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1.
The first five Titan flybys with Cassini's Synthetic Aperture RADAR (SAR) and radiometer are examined with emphasis on the calibration and interpretation of the high-resolution radiometry data acquired during the SAR mode (SAR-radiometry). Maps of the 2-cm wavelength brightness temperature are obtained coincident with the SAR swath imaging, with spatial resolution approaching 6 km. A preliminary calibration shows that brightness temperature in these maps varies from 64 to 89 K. Surface features and physical properties derived from the SAR-radiometry maps and SAR imaging are strongly correlated; in general, we find that surface features with high radar reflectivity are associated with radiometrically cold regions, while surface features with low radar reflectivity correlate with radiometrically warm regions. We examined scatterplots of the normalized radar cross-section σ0 versus brightness temperature, finding differing signatures that characterize various terrains and surface features. Implications for the physical and compositional properties of these features are discussed. The results indicate that volume scattering is important in many areas of Titan's surface, particularly Xanadu, while other areas exhibit complex brightness temperature variations consistent with variable slopes or surface material and compositional properties.  相似文献   

2.
The first comprehensive calibration and mapping of the thermal microwave emission from Titan's surface is reported based on radiometric data obtained at 2.2-cm wavelength by the passive radiometer included in the Cassini Radar instrument. The data reported were accumulated from 69 separate observational segments in Titan passes from Ta (October 2004) through T30 (May 2007) and include emission from 94% of Titan's surface. They are diverse in the key observing parameters of emission angle, polarization, and spatial resolution, and their reduction into calibrated global mosaic maps involved several steps. Analysis of the polarimetry obtained at low to moderate resolution (50+ km) enabled integration of the radiometry into a single mosaic of the equivalent brightness temperature at normal incidence with a relative precision of about 1 K. The Huygens probe measurement of Titan's surface temperature and radiometry obtained on Titan's dune fields allowed us to infer an absolute calibration estimated to be accurate to a level approaching 1 K. The results provide evidence for a surface that is complex and varied on large scales. The radiometry primarily constrains physical properties of the surface, where we see strong evidence for subsurface (volume) scattering as a dominant mechanism that determines the emissivity, with the possibility of a fluffy or graded-density surface layer in many regions. The results are consistent with, but not necessarily definitive of a surface composition resulting from the slow deposition and processing of organic compounds from the atmosphere.  相似文献   

3.
G.J. Black  D.B. Campbell 《Icarus》2011,212(1):300-320
We have observed Titan with the Arecibo Observatory’s 12.6 cm wavelength radar system during the last eight oppositions of the Saturn system with sufficient sensitivity to characterize its scattering properties as a function of sub-Earth longitude. In a few sessions the Green Bank Telescope was used as the receiving instrument in a bistatic configuration to boost sub-radar track length and integration time. Radar echo spectra have been obtained for a total of 92 viewing geometries with sub-Earth locations scattered through all longitudes and at latitudes between 7.6°S and 26.3°S, close to the maximum southern excursion of the sub-Earth track. We find Titan to have globally average radar albedos at this wavelength of 0.161 in the opposite circular polarization sense as that transmitted (OC) and 0.074 in the same sense (SC), giving a polarization ratio SC/OC of 0.46. These values are intermediate between lower reflectivity rocky surfaces and higher reflectivity clean icy surfaces. The variations with longitude in general mirror the surface brightness variations seen through the infrared atmospheric windows. Xanadu Regio’s radar reflectivity and polarization ratio are higher than the global averages, and suggest that its composition is relatively cleaner water ice or, possibly, some other material with low propagation loss at radio wavelengths. For all echo spectra most of the power is in a broad diffuse component but with a specular component whose strength and narrowness is highly variable as a function of surface location. For all data we fit a sum of the standard Hagfors scattering law describing the specular component and an empirical diffuse radar scattering model to extract bulk parameters of the surface. Many areas exhibit very narrow specular reflections implying terrain that are quite flat on centimeter to meter scales over spans of tens to perhaps hundreds of kilometers. The proportion of spectra showing these narrow specular echoes has fallen significantly over the observational time span, indicating either a latitudinal effect related to terrain differences or changing surface conditions over the past several years. A few radar tracks, especially those from the 2008 session, overlap some high resolution Cassini RADAR imagery swaths to allow a direct comparison with terrain.  相似文献   

4.
Large expanses of linear dunes cover Titan’s equatorial regions. As the Cassini mission continues, more dune fields are becoming unveiled and examined by the microwave radar in all its modes of operation (SAR, radiometry, scatterometry, altimetry) and with an increasing variety of observational geometries. In this paper, we report on Cassini’s radar instrument observations of the dune fields mapped through May 2009 and present our key findings in terms of Titan’s geology and climate. We estimate that dune fields cover ∼12.5% of Titan’s surface, which corresponds to an area of ∼10 million km2, roughly the area of the United States. If dune sand-sized particles are mainly composed of solid organics as suggested by VIMS observations (Cassini Visual and Infrared Mapping Spectrometer) and atmospheric modeling and supported by radiometry data, dune fields are the largest known organic reservoir on Titan. Dune regions are, with the exception of the polar lakes and seas, the least reflective and most emissive features on this moon. Interestingly, we also find a latitudinal dependence in the dune field microwave properties: up to a latitude of ∼11°, dune fields tend to become less emissive and brighter as one moves northward. Above ∼11° this trend is reversed. The microwave signatures of the dune regions are thought to be primarily controlled by the interdune proportion (relative to that of the dune), roughness and degree of sand cover. In agreement with radiometry and scatterometry observations, SAR images suggest that the fraction of interdunes increases northward up to a latitude of ∼14°. In general, scattering from the subsurface (volume scattering and surface scattering from buried interfaces) makes interdunal regions brighter than the dunes. The observed latitudinal trend may therefore also be partially caused by a gradual thinning of the interdunal sand cover or surrounding sand sheets to the north, thus allowing wave penetration in the underlying substrate. Altimetry measurements over dunes have highlighted a region located in the Fensal dune field (∼5° latitude) where the icy bedrock of Titan is likely exposed within smooth interdune areas. The hemispherical assymetry of dune field properties may point to a general reduction in the availability of sediments and/or an increase in the ground humidity toward the north, which could be related to Titan’s asymmetric seasonal polar insolation. Alternatively, it may indicate that either the wind pattern or the topography is less favorable for dune formation in Titan’s northern tropics.  相似文献   

5.
J. Mouginot  W. Kofman 《Icarus》2009,201(2):454-459
The south residual cap of Mars is commonly described as a thin and bright layer of CO2-ice. The Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) is a low-frequency radar on board Mars Express operating at the wavelength between 55 and 230 m in vacuum. The reflection of the radar wave on a stratified medium like the residual cap can generate interferences, causing weaker surface reflections compared to reflections from a pure water ice surface. In order to understand this anomalous low reflectivity, we propose a stratified medium model, which allows us to estimate both the thickness and the dielectric constant of the optically thin slab. First, we consider the residual cap as single unit and show that the decrease in the reflected echo strength is well explained by a mean thickness of 11 m and a mean dielectric constant of 2.2. This value of dielectric constant is close to the experimental value 2.12 for pure CO2-ice. Second, we study the spatial variability of the radar surface reflectivity. We observe that the reflectivity is not homogeneous over the residual cap. This heterogeneity can be modeled either by variable thickness or variable dielectric constant. The surface reflectivity shows that two different units comprise the residual cap, one central unit with high reflectivity and surrounding, less reflective units.  相似文献   

6.
This paper reports on the analysis of the highest spatial resolution hyperspectral images acquired by the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft during its prime mission. A bright area matches a flow-like feature coming out of a caldera-like feature observed in Synthetic Aperture Radar (SAR) data recorded by the Cassini radar experiment [Lopes et al., 2007. Cryovolcanic features on Titan's surface as revealed by the Cassini Titan Radar Mapper. Icarus 186, 395-412, doi:10.1016/j.icarus.2006.09.006]. In this SAR image, the flow extends about 160 km east of the caldera. The contrast in brightness between the flow and the surroundings progressively vanishes, suggesting alteration or evolution of the composition of the cryolava during the lifetime of the eruptions. Dunes seem to cover part of this flow on its eastern end. We analyze the different terrains using the Spectral Mixing Analysis (SMA) approach of the Multiple-Endmember Linear Unmixing Model (MELSUM, Combe et al., 2008). The study area can be fully modeled by using only two types of terrains. Then, the VIMS spectra are compared with laboratory spectra of known materials in the relevant atmospheric windows (from 1 to 2.78 μm). We considered simple molecules that could be produced during cryovolcanic events, including H2O, CO2 (using two different grain sizes), CH4 and NH3. We find that the mean spectrum of the cryoflow-like feature is not consistent with pure water ice. It can be best fitted by linear combinations of spectra of the candidate materials, showing that its composition is compatible with a mixture of H2O, CH4 and CO2.  相似文献   

7.
Variations in total solar irradiance (TSI) correlate well with changes in projected area of photospheric magnetic flux tubes associated with dark sunspots and bright faculae in active regions and network. This correlation does not, however, rule out possible TSI contributions from photospheric brightness inhomogeneities located outside flux tubes and spatially correlated with them. Previous reconstructions of TSI report agreement with radiometry that seems to rule out significant “extra-flux-tube” contributions. We show that these reconstructions are more sensitive to the facular contrasts used than has been generally recognized. Measurements with the Solar Bolometric Imager (SBI) provide the first reliable support for the relatively high, wide-band, disk-center contrasts required to produce 10% rms agreement. Longer term bolometric imaging will be required to determine whether the small but systematic TSI residuals we see here are caused by remaining errors in spot and facular areas and contrasts or by extra-flux-tube brightness structures such as bright rings around sunspots or “convective stirring” around active regions.  相似文献   

8.
Twenty-one lunar craters have radar bright ring appearances which are analogous to eleven complete ring features in the earth-based 12.5 cm observations of Venus. Radar ring diameters and widths for the lunar and Venusian features overlap for sizes from 45 to 100 km. Radar bright areas for the lunar craters are associated with the slopes of the inner and outer rim walls, while level crater floors and level ejecta fields beyond the raised portion of the rim have average radar backscatter. We propose that the radar bright areas of the Venusian rings are also associated with the slopes on the rims of craters.The lunar craters have evolved to radar bright rings via mass wasting of crater rim walls and via post impact flooding of crater floors. Aeolian deposits of fine-grained material on Venusian crater floors may produce radar scattering effects similar to lunar crater floor flooding. These Venusian aeolian deposits may preferentially cover blocky crater floors producing a radar bright ring appearance.We propose that the Venusian features with complete bright ring appearances and sizes less than 100 km are impact craters. They have the same sizes as lunar craters and could have evolved to radar bright rings via analogous surface processes.  相似文献   

9.
Abstract— Ten terrestrial impact structures were imaged during two flights of the 1994 space radar laboratory (SRL) experiment. These craters include Wolf Creek, Australia; Roter Kamm, Namibia; Zhamanshin, Kazakhstan; BP and Oasis, Libya; Aorounga, Chad; Amguid, Algeria; and Spider, Connolly Basin and Henbury, Australia. SRL contained two co‐registered instruments; the United States shuttle imaging radar‐C (SIR‐C) polarimetric radar system operating in L‐band (λ = 24 cm) and C‐band (λ = 5.6 cm), and the joint German/Italian synthetic aperture radar (X‐SAR) operating in vertically‐polarized X‐band (λ = 3 cm). Comparisons show SRL images to be complementary to, or in some cases superior to, corresponding optical images for evaluating size, location, and relative age of impact features. Regardless of wavelength or polarization, craters with significant relief appear prominently on radar as a result of slope and roughness effects. In desert regions, longer wavelengths penetrate dry sand mantles to reveal hidden crater dimensions or associated buried landforms. Radar polarities and wavelengths are particularly sensitive to vegetation, surface roughness, and soil moisture or electrical properties. In the more temperate environments of Kazakhstan and Australia, SRL images show detailed stream patterns that reveal the location and structure of otherwise obscured impact features.  相似文献   

10.
G.J. Black  D.B. Campbell 《Icarus》2010,209(1):224-229
We present radar imaging of Mercury using the Arecibo Observatory’s 70-cm wavelength radar system during the inferior conjunction of July 1999. At that time the sub-Earth latitude was ∼11°N and the highly reflective region at Mercury’s north pole that was first identified in radar images at the shorter wavelengths of 3.6 cm [Slade, M.A., Butler, B.J., Muhleman, D.O., 1992. Science 258, 635-640] and 13 cm [Harmon, J.K., Slade, M.A., 1992. Science 258, 640-643] was again clearly detected. The reflectivity averaged over a 75,000 km2 region including the pole is similar to that measured at the other wavelengths over a comparable area, and the 70 cm circular polarization ratio of μC0.87 is possibly slightly lower. If this strong backscattering results from volume scattering in low absorption layers, the persistence of this effect over more than an order of magnitude change in wavelength scale has implications for the depth and thickness of the deposits responsible. The resolution of the radar maps at this wavelength is not sufficient to resolve individual craters, nor to discern features at other latitudes, but the planet’s total reflectivity is consistent with previous work and the scattering function suggests a surface roughness at this wavelength similar to the lunar highlands.  相似文献   

11.
The Cassini spacecraft has acquired 25 radar altimeter elevation profiles along Titan's surface as of April 2008, and we have analyzed 18 of these for which there are currently reconstructed ephemeris data. Altimeter measurements were collected at spatial footprint sizes from 6-60 km along ground tracks of length 400-3600 km. The elevation profiles yield topographic information at this resolution with a statistical height accuracy of 35-50 m and kilometer-scale errors several times greater. The data exhibit significant variations in terrain, from flat regions with little topographic expression to very rugged Titanscapes. The bandwidth of the transmitted waveform admits vertical resolution of the terrain height to 35 m at each observed location on the surface. Variations in antenna pointing and changes in surface statistics cause the range-compressed radar echoes to exhibit strong systematic and time-variable biases of hundreds of meters in delay. It is necessary to correct the received echoes for these changes, and we have derived correction algorithms such that the derived echo profiles are accurate at the 100 m level for off-nadir pointing errors of 0.3° and 0.6°, for leading edge and echo centroid estimators, respectively. The leading edge of the echo yields the elevation of the highest points on the surface, which we take to be the peaks of any terrain variation. The mean value of the echo delay is more representative of the mean elevation, so that the difference of these values gives an estimate of any local mountain heights. Finding locations where these values diverge indicates higher-relief terrain. Elevation features are readily seen in the height profiles. Several of the passes show mountains of several hundred m altitude, spread over 10's or even 100's of km in spatial extent, so that slopes are very small. Large expanses of sub-100 m topography are commonplace on Titan, so it is rather smooth in many locations. Other areas exhibit more relief, although the overall observed variation in surface height on any pass is less than about 1 km. Some elevation features correspond to observed changes in brightness in Cassini infrared images, but many do not. Correspondence between the imaging SAR ground tracks and the altimeter paths is limited, so that identifying elevation changes with higher resolution SAR features is premature at present.  相似文献   

12.
A technique, referred to as SARTopo, has been developed for obtaining surface height estimates with 10 km horizontal resolution and 75 m vertical resolution of the surface of Titan along each Cassini Synthetic Aperture Radar (SAR) swath. We describe the technique and present maps of the co-located data sets. A global map and regional maps of Xanadu and the northern hemisphere hydrocarbon lakes district are included in the results. A strength of the technique is that it provides topographic information co-located with SAR imagery. Having a topographic context vastly improves the interpretability of the SAR imagery and is essential for understanding Titan.SARTopo is capable of estimating surface heights for most of the SAR-imaged surface of Titan. Currently nearly 30% of the surface is within 100 km of a SARTopo height profile. Other competing techniques provide orders of magnitude less coverage.We validate the SARTopo technique through comparison with known geomorphological features such as mountain ranges and craters, and by comparison with co-located nadir altimetry, including a 3000 km strip that had been observed by SAR a month earlier. In this area, the SARTopo and nadir altimetry data sets are co-located tightly (within 5-10 km for one 500 km section), have similar resolution, and as expected agree closely in surface height. Furthermore the region contains prominent high spatial resolution topography, so it provides an excellent test of the resolution and precision of both techniques.  相似文献   

13.
Solar observations through the atmospheric pass-band centred at 250 GHz have been made in the form of isophote maps. These show chromospheric features which have higher brightness temperatures than the mean disc temperature by up to 10%. Examination of corresponding maps at lower frequencies and also of Caii and H spectroheliograms reveals that the hot areas lie above photospheric active regions, and are regular features of the chromospheric millimetric emission having stable structure and duration of several weeks. Less frequently observed variable enhancements are also described, and linked with the formation of the stable active regions.  相似文献   

14.
Radar imaging results for Mercury's non-polar regions are presented. The dual-polarization, delay-Doppler images were obtained from several years of observations with the upgraded Arecibo S-band (λ12.6-cm) radar telescope. The images are dominated by radar-bright features associated with fresh impact craters. As was found from earlier Goldstone-VLA and pre-upgrade Arecibo imaging, three of the most prominent crater features are located in the Mariner-unimaged hemisphere. These are: “A,” an 85-km-diameter crater (348° W, 34° S) whose radar ray system may be the most spectacular in the Solar System; “B,” a 95-km-diameter crater (343° W, 58° N) with a very bright halo but less distinct ray system; and “C,” an irregular feature with bright ejecta and rays distributed asymmetrically about a 125-km source crater (246° W, 11° N). Due south of “C” lies a “ghost” feature (242° W, 27° S) that resembles “A” but is much fainter. An even fainter such feature is associated with Bartok Crater. These may be two of the best mercurian examples of large ejecta/ray systems observed in an intermediate state of degradation. Virtually all of the bright rayed craters in the Mariner 10 images show radar rays and/or bright rim rings, with radar rays being less common than optical rays. Radar-bright craters are particularly common in the H-7 quadrangle. Some diffuse radar albedo variations are seen that have no obvious association with impact ejecta. In particular, some smooth plains regions such as the circum-Caloris plains in Tir, Budh, and Sobkou Planitiae and the interiors of Tolstoj and “Skinakas” basins show high depolarized brightness relative to their surroundings, which is the reverse of the mare/highlands contrast seen in lunar radar images. Caloris Basin, on the other hand, appears dark and featureless in the images.  相似文献   

15.
We compare surface brightness and magnetic field surface maps for the K0 dwarf AB Doradus, obtained using two independently developed Zeeman Doppler imaging codes. We find that even the fine structure in the two sets of images shows excellent agreement. Magnetic field maps appear to be less sensitive to line-modelling effects than brightness maps. We argue that these results point to the consistency and reliability of Doppler imaging techniques even when using poorly sampled data sets, provided that the spectra used are of sufficiently high signal-to-noise ratio.  相似文献   

16.
One of the intrinsic properties of particulate sulfur allotropes is a change in UV-visible reflectivity with temperature change of the material. The surface of Io experiences temperature changes during eclipse which are sufficient to cause a detectable change in the spectral reflectivity of sulfur; thus, if the surface of Io is composed primarily of sulfur allotropes, a change in reflectivity at certain wavelengths should be observable shortly after eclipse reappearance. We observed four eclipse reappearances during July and August of 1983 and saw no posteclipse brightening effects in filter bands selected for sensitivity to color changes in sulfur. Our model of the brightness change for S8 (“yellow” sulfur) implies that this material covers less than 50% of Io's surface. Negative posteclipse brightening observations were also obtained with a filter chosen for the high contrast between SO2 frost and the average albedo of the surface of Io at that wavelength. We conclude that no significant condensation of optically thick SO2 occurred on the surface of Io during these eclipses.  相似文献   

17.
We present aperture synthesis maps of the Saturn system at a wavelength of 3.71 cm. The data used to make the maps were obtained in May–June 1976 at the Owens Valley Radio Observatory on 13 interferometer baselines. The aperture synthesis maps contain few assumptions about the brightness structure of Saturn and the rings and, therefore, may be used to check previous model-fitting results as well as search for new unmodeled features. Generally, the maps confirm the previous model-fitting results. An exception to this is that the brightness temperature of the planet that is implied by the maps is about 4% less than that deduced from model fitting. The likely explanation of this discrepancy is that random errors on the phase of the visibility function have led to an underestimate of the planet brightness temperature in the map. Maps of the residuals to the model fits have shown that the position of Saturn given in the American Ephemeris and Nautical Almanac may be in error by about 0.25 arcsec. Maps of the residuals to model fits including a position offset show that no new features of the Saturn brightness structure are required to match the present data. In particular, no azimuthal variations in the brightness temperature of the rings were detected.  相似文献   

18.
Cassini's third and fourth radar flybys, T7 and T8, covered diverse terrains in the high southern and equatorial latitudes, respectively. The T7 synthetic aperture radar (SAR) swath is somewhat more straightforward to understand in terms of a progressive poleward descent from a high, dissected, and partly hilly terrain down to a low flat plain with embayments and deposits suggestive of the past or even current presence of hydrocarbon liquids. The T8 swath is dominated by dunes likely made of organic solids, but also contain somewhat enigmatic, probably tectonic, features that may be partly buried or degraded by erosion or relaxation in a thin crust. The dark areas in T7 show no dune morphology, unlike the dark areas in T8, but are radiometrically warm like the dunes. The Huygens landing site lies on the edge of the T8 swath; correlation of the radar and Huygens DISR images allows accurate determination of its coordinates, and indicates that to the north of the landing site sit two large longitudinal dunes. Indeed, had the Huygens probe trajectory been just 10 km north of where it actually was, images of large sand dunes would have been returned in place of the fluvially dissected terrain actually seen—illustrating the strong diversity of Titan's landscapes even at local scales.  相似文献   

19.
Images from three filters of the Voyager 1 wide-angle camera were used to measure the continuum reflectivity and spectral gradient near 6000 Å and the 6190-Å band methane/continuum ratio for a variety of cloud features in Jupiter's atmosphere. The dark “barge” features in the North Equatorial Belt have anomalously strong positive continuum spectral gradients suggesting unique composition, probably not elemental sulfur. Methane absorption was shown at unprecedented spatial scales for the Great Red Spot and its immediate environment, for a dark barge feature in the North Equatorial Belt, and for two hot spot and plume regions in the North Equatorial Belt. Some small-scale features, unresolvable at ground-based resolution, show significant enhancement in methane absorption. Any enhancement in methane absorption is conspicuously absent in both hot spot regions with 5-μm brightness temperature 255°K. Methane absorption and 5-μm emission are correlated in the vicinity of the Great Red Spot but are anticorrelated in one of the plume hot spot regions. Methane absorption and simultaneously maps of 5-μm brightness temperature were quantitatively compared to realistic cloud structure models which include multiple scattering at 5 μm as well as in the visible. A curve in parameter space defines the solution to any observed quantity, ranging from a shallow atmosphere and thin NH3 cloud to a deep atmosphere with a thick ammonia cloud. Without additional constraints, such as center-to-limb information, it is impossible to specify the NH3 cloud optical depth and pressure of a deeper cloud top independently. Variability in H2 quadrupole lines was also investigated and it was found that the constancy of the 4-0 S(1)-line equivalent width is consistent with the constancy of the methane 6190-Å band equivalent width at ground-based resolution, but the much greater variability of the 3-0 S(1) line is inconsistent with either the methane band or 4-0 S(1) line. In hot spot regions the 255°K brightness temperature requires a cloud optical depth of about 2 or less at 5 μm in the NH3 cloud layer. To be consistent with the observed 6190-Å methane absorption in hot spot regions, the NH3 cloud optical depth in the visible is about 7.5, implying that aerosols in hot spot regions have effective radii near 1 μm or less.  相似文献   

20.
We extracted the surface echo power from 2 years of MARSIS measurements. The retrieved values are calibrated to compensate for changes in the distance of the spacecraft to the surface and for the attenuation of the signal by the ionosphere. The results are used to build the first global map of surface echo power at 3–5 MHz. The surface echo power variations are primarily caused by kilometer-scale surface roughness. Then, we derive the values of dielectric constant of the shallow subsurface materials by normalizing the surface echo power map using a simulation of MARSIS signal from the MOLA topography. As a result, we obtain a map that characterizes the dielectric properties of the materials down to a few decameters below the surface. Dielectric properties vary with latitude, with high values in mid-latitudes belts (20–40°) and lower values at both equatorial and high latitudes. From the comparison of MARSIS reflectivity map to GRS observations, we conclude that the reflectivity decrease observed poleward of 50–60° corresponds to the onset of water-ice occurrence within the regolith. Assuming homogenous ground composition and texture at the scale of the MARSIS resolution cell, our inferred volume of ground water ice is of 106 km3, equivalent to a polar cap. Low reflectivity areas are also observed in equatorial regions. From radar studies alone, equatorial low dielectric constant values could have different interpretations but the correlation with GRS hydrogen distribution rather points toward a water-related explanation.  相似文献   

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