Surface slope probabilities from the spectra of weak radar echoes: Application to Mars

Slope probability densities were derived from the power spectra of radar echoes from Mars using integral inversion. The inverse problem is ill-posed; that is, small changes in the data can lead to large changes in the solution. We describe a method of stabilizing the inversion, which was necessary for echoes with signal-to-noise power spectral densities on the order of unity, and for those with broad spectral distributions. The resulting slope probabilities usually consisted of a component due to quasi-specular reflection which decreased rapidly with tilt, plus a broad, slowly decreasing, “diffuse” component due to scattering from (1) surface scales small compared with a radar wavelength, or (2) larger features with high slopes. In the absence of more complete polarization measurements, we are unable to In the absence of more complete polarization measurements, we are unable to distinguish between these possibilities. Root mean square tilts have been determined separately for the two cases. For case (1), values of rms tilt associated with surface features responsible for the quasi-specular echo are normally less than 3°; for case (2), values greater than 8° are common. Knowledge of the depolarization of radar returns would help distinguish between these possibilities.     

Mars: Dual-polarization radar observations with extended coverage

Thirteen-centimeter-wavelength radar observations of Mars made in 1982 at Arecibo Observatory yield accurate measurements of the full backscatter spectrum in two orthogonal polarizations. The data, which were obtained for several widely separated subradar longitudes at 24°N latitude, provide the first global view of the distribution of small-scale surface roughness on Mars. The diffuse component of the echo exhibits strong spatial variations. Areas of maximum depolarization correlate well with volcanic regions (Tharsis and Elysium), while the heavily cratered upland terrain yields relatively low depolarization. Parts of Tharsis give near-complete depolarization (polaziation ratio $\text{μ}{}_{\mathrm{<mtext>c</mtext>}}\text{? 1}$ when viewed at oblique angles of incidence). Northern Martian plains regions (Tharsis, Elysium, and Amazonis) may comprise the most extensive area of severe decimeter-scale surface roughness in the inner Solar System. On the average, the northern Martian tropics yield higher diffuse radar cross sections (σ^D = 0.05–0.12) and a higher of degree disk-integrated depolarization (μ_c = 0.1–0.4) than is found for the Moon, Mercury, and Venus. Comparisons between the Moon and Mars using radar data, ground truth, and simple scattering models suggest that Mars possesses a relatively high average coverage by decimeter-scale rocks. Also discussed are several of the more interesting quasispecular scattering results, the most unsual of which were obtained over the Olympus Mons aureole region.     

Atlas of lunar radar maps at 70-cm wavelength

The intensity distribution of lunar radar echoes has been mapped for two-thirds of the earth-visible lunar surface at a wavelength of 70 cm. The depolarizing effects of the lunar surface were observed by simultaneously receiving the radar echoes in opposite polarizations. These echoes were mapped with areal resolutions of 25–100 km². Mappings with this resolution confirmed that the young craters have enhanced returns. A few craters were found to have enhanced echoes only from their rims. Backscattering differences were also observed between various areas within a mare, between different highland areas, and between maria and adjacent highlands. These scattering differences were interpreted with a simple model, which assumed that the surface backscattered with varying amounts of quasi-specular and diffuse power. Only an increase in the diffuse power was needed to give the numerical values of the enhancements.     

Ground-based radar observations of Titan: 2000-2008

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.     

Radar studies of the Martian surface at centimeter wavelengths: The 1975 opposition

The Goldstone radar system was operated at wavelengths of 3.5 and 12.6 cm to probe the Martian surface during the 1975 opposition. Regions studied in detail by range-Doppler techniques are Syrtis Major, Sinus Meridiani, and the crater Schiaparelli. Average rms slopes of 1.6° and 1.1° were measured in Syrtis Major at 3.5 and 12.6 cm, respectively, while the average reflectivity was 0.064 ± 0.02 at both wavelengths. No wavelength dependence of surface roughness was seen in Sinus Meridiani, where rms surface slopes averaged 1.8° and the reflectivity was 0.08 ± 0.02. The regions around Schiaparelli were probed at a 12.6-cm wavelength. The echo from the bottom of the crater was undetectable. Hence _ρ0C < 25, where _ρ0 is the reflectivity and C is the Hagfors roughness parameter. Operating at 3.5 cm during May and June of 1976, 149 continous-wave echo spectra were obtained near latitude 18°, sampling most longitudes including the early Viking landing sites A1 and A2. The average total radar cross section is 4.8% of the geometrical cross section. The diffuse component was estimated to be 1.9%, leaving 2.9% to the average quasi-specular component. The average rms slope is 4.1°. Six spectra obtained at site A1 indicate that rms slopes are 5 to 9° between latitudes 17 and 19°. Three spectra obtained at s site A2 indicate an rms slope of 3.9°.     

High-resolution radar maps of the lunar surface at 3.8-cm wavelength

The entire earth-facing lunar surface has been mapped at a resolution of 2 km using the 3.8-cm radar of Haystack Observatory. The observations yield the distribution of relative radar backscattering efficiency with an accuracy of about 10% for both the polarized (primarily quasispecular or coherent) and depolarized (diffuse or incoherent) scattered components. The results show a variety of discrete radar features, many of which are correlated with craters or other features of optical photographs. Particular interest, however, attaches to those features with substantially different radio and optical contrasts. An anomaly near 63° is noted in the mean angular scattering law obtained from a summary of the radar data.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Icy craters on the Galilean satellites?

A model which possibly accounts for the unusual radar scattering behavior observed for Europa, Ganymede, and Callisto postulates a thick surface layer of ice saturated with nearly hemispherical craters. In the development of this model it is noted that a single reflection at normal incidence reverses the rotational sense of circularly polarized incident radiation, in conflict with the radar observations which show an echo predominantly not reversed. Furthermore, an ensemble of backscattering events, each the result of a large number of successive dielectric reflections, tends to produce a weak and unpolarized echo. However, two coupled reflections can produce the observed backscattering behavior, provided the angles of incidence lie between the Brewster angle and its complement. The effect is maximum when the angles equal 45°, and, for water ice, yields a ratio of 1.9 for components of the echo received in rotational senses the same as, and opposite to, the sense transmitted. Randomly oriented reflecting facets, either of ice on the surface or of rocks in the interior, cannot yield the observed behavior since too few of the total possible backscattering configurations meet the above requirement. Hemispherical surface craters, on the other hand, favor 45° dual reflection. A model consisting of such craters in ice is investigated and found capable of explaining the observed results, not only in respect to polarization, but in respect to albedo and angular scattering law as well.     

The rings of Saturn: Two-frequency radar observations

Observations of 3.5- and 12.6-cm radar echoes from the rings of Saturn suggest that no significant difference in scattering properties exists in this wavelength interval. The echoes are largely unpolarized at both wavelengths, and yield a radar cross section at 3.5 cm of 7.32 ± 0.84 × 10⁹ km² for each polarization. The combined radar cross sections for both polarizations correspond to 1.37 ± 0.16 times the optically observed projected A- and B-ring areas (excluding that part of the rings shadowed by the planet). The shape of the echo spectrum is compatible with a homogeneous ring scattering model, except in having excess power at frequencies near the center of the spectrum. A number of possible explanations for the observed scattering properties are explored.     

Radar Backscatter from Underdense Meteors and Diffusion Rates

Many meteoroids burn up between about 120 km and 70 km, deposit metals and dust and form ionized trails which are detected by radars. Model studies about the influence of neutral or positively charged background dust on the ambipolar diffusion indicate that significant smaller decay times should be observed for weak meteor echoes compared to strong meteor echoes which can affect the estimation of temperatures. The variation of meteor decay times in dependence on echo strength, height, and season was studied using radar observations at 69° N, 22° S, and 67° S. Significantly reduced decay times were found for weak echoes below about 88 km at low latitudes throughout the year, and at high latitudes with the exception of summer. In summer at high latitudes, decreasing decay times of weak and strong meteors are observed at altitudes below about 85 km during the appearance of noctilucent clouds. The impact of reduced decay times on the estimation of neutral temperatures from decay times is discussed.     

Arecibo radar observations of Mars surface characteristics in the northern hemisphere

Mars surface characteristics at and near the Viking Chryse and Tritonis Lacus landing areas were determined by radio scatter using the new 12.6 cm radar at the Arecibo Observatory during 1975–1976. Interpretation of each power spectrum suggests rms surface tilts of 4° at the final A1WNW (47.9°W, 22.5°N) site, 5° near the original A1 site, and 6° between the two. At the back-up site (A2) surface roughness estimates were about 4°. Striking changes in surface texture have been found near the eastern bases of Tharsis Montes and Albor Tholus, each volcanic feature marking the western boundary of very smooth surface units. The roughness sensed at 1 to 100 m scales by radar appears to be relatively independent of the surface units defined at large scale lengths by photogeologists. Radar properties thus provide an additional means by which planetary surfaces may be characterized.     

Prospects for detecting light echoes of galactic supernovae by wide-angle polarimetry

We propose to use a global (wide-angle, of the order of several degrees) distribution of linearly polarized emission over the sky to detect light echoes of historical supernovae exploded in our Galaxy. The echo emission must be polarized tangential to the direction of the supernova explosion site, and its degree of polarization must exhibit a characteristic dependence on angular distance. The near infrared is an optimum spectral range for detection. A spotted structure in the shape of a ring ～5° in diameter and ～3° in width with a total brightness of ～12–13^m in polarized light with a tangential orientation of the electric vector must be currently seen in the direction where Tycho Brahe observed a supernova explosion in 1572. A comparison of the expected intensity of the echo with the intensities of the zodiacal light and the atmosphere shows that it can be detected in principle during long-term observations from space and, under favorable conditions, even from the ground.     

Mars surface properties observed by earth-based radar at 70-, 12.5-, and 3.8-cm wavelengths

A review of Mars radar data obtained through the 1973 opposition confirms that the surface of the planet has many diverse characteristics. Analysis of the quasi-specular echo component shows changes in apparent reflectivity of at least 5 to 1. If attributed entirely to variations in surface material, these correspond to dielectric constants between 1.6 and 4.0. Values of rms surface slope on 1- to 100-m scales range from as low as 0.5° in tablelands near Vlles Marineris to more than 3.0° (the upper limit for which these analysis techniques are appropriate) in certain other areas such as inside Coprates Chasma itself. There is weak correlation between the small-scale surface characteristics inferred from radar and those inferred from Mariner 9 images, geologic maps derived from those images, and other remote sensing data sets. Topography, a large-scale surface characteristic for which good correlation exists between radar and other data sets, was not considered in this study. A search for guidelines which would allow extrapolation of radar properties to new areas on the basis of those studied has been singularly unsuccessful. Data obtained during the 1973 opposition at Arecibo, Goldstone, and Haystack Observatories indicate that the scattering behavior of Mars varies little over the 70- to 3.8-cm wavelength range. Comparison of 1971 and 1973 Goldstone results shows no detectable variation with time.     

Galilean satellites: 1976 radar results

Radar observations of the Galilean satellites, made in late 1976 using the 12.6-cm radar system of the Arecibo Observatory, have yielded mean geometric albedos of 0.04 ± , 0.69 ± 0.17, 0.37 ± 0.09, and 0.15 ± 0.04, for Io, Europa, Ganymede, and Callisto, respectively. The albedo for Io is about 40% smaller than that obtained approximately a year earlier, while the albedos for the outer three satellites average about 70% larger than the values previously reported for late 1975, raising the possibility of temporal variation. Very little dependence on orbital phase is noted; however, some regional scattering inhomogeneities are seen on the outer three satellites. For Europa, Ganymede, and Callisto, the ratios of the echo received in one mode of circular polarization to that received in the other were: 1.61 ± 0.20 1.48 ± 0.27, and 1.24 ± 0.19, respectively, with the dominant component having the same sence of circularity as that transmitted. This behavior has not previously been encountered in radar studies of solar system objects, whereas the corresponding observations with linear polarization are “normal.” Radii determined from the 1976 radar data for Europa and Ganymede are: 1530 ± 30 and 2670 ± 50 km, in fair agreement with the results from the 1975 radar observations and the best recent optical determinations. Doppler shifts of the radar echoes, useful for the improvement of the orbits of Jupiter and some of the Galilean satellites, are given for 12 nights in 1976 and 10 nights in 1975.     

Detection of large grains in the coma of Comet C/2001 A2 (LINEAR) from Arecibo radar observations

Arecibo S-band () radar observations of Comet C/2001 A2 (LINEAR) on 2001 July 7-9 showed a strong echo from large coma grains. This echo was significantly depolarized. This is the first firm detection of depolarization in a grain-coma radar echo and indicates that the largest grains are at least λ/2π or 2 cm in radius. The grains are moving at tens of m s⁻¹ with respect to the nucleus. The nondetection of the nucleus places an upper limit of 3 km on its diameter. The broad, asymmetric echo power spectrum suggests a fan of grains that have a steep (differential number ∼a⁻⁴) size distribution at cm-scales, though the observed fragmentation of this comet complicates that picture.     

Meteoric head echoes

Results of the analysis of 3261 radar meteor head echoes observed during the Orionid and Lyrid periods by the high-power radar of the Springhill Meteor Observatory are given. Dependence of the occurence of head echoes on the geometrical factors and physical properties of the meteoroids has been studied. Increas of the head echo rates with the elevation of the shower radiant and with the velocity of meteoroids has been observed.     

Power Fluctuations in Meteor Head Echoes Observed with the EISCAT VHF Radar

We present observations and preliminary results from a meteor experiment carried out with the 224 MHz EISCAT VHF radar in Tromsø, Norway, which was run for 6 h on November 26, 2003. The data set contains echoes with peculiar pulsations in received power in the frequency range 20–200 Hz, limited by instrumental parameters. The process causing the echo power pulsations has not yet been identified. Plasma effects are the most likely cause, a possible mechanism is for instance asymmetrical dust grains in rotation causing a modulation of the ionization rate.     

A low cost meteor observation system using radio forward scattering and the interferometry technique

We present a low cost meteor observation system based on the radio forward scattering and interferometry technique at Kochi University of Technology (KUT). The system can be a suitable model for low budget educational institutes that target practical learning of astronomical objects and upper atmospheric characteristics. The system methodology for the automatic counting of meteor echoes, filtering noise and detecting meteor echo directions is described. Detection of the meteor echo directions, which is the basic element for determining the meteor trajectories and the orbital parameters of parent comets, is based on a software system developed for analysis of phase differences detected by interferometry. Randomly selected observation samples measured by the radio interferometer are compared to simultaneous optical observations by video cameras to verify the system accuracy. Preliminary error analysis revealed that the system accuracy is directly related to the duration of observed meteor echoes. Eighty percent of meteor echo samples with durations longer than 3 s showed agreement in azimuth and elevation angles measurements to within a 10° error range, while meteor echo samples with shorter durations showed lower agreement levels probably due to the low system sampling resolution of 0.1 s. The reasonable agreement level of meteor echoes with duration longer than 3 s demonstrated the applicability of the system methodology. Accurate observation of shorter duration meteor echoes could possibly be achieved by improving the system resolution.     

Tectonic patterns on a reoriented planet: Mars

Both geologic and free-air-gravity data suggest that the positive mass anomaly associated with the Tharsis volcanoes may have reoriented Mars' lithosphere by as much as 25°. Since Mars is oblate (with flattening $\text{? ?0.005}$), rotation of the lithosphere over the equatorial bulge by 25° produces membrane stresses of several kilobars, large enough to initiate faulting. These stresses were first evaluated by F.A. Vening-Meinesz (1947, Trans. Amer. Geophys. Union28, 1–61) who treated the lithosphere as a thin elastic shell. The fracture patterns which result from these stresses are determined by the relation between stress and faulting proposed by E.M. Anderson (1951, The Dynamics of Faulting, Oliver & Boyd, Edinburgh). Plots of the magnitude and direction of stresses in a reoriented planet show that near Tharsis the dominant fault type should be north-south- trending normal faults. This normal fault province is centered about 30°N latitude and extends about 45° east and west in longitude. Similar faults should occur at the antipodes, north of Hellas Planitia. The polar regions should be occupied by roughly north-south-trending thrust faults which extend close to the equator south of Tharsis and north of Hellas. The regions between Tharsis and Hellas are subject to compression on a NE-trending axis and extension along a NW axis east of Tharsis (west of Tharsis the directions are NW compression and NE extension), thus predicting a zone of NNW and ENE strike slip faults east of Tharsis (NNE and WNW west of Tharsis). Although these patterns, except for the north-south normal faults north of Tharsis, have not yet been recognized, the discovery of such a tectonic system of the same age as Tharsis would provide strong support for the reorientation idea. Stresses due to reorientation appear to have little to do with Valles Marineris, since the stress normal to the axis of the Valles is predicted to be compressive, whereas geologic evidence suggests extension.