dB km^-1. This work shows how to calculate englacial radar attenuation using ice chemistry and temperature data and establishes a basis for mapping spatial variations in radar attenuation across an ice sheet.

This paper presents predictions of classical electromagnetic scattering from granular material illuminated by a terahertz (THz) source. Random media models are created to represent the explosive grains, air voids and filler material commonly found in explosive devices. These constituents can cause significant volume scattering that may alter or obscure the chemical response of the explosive, thus impacting THz detection of explosives. Furthermore, the air-explosive interface may have significant roughness, and scattering from this interface may be a dominant factor - particularly in reflection spectroscopy. The volume scattering is calculated using the Quasi-Crystalline Approximation (QCA) and a Finite Difference Time Domain (FDTD) calculation; the FDTD method is also used to estimate the rough surface scattering. Results from these calculations are provided for mixtures that are representative of common classes of explosives.

The acquisition and interpretation of increasingly high-resolution climate data from polar ice and firn cores motivates the question: What is the finest depth or timescale on which measurements on cores arrayed over a given area correlate? We analyze dated depth series of electrical and oxygen isotope measurements from a spatial array of firn cores with 3.5–7 km spacing in Dronning Maud Land, Antarctica, each with a temporal span of approximately 200 years. We use wavelet analysis to decompose the series into components associated with changes of averages on different scales, and thus deduce which scales are dominated by environmental noise, and which may contain a common signal. We find that common signals in electrical records have timescales of approximately 1–3 years. We identify only one electrical signal which rises significantly above the background in our 200-year records, evidently corresponding to the Tambora eruption. Several smaller signals correlate in a few of pairs of cores, one of which may correspond to a known volcanic event, but the others appear to be spurious. We present a simulation-based method for testing the significance of apparent electrical signal correlations, and highlight the importance of accurate relative dating between cores. In the case of oxygen-isotope records, we find, surprisingly, no significant correlation on any scale in the records, for any of the pairs of cores. There is, however, a weak trend toward positive correlation at longer timescales (up to 16 years). Statistical theory for the relevant confidence intervals and the observed statistics of the records permit estimation of the length of a data series necessary to reliably detect a hypothetical correlation equal to that observed. For the highest correlation observed on 16-year scales, core records of about 380 years (approximately 30 m at the Dronning Maud Land site) would be necessary to establish significance.

Different parts of Antarctica receive different amounts of snowfall each year. In this paper we map the variations of the mean annual snow accumulation across the ice sheet. We also quantify the uncertainty in our estimates more objectively than has been possible for earlier maps. The new map is produced using observations from satellites and ground-based measurements. After a logarithmic transformation, these are combined using the geostatistical method of continuous-part universal kriging to give an estimate of the snow accumulation within each cell of a rectangular grid covering Antarctica. We also derive spatial averages over the major drainage systems of the ice sheet, along with their confidence intervals. We obtain a value of 143 ± 4 kg m^-2 a^-1 for the average rate of snow accumulation upon the grounded ice sheet of Antarctica.

Accurate predictions of sea level rise over the coming century will require improved knowledge of the processes controlling accumulation on the great ice sheets. The sparsity of accumulation rate observations, both temporally and spatially, hinder development of this understanding. We introduce a new method to observe accumulation rates (averaged over roughly a decade) using satellite observations of microwave emission at 4.5-cm wavelength, focusing in this paper on Greenland. At this wavelength, scattering by the grain fabric in firn is unimportant relative to quasi-reflection from density (and thus dielectric permittivity) stratification. We show observationally a strong link between random firn density stratification, on scales of millimeters to centimeters, and accumulation rate. We then show theoretically how the observed density stratification can produce and is consistent with observations of polarization of 4.5-cm-wavelength emission. We employ observations from the Scanning Multichannel Microwave Radiometer (SMMR) and previously published ground observations of accumulation rates in Greenland to complete specification of the relationship between accumulation rate and polarization. The relationship is sufficiently accurate to serve as a basis for mapping accumulation rate fields. We compare our satellite-derived maps with previously published maps based on syntheses of ground data. We find broad agreement between the two types of maps, though the satellite-derived map indicates more strongly the importance of topography and prevailing weather patterns in determining detailed accumulation rate patterns. Finally, we discuss possible refinements and the prospects for improved satellite-derived maps based on a new generation of sensors about to be launched.

Large dune fields occupy more than 500,000 km² of the East Antarctic Plateau. The "megadunes", or long-wavelength surface ripples, have amplitudes of only a few meters, wavelengths of a few kilometers, and parallel crests which can extend one hundred kilometers. They occur in areas characterized by low accumulation, extensively recrystallized snow, and strong scattering of the microwave part of the spectrum. Dune crests are oriented perpendicular to the regional katabatic wind direction. Snow megadunes are unlikely to be formed by simple wind transport of snow particles.

Understanding the density evolution of any ice deposits on the martian north polar residual cap is key to understanding whether the cap contains a climate record in the form of occluded samples of past atmospheres. We present a physical model for densification of water ice deposits on the cap due to gravity-driven sintering and temperature-gradient-driven vapor transport. The model predicts the steady-state profile of porosity versus depth in the ice cap for specified, time-independent mass accumulation rate and surface deposition density and for surface temperatures with specified diurnal and seasonal variations that comprise an invariant annual cycle. We find that, in contrast to the analogous situation on Earth, vapor transport dominates densification in the current martian climate. This mechanism can produce very low-porosity near-surface ice, even when accumulation rates are small but positive, comparable to those presently thought to occur. Thus recent inferences of high thermal inertia on the cap may not necessarily imply that the cap is ablating. The model predicts a sharp transition between temperature and accumulation conditions under which a deep firn column results and those characterized by very low surface porosity. Finally, we derive a temporal-frequency-dependent thermal inertia for a vertically inhomogeneous medium. Observations of this quantity are, at least in principle, useful for remote estimation of the ice cap density variations within about 10 m of the surface.