Venus’ radar-bright highlands: Different signatures and materials on Ovda Regio and on Maxwell Montes

Venus’ radar-bright highlands: Different signatures and materials on Ovda Regio and on Maxwell Montes

Accepted Manuscript Venus’ Radar-Bright Highlands: Different Signatures and Materials on Ovda Regio and on Maxwell Montes Allan Treiman , Elise Harri...

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Accepted Manuscript

Venus’ Radar-Bright Highlands: Different Signatures and Materials on Ovda Regio and on Maxwell Montes Allan Treiman , Elise Harrington , Virgil Sharpton PII: DOI: Reference:

S0019-1035(16)30363-3 10.1016/j.icarus.2016.07.001 YICAR 12116

To appear in:

Icarus

Received date: Revised date: Accepted date:

30 November 2015 27 June 2016 3 July 2016

Please cite this article as: Allan Treiman , Elise Harrington , Virgil Sharpton , Venus’ Radar-Bright Highlands: Different Signatures and Materials on Ovda Regio and on Maxwell Montes, Icarus (2016), doi: 10.1016/j.icarus.2016.07.001

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Highlights

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An enduring puzzle about Venus is why its highlands are bright in reflected radar (i.e., have surfaces of high apparent permittivity). On equatorial highlands, the pattern or radar reflectance is consistent with the presence of a ferroelectric substance, confirming earlier work. The ferroelectric substance on the equatorial highlands is likely chlorapatite, formed by reaction between igneous fluorapatite and HCl in the Venus atmosphere. On the highlands of Maxwell Montes, the pattern of radar reflectance is consistent with presence of a semiconductor substance formed in chemical reaction between the atmosphere and the surface, not a ferro-electric like chlorapatite. The radar difference between the equatorial highlands and Maxwell Montes apparently represents significant differences either in bedrock type or in atmosphere composition & temperature.

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Venus’ Radar-Bright Highlands: Different Signatures and Materials on Ovda Regio and on Maxwell Montes Allan Treiman 1*, Elise Harrington 2†, and Virgil Sharpton 1. Lunar and Planetary Institute, 3600 Bay Area Boulevard, Houston, TX, USA 77586 2

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Department of Earth Sciences, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6



Now at Centre for Planetary Science and Exploration, University of Western Ontario,

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London ON, Canada, N6A 3K7.

* Corresponding author: [email protected]

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ABSTRACT

Venus‟ highlands appear much brighter than its lowland plains in reflected radar, which

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has been explained by several conflicting hypotheses. We study this transition at higher spatial and elevation resolution than previously possible by combining Magellan synthetic aperture

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radar (SAR) images with Magellan SAR stereo elevations. We confirm that SAR backscatter

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over Ovda Regio (5° N to 15° S) grades from low to high as elevation increases (2 to 4.5 km above the datum), and then drops precipitously above ~4.5 km (T= ~702 K). This pattern is

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consistent with presence of a substance that undergoes a phase transition from ferroelectric to normal dielectric at ~700 K; the mineral chlorapatite is a likely candidate. This pattern is seen across Ovda, on other near-equatorial highlands, and on some shield volcanoes like the Tepev Montes. We also confirm that Maxwell Montes (60-68° N) shows a different pattern; its surface transitions abruptly from low backscatter to high backscatter at ~4.5 km above the datum, and

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remains so to nearly its highest elevations (~10 km). This pattern is consistent with the presence of a semiconductor material either precipitated from the atmosphere (e.g., a frost) or produced by atmosphere-surface interaction. If a ferroelectric substance were in the rock at Maxwell (as at Ovda), it could be invisible beneath the coating of semiconductor material. However, the absence

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of a semiconductor material on Ovda requires either that [1] the atmosphere compositions at Maxwell and Ovda are substantially different, or [2] that the semiconductor at Maxwell forms by atmosphere-surface reaction (not as an atmospheric precipitate) and that the surface materials at

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Ovda and Maxwell are substantially different.

Introduction

One of the enduring mysteries about Venus‟ surface is the huge contrast in radar

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backscattered brightness (and likewise emissivity) across its surface; Venus‟s highlands appear far brighter in backscattered radar than do its lowlands (Figure 1). This difference has been

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known since the first radar images from orbiting spacecraft: Venera 15 & 16, Pioneer Venus, and Magellan (Campbell et al., 1976; Masursky et al., 1980; Pettengill et al., 1982; McGill et al.,

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1983; Garvin et al., 1985; Barsukov et al., 1986; Pettengill et al., 1988). However, the cause of

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the difference remains uncertain. Surface temperature and or pressure are inferred to control the difference in some respects, because both the temperature and pressure of Venus‟ atmosphere

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decline adiabatically from the surface upwards (Seiff et al., 1980); whatever substances or material properties cause the difference in radar reflectivity must change with temperature and/or pressure, so that higher elevations have greater radar backscatter. Early works suggested that the highlands were surfaced by an electrical semiconductor material (like a sulfide mineral) with a dielectric permittivity near 80, or that the highlands‟ surface materials contained abundant void spaces so as to permit multiple internal scattering (Pettengill et al., 1988; Pettengill et al., 1992).

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The nature of the radar-reflective material in the highlands came to an acute controversy in 1997. One research group argued that the high radar reflectivity arose from the presence of a common sulfide mineral, FeS2 (Klose et al., 1992; Pettengill et al., 1996; Wood, 1997). An opposing research group argued that that FeS2 was thermochemically unstable on Venus‟ highlands, and

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that more exotic materials were required (Arvidson et al., 1994; Shepard et al., 1994; Brackett et al., 1995; Fegley, 1997; Fegley et al., 1997). Suggested alternatives to FeS2 included:

chalcogenide compounds like SbSI, PbTe, PbSe (Brackett et al., 1995); ferroelectric materials like WO3, Рb(Ва,Sr,Са)TiO3, Nа(Nb,Та)О3, or Pb2Bi(Ta,Nb)O6 (Arvidson et al., 1994; Shepard

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et al., 1994; Brackett et al., 1995); and „heavy metal frosts‟ like PbS, Te, and Bi2S3 (Pettengill et al., 1996; Schaefer and Fegley, 2004). An unexplored distinction among these suggested highlands materials is that the chalcogenides and „frost‟ compounds are radar-bright at all

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temperatures and elevations at which they are present (Brackett et al., 1995; Schaefer and Fegley, 2004), while ferroelectric compounds are radar-bright at lower elevations (higher

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temperatures) and become radar-dark at high elevations (Arvidson et al., 1994; Brackett et al., 1995).

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Since the Magellan mission, there has been little new relevant data from Venus. The

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composition of Venus‟ near-surface atmosphere remains uncertain, so that calculations of the stability or instability of FeS2 remain uncertain. The Venus Express orbiter mission provided

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some radar data from Venus‟ highlands, which showed that polarized bistatic radar returns from Maxwell Montes (Fig. 1) were consistent with those of a semiconductor material (Simpson et al., 2009). However, the Venus Express radar instrument failed before more definitive measurements could be acquired.

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In this near-absence of Venus data since Magellan, work has focused on experimental studies of the stabilities of possible radar-reflective materials. These experiments have shown that most of the compounds suggested to cause the high radar reflectivity of the Venus highlands are not suitable because they are not stable at highlands surface conditions, or are stable at both

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highlands and lowlands conditions (Kohler et al., 2012; Kohler et al., 2013; Guandique et al., 2014; Kohler et al., 2014; Kohler and Johnson, 2015; Kohler et al., 2015; Radoman-Shaw et al., 2015). At this writing, HgTe (the mineral coloradoite) remains as a possible candidate substance and FeS2 (the mineral pyrite) may again be possible (Kohler et al., 2014; Kohler et al., 2015), but

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these laboratory experiments depend critically on the poorly known composition (especially the oxidation state) of Venus‟ near-surface atmosphere. Higher Spatial Resolution:

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These results and inferences from them rely almost entirely on Magellan radar altimetry and measurements of radar emissivity (Klose et al., 1992; Wood, 1997), both of which have

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footprints (8x10km and 18x23km respectively on Ovda, 8x10km and 41x55km on Maxwell) that are larger than many of the relevant radar-bright and radar-dark features; the Magellan Synthetic

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Aperture Radar (SAR) had a pixel size of 75-150 m. Recognizing that nearly all of the radar-dark

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areas at high elevation are smaller than the altimetry and emissivity footprints, Arvidson et al. (1994) created stereogrammetric digital elevation models (DEMs) for selected areas in Ovda

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Regio using Magellan cycle 1 and cycle 3 SAR images; these images are both left-looking, but at different incidence angles. With these stereo DEMs, Arvidson et al. (1994) were able to refine the relationship between elevation and emissivity. Here, we take the approach of Arvidson et al. (1994) one step farther – using DEMs derived from stereo SAR, and SAR backscatter coefficient in place of emissivity. The advantage

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of this approach is that a radar property (the backscatter coefficient) is known to approximately the same spatial resolution as the elevation; the disadvantage is that SAR backscatter coefficient is not a simple property of the surface material (as is reflectivity), but is also affected by slope angle, porosity, and roughness. In general as shown below, Magellan SAR backscatter

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coefficients show the same sense of variation on Venus as does its reflectivity (i.e., „1 –

emissivity‟), implying in a general sense that the effects of slope angle, porosity, and roughness are of lesser importance than material properties at the scale we consider here. Because radar reflectivity is approximately the complement of emissivity, our results can be compared

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qualitatively to those of earlier studies like Klose et al. (1992) and Arvidson et al. (1994).

Foreshadowing our results, we confirm the inferences of Arvidson et al. (1994) for Ovda Regio and of Klose et al. (1992) and others for Maxwell Montes, and find that these two areas have

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distinctly different patterns of radar reflectivity versus elevation. The existence of these different patterns suggests either that these two highlands regions are composed of different materials, or

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that they were subject to different surfaces processes (geological, chemical, or atmospheric). Data and METHOD

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Materials and Radar

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This work requires only a few facts and relations from the complex interactions of materials with microwave electromagnetic waves, i.e., Radar (Campbell, 2002). A fundamental

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property in these interactions is a material‟s permittivity, in effect the ratio of the strength of the material‟s electromagnetic response to the strength of the incident radar signal. Permittivity is usually compared to that of free space, and the ratio is the relative permittivity (also called the dielectric constant). The permittivity of solid material like Venus‟ surface can be treated as a complex number, with the real part ‟ representing energy that is „stored‟ and can be re-radiated

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or reflected, and the complex part ” representing absorption by (loss into) the material. Rocks have low permittivites, with bulk ‟ ranging from ~4 for quarzite to ~8 for basalt, and with low values of ” (Campbell and Ulrichs, 1969); these values change little with temperature. Porous materials, being mixtures of rock and „near-free-space,‟ have lower permittivities.

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Semiconductors have significantly greater permittivities in both real and complex parts; for example, the semiconductor mineral pyrite (FeS2) has ‟ = 125 and ” = i50 at ~ 450°C and 2.45 GHz (Peng et al., 2014). The permittivity of a good electrical conductor approaches infinity.

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The Magellan radar did not measure permittivity directly, but only the backscatter

coefficients of the surface. Backscatter has a dependence on Fresnel reflectivity that may be larger than that of roughness when the material properties of the surface exhibit large swings in permittivity; if the roughness is low or if its effects can be estimated, then radar permittivity can

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be estimated. In its passive mode, the Magellan radar system measured Venus‟ surface emissivity, the intensity of microwaves emitted from its surface. Emissivity is, in simplest form,

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a function of both surface temperature and permittivity; if the temperature of a spot is known

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from its elevation (Seiff et al., 1980), then permittivity can be calculated directly. MAGELLAN RADAR DATA

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All data used here are from radar instruments on the Magellan spacecraft (Saunders et al., 1990; Pettengill et al., 1991), which collected three types of data: backscatter by synthetic

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aperture radar, SAR, at 2.385 GHz (Fig. 1); altimetry, and emissivity. Magellan radar backscatter data come from its active SAR mode, which has spatial resolutions of ~75-150 meters depending on the spacecraft‟s elevation (periapsis was at ~10° N). Magellan collected SAR data looking to the spacecraft‟s side (for most orbits, the left), and data for each half-orbit were processed on the ground into FBIDRs (full-resolution binary image data records), which are strip images, or

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„noodles.‟ In FBIDRs, the brightness at each pixel (its digital number, or DN) is related to the proportion of emitted radar that was scattered back towards the spacecraft, relative to an average proportion for the planet (Ford, 1993), to reduce image variations with incidence angle, which changed with latitude. The FBIDRs were mosaicked to yield FMIDRs (full-resolution

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mosaicked image data records), the familiar radar maps of Venus (Fig. 1). The FMIDRs contain some artifacts related to misregistration and misalignment during mosaicking of the FBIDR noodles; the artifacts are barely apparent in the FMIDRs themselves, but can be striking in stereo altimetry derived from them (Herrick and Rumpf, 2011).

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A significant portion of Venus‟ surface was imaged in SAR at two different look angles, and these SAR image pairs allow generation of stereo digital elevation models (Leberl et al., 1992; Herrick et al., 2010; Herrick et al., 2012). Under ideal circumstances, this technique can

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generate elevation values with an average horizontal resolution equivalent to ~5 times the 75

pixel (Leberl et al., 1992).

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meter spatial resolution of the original SAR images, i.e. a map of elevations at ~400 meters per

Magellan radar altimetry comes from a nadir-looking antenna horn, compiled as a near-

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global map of Venus‟s surface elevation at a spatial resolution of ~8 by 10 km (Ford and

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Pettengill, 1992). Altitudes are calculated from the time interval between emission of a radar altimetry pulse and acquisition of its return reflection from the surface, knowing the spacecraft

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orbit relative to Venus‟ center of mass. Of relevance here, “…elevations of individual altimeter footprints can be in error by several kilometers at high-contrast boundaries in the surface scattering function…” Howington-Kraus et al. (2006), see also Plaut (1992), Jankowski and Squyres (1995), and Keddie and Head (1994). This artifact arises when an altimeter footprint is centered on material of extremely low radar reflectivity, with material of much higher reflectivity

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toward the edge of the footprint (Figure 2). In such cases, the nadir reflection may be missed, and a later, stronger off-nadir reflection from the high-backscatter material implies an erroneously low elevation. Magellan radar emissivity values were acquired by the spacecraft‟s high-gain antenna in

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passive mode (Pettengill et al., 1991). The antenna pointed off nadir, giving a minimum footprint for emissivity values of ~15 by 23 km at periapsis (Pettengill et al., 1992). Magellan emissivity data are used here only as a guide to understanding its radar backscatter data because (by

surface roughness. Stereo Digital Elevation Model

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Kirchoff‟s law) emissivity and reflectivity are complementary, if one ignores the effects of

Magellan SAR data were collected at several look angles, which allows the possibility of

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stereogrammetry and of creation of digital elevation models with spatial resolution significantly better than that of the radar altimetry (Leberl et al., 1991; Arvidson et al., 1994; Howington-

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Kraus et al., 2006; Herrick et al., 2010; Herrick et al., 2012; Lee, 2012). Here, we use the publically available stereo DEMs provided by R. Herrick et al. (2012), available in GIS formats

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at the website . Herrick‟s DEMs are built

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by overlaying radar stereo results onto a smoothed model of the Magellan radar altimetry: “The basic processing stream involved using an iterative, weighted, cross-correlation

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algorithm to determine match points in FMAP (75 m/pixel) mosaics to determine relative elevations. These data were combined with Magellan altimetry, in the form of the GTDR mosaics, with complementary high-pass/low-pass filters to produce absolute elevations. The final data product has a horizontal resolution of ~1-2 km and a vertical resolution of ~100 m.”

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Obviously, artifacts in both the altimetry and SAR datasets are propagated into this stereo DEM, which therefore must be evaluated for self-consistency and consistency with inferences from the images. All elevations here are referenced to a planetocenctric radius of 6051.0 km. Radar Backscatter Data

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To retrieve the radar properties of the Venus surface, we started with the SAR DN

(digital number) values in the same FMIDR mosaics that were used to generate the stereo DEM (i.e., ~75 meter footprints). DNs in the relevant FMIDR mosaics were converted to SAR radar backscatter coefficients (σo), using equation 1 of Campbell (1995). The SAR backscatter

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coefficient is the ratio of the observed scattered intensity to that expected from a purely isotropic blackbody surface of the same area, and is controlled by its material properties (i.e., its permittivity), its porosity and granularity, and the orientation and roughness of its surface

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relative to the vectors of the incoming radar beam and to the radar detector. The backscatter coefficient can be greater than unity for rough or strongly oriented surfaces. Thus, our results

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using backscatter coefficients can be compared only qualitatively to true radar reflectivity derived from emissivity data (Klose et al., 1992; Arvidson et al., 1994). In general, however,

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SAR backscatter trends do correlate closely with the altitude dependent trends observed in radar

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reflectivity data, see Figures 5 and 6 (Klose et al., 1992; Arvidson et al., 1994), implying that the effects of surface roughness and orientation are secondary.

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In Ovda Regio we focused on two regions affably named the “ramp” and “golf” (Figure 3), each of which is of ~150-200 km extent with elevations from ~2 to ~5 km above the datum. The “festoon flow” area studied by (Arvidson et al., 1994) is east of the areas studied here, but has a similar elevation range. We excluded areas where obvious artifacts from radar altimetry were propagated into the stereo DEM (e.g., small radar-dark areas can appear to be at

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unrealistically low elevations; (Howington-Kraus et al., 2006). For each studied area, we collected average elevations and SAR backscatter coefficients for a total of 1784 polygons (from ~0.2 to 30 km2 in extent, averaging ~ 3 km2) of relatively constant backscatter coefficient and elevation. For each polygon, we calculated an average elevation and radar backscatter

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coefficient.

In Maxwell Montes, we collected data along three BIDR tracks or noodles from its

southern flank; the noodles are oriented approximately NNW-SSE, and range in width from 1436 km and length from 142-292 km. The range of DN values along theses noodles was far

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greater that in the Ovda region, in part because of its steep slopes and surface roughness. We collected data from approximately 500 polygons in these noodles (~0.8–50 km2 extent, averaging 7.9 km2), as shown in Figure 4.

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Results

The derived average Magellan radar backscatter coefficients, as functions of altitude for

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our selected areas in Ovda Regio and Maxwell Montes, are shown in Figures 5 and 6. The results are graphed with those of Magellan radar emissivity versus elevation from Arvidson et al. (1994)

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and Klose et al. (1992). Our results are entirely consistent with those earlier studies, recognizing

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that reflectance and emissivity are approximately complementary (not considering surface roughness). Ovda and Maxwell show distinctly different trends of radar backscatter coefficient

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and elevation, which are described below. Ovda Regio In both of the study areas in Ovda Regio, „ramp‟ and „golf,‟ we found the same relation

between radar backscatter coefficient and elevation as did Arvidson et al. (1994) and Shepard et al. (1994) for the „festoon flow‟ area (Fig. 3a). Our results for the „ramp‟ and „golf‟ areas have

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the identical relationships between backscatter coefficient and elevation. In both areas, the lowest elevations have low backscatter coefficients (σo ~ 0.01 at 2 km above the datum), which rise smoothly with elevation to a sharp maximum (σo ~ 0.2 at 4.5 km), and then drop precipitously to the highest elevations (σo ~ 0.02 at 4.7 km). The elevation of this sharp maximum in radar

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backscatter corresponds to a temperature of ~702 K (Seiff et al., 1980). The trend at lowest

elevations is best seen in the „ramp‟ of Figure 3, which extends from the lowland plains into the highlands. On either side of the „ramp‟ (Fig. 3) are higher, radar-bright plateaux. The smooth change from low dark regions to higher bright regions is also obvious in the „golf‟ region, where

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radar-dark lava flows fill a golf-club shaped depression north of a radar-bright plateau (Fig. 4). In both areas, the highest elevations are radar-dark, i.e., with low backscatter coefficients (Figs. 3, 4).

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Klose et al. (1992) and Arvidson et al. (1994) found the inverse of this relationship for Magellan radar emissivity and altimetry across all of Ovda Regio: emissivity decreases from the

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plains upwards into the highlands, and a few areas at the highest elevations again show high emissivity. However, few of the dark areas at high elevation (seen in SAR) are large enough to

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fill a footprint of either emissivity or altimetry, and (as noted above) the radar altimetry of such

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dark regions can be unreliable. In our approach, with smaller pixel sizes, we clearly confirm Arvidson et al. (1994)‟s observation that the highest elevations in Ovda have anomalously low

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radar backscatter.

Maxwell Montes The relationship between radar properties and elevation in Maxwell Montes is quite

different from that in Ovda Regio. The low-elevation foothills of Maxwell show a similar low backscatter coefficient that increases smoothly with altitude (Fig. 4), although this trend is

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significantly steeper than at Ovda (e.g., σo ~0.1 at 2 km above the datum). This trend continues to ~4.5-5.5 km altitude, at which point the average backscatter coefficient jumps dramatically (to σo ~1.7 at ~6 km), coincident with a significant drop in radar emissivity (Klose et al., 1992; Pettengill et al., 1992). The change in average backscatter coefficient is the „snow line‟ of

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Schaefer and Fegley (2004). The elevation of this sharp transition is different for different DEM swaths or noodles (Fig. 5), which could reflect real changes in the „snow line‟ elevation or

merely inconsistencies or misregistrations in the FMIDR images used in stereogrammetry. At elevations above ~ 5 km on Maxwell, radar backscatter coefficients vary widely (Fig. 5); the

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cause of this variation is likely to be strong variations in roughness and slope angle (high values representing specular radar reflection back to the spacecraft, and low values representing slopes away from the Magellan spacecraft). At the highest elevations on Maxwell (> 8 km or so), the

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backscatter coefficients decrease with elevation to values only slightly greater than those of Maxwell‟s foothills, Fig. 4B and see Campbell et al. (1999). This decline in backscatter

Related Sites

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coefficient seems gradual with elevation, unlike the precipitous drop observed on Ovda.

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The relationship between elevation and radar backscatter coefficient seen on Maxwell

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Montes is also present elsewhere in the mountain ranges around Ishtar Terra (Fig. 1). Specifically, “snow lines” are apparent on Akna Montes, Freyja Montes, and Danu Montes,

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which are respectively on the northwestern, northern, and southeastern boundaries of Ishtar Terra, Figure 1. These jumps in backscatter coefficient are mirrored by abrupt decreases in radar emissivity (Klose et al., 1992). DiscussionS Ovda Etc.: a Ferroelectric Substance

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In Ovda Regio, the rapid increase and precipitous drop in radar backscatter coefficient with increasing elevation has been ascribed to the presence of a ferroelectric substance (Arvidson et al., 1994; Shepard et al., 1994), possibly augmented by development of a mantle of porous or fragmental material (Campbell et al., 1999; Carter et al., 2006a). Our data are consistent with the

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former hypothesis, that these surfaces in Venus‟ highlands contain a substance that transitions from ferroelectric to paraelectric at ~702 K (Seiff et al., 1980), the temperature corresponding to the altitude of the change in backscatter coefficient.

The hypothesis that the highest elevations of Ovda are mantled by fragmental material

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(Campbell et al., 1999; Carter et al., 2006a), proposed to explain both their reduced radar

backscatter and their apparent absence of surface morphologic features, seems inconsistent with both radar properties and geologic relationships. If the change in radar properties at a critical

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elevation is represents the presence of a ferroelectric substance (Arvidson et al., 1994; Shepard et al., 1994), it must be present both above and below the critical elevation. Thus, the change in

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radar properties need not represent a change in the proportion of the ferroelectric substance nor of the properties of the rock in which it resides. Thus, a correlation between the atomic-scale

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necessary.

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transition from ferro- to paraelectric and a significant change in host-rock porosity is not

Also, we are aware of no mechanism for, and no natural analogs of, deposition or

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formation of fine-grained, fragmental material only at high altitudes above a sharply defined elevation (Figs. 3, 5). If the radar-dark material at high elevations were a “… mantling deposit … of significant depth…” (Carter et al., 2006a), one should expect occasionally to see massmovements of this deposit to lower elevations, or wind-blown plumes of the material (if it is fine-grained enough). Although mass movements of rock and regolith are recognized in the

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Venus highlands (Malin, 1992), no such deposits of radar-dark material were observed here, or have been reported in the literature on Ovda (Arvidson et al., 1994; Romeo and Capote, 2011). However, the apparent absence of surface morphology (i.e., roughness elements) on lowbackscatter surfaces (Campbell et al., 1999; Carter et al., 2006a) is not immediately explained by

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the ferro-electric substance model. Growth of a ferro-electric substance in or on rock would not remove its surface roughness. This is obviously an area for additional study; a possible

explanation is that the backscatter contrast across roughness elements will approach zero as the radar backscatter coefficient of the material approaches zero.

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Other Tessera Sites

This relationship between elevation and radar backscatter coefficient is not unique to the tesserae of Ovda Regio. East of Ovda, and also within the broad Aphrodite Terra region, radar

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bright areas at high elevations are present in: Thetis Regio (~ -7.5°, 125°), with radar dark regions at the highest altitudes (-12.5°, 132.5° and 11.75°, 136°); the mountain belts surrounding

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Artemis Corona (~-32.5, 132.5); ridges south and west of Dali Chasma (-17°, 170°; -18°, 162.5°); and a ridge belt on the southern flank of Maat Mons (-2.2°, -165.5°).

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The Tepev Montes Volcanoes

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An important site outside Aphrodite Terra is Tepev Montes, a pair of shield volcanoes in Bell Regio at ~30°N, 45°E (Janle et al., 1987; Janle et al., 1988; Campbell and Rogers, 1994;

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Carter et al., 2006a), Figure 7. The Tepev Montes shields show the same SAR backscatter trend as does Ovda – intensity increasing upwards from the lowland plains to a critical elevation (~5.4 km above the datum), and a sudden drop in backscatter above that elevation (Fig. 7). As with Ovda, the inverse pattern is seen in radar emissivity. The changes in SAR backscatter and in emissivity on Tepev Montes have been interpreted to represent summit calderas or bowls

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surfaced with fragmental material (like ash) that reflects radar poorly (Campbell and Rogers, 1994; Carter et al., 2006a). As above for Ovda, we do not support this interpretation. The objections we raised above for Ovda Regio also hold for Tepev Montes. In addition, Magellan altimetry shows that neither shield on Tepev Montes has a summit caldera or basin, see Figure 7

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and Herrick et al. (2005). If neither summit has a topographic depression, there is no reason to expect that a coating of volcanic ash (or other fragmental material) could be present at identical elevations on both the high eastern summit and low western summit, and remain confined only to those elevations.

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Thus, we interpret the these variations in radar backscatter on Tepev Montes to represent the presence of a substance undergoing a ferroelectric – paraelectric transition (Arvidson et al., 1994; Shepard et al., 1994). Tepev is different from Ovda in that the elevation of the change in

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radar backscatter is ~5.4 km above datum rather than ~4.5 km on Ovda; this corresponds to a temperature rather small temperature difference of ~695K rather than ~702K (Seiff et al., 1980).

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Other Near-Equatorial Volcanoes

Tepev Montes is unique on Venus in being an undisputed volcanic construct with the

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pattern of radar properties exemplified in Ovda Regio: increasing backscatter with and abrupt

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transition to low backscatter. Many of the other Venusian volcanoes also show increases in radar reflectivity uphill, and some also have patches of low backscatter material near their summits.

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However, their patterns of SAR backscatter are not as clear-cut as those in Ovda and on Tepev, and can be ascribed (at least in part) to other geological causes, including roughness and age. Theia Mons, in Beta Regio (24°, -80°), has a low backscatter summit region at ~6 km

above the datum (Senske et al., 1992; Campbell et al., 1999), coincident with a strong high in radar emissivity (Campbell et al., 1999). Oddly this high emissivity at high altitude does not

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appear in the Klose et al. (1992) graph of emissivity and elevation for Beta Regio. Below this summit region, the slopes of Theia show a strong increase in backscatter moving uphill, with a corresponding decrease in radar emissivity (Campbell et al., 1999) exactly as observed in Ovda and other tesserae (Klose et al., 1992). The general relationship between radar properties and

from high to low radar backscatter at ~5 km above the datum.

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elevation for Theia are consistent with those of Ovda and especially of Tepev, with a transition

Several of Venus‟ volcanoes have, near their summits, low backscatter areas that are clearly lava flows, and are not related to the low backscatter areas on Ovda and Tepev. These

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volcanoes include: Sif Mons, summit at 2.2 km (Campbell and Campbell, 1990; Senske et al., 1992; Stofan et al., 2001); Ushas Mons, summit at 2.4 km (Keddie and Head, 1995), and Sapas Mons, summit at ~4.5 km (Keddie and Head, 1994). Sapas Mons, at (8.25°, 188.5°), is tall

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enough to have Ovda-like trends in radar backscatter, and its summits do have high radar emissivity relative to nearby lower elevations (Klose et al., 1992; Palazzari et al., 1995).

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However, some of the SAR-dark material descends from the summits in lobes and streaks; the summits here are interpreted as scallop-margined domes from which material has flowed or

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fallen as debris (Keddie and Head, 1994). Thus, the pattern of SAR backscatter on Sapas Mons

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cannot be solely from the presence of a ferroelectric substance. The summit of Ozza Mons (4°, 199.75°) is at ~7.5 km relative to the datum, has low

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radar backscatter and high emissivity; the slopes surrounding the summit region have, for the most part, high radar backscatter and low emissivity (Pettengill et al., 1992; Senske et al., 1992; Campbell et al., 1999). However, the low backscatter material at the Ozza summit embays brighter, heavily fractured surfaces and extends outwards (downslope?) in tongues, which may represents flows of lava or debris rather than the material or process apparent on Ovda and

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Tepev. In addition, the slopes below the summit show no strong transition in radar backscatter near the critical elevations of 4-5 km seen on Ovda and Tepev. Finally, Maat Mons, in Atla Regio at (2.5°, 194.5°), is the tallest volcano on Venus; with its summit at ~10.2 km above the datum. The surface of Maat Mons has a wide range of radar

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backscatter coefficients but with a limited range of radar emissivities (Klose et al., 1992). On Maat, there is no discernable relationship between elevation and radar backscatter coefficient or with emissivity (Campbell et al., 1999); individual lava flows can be distinguished by their

backscatter coefficients, which are clearly unrelated to elevation and apparently unrelated to

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relative age; i.e. SAR-bright flows have overridden SAR-dark flows, and vice versa. Ferroelectric Substance: Distribution and Formation

Our data are consistent with the hypothesis that these surfaces in Venus‟ highlands

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contain a ferroelectric substance (Arvidson et al., 1994; Shepard et al., 1994). More precisely, the radar properties of Ovda are consistent with the widespread presence of a substance that is

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ferroelectric at higher elevations and lower temperatures, and „normal‟ (i.e., paraelectric) at lower elevations and higher temperatures.

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A ferroelectric material is ordered on the atomic or molecular level so that the whole

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material (or domains within it) can maintain an electrical dipole (i.e., has a spontaneous electrical polarization) that can be reversed under a sufficient electrical potential (Jona and Shirane, 1962),

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see Figure 8. The electrical potential needed to reverse the dipole decreases with increasing temperature because of thermal motion of its atoms (Fig. 8). At the substance‟s critical temperature, TC, thermal perturbations of the atoms are so strong that an arbitrarily small applied potential (e.g., that of a radar beam) can flip the polarity of the dipole, which then implies an extreme value for the permittivity. Above the critical temperature the material is electrically

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„normal‟ or paraelectric (i.e. without a permanent electrical dipole), and its permittivity declines with temperature from a peak at TC. Ferroelectricity is possible only in materials of non-centrosymmetric atomic arrangements (Jona and Shirane, 1962; Halasyamani and Poeppelmeier, 1998). Nearly all of the

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common rock-forming minerals are centrosymmetric (e.g., olivine, pyroxenes, feldspars,

amphiboles, micas), as are nearly all of the common minor minerals (e.g., zircon, baddeleyite, rutile, sphene (titanite), hydroxyl- and fluorapatite [Ca5(PO4)3(F,OH)], and silica phases except quartz). Quartz is not centrosymmetric and can be abundant in Earth rocks, but its symmetry

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precludes a ferroelectric effect (Halasyamani and Poeppelmeier, 1998). A common non-

centrosymmetric minor mineral is tourmaline, but it is not ferroelectric because its electrical dipole cannot be reversed by an applied electrical field.

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Of the ferroelectric compounds suggested earlier for Venus‟ highlands (Shepard et al., 1994; Brackett et al., 1995), only Na(Nb,Ta)O3 is known in on Earth as the mineral lueshite.

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Lueshite is exceedingly rare, and occurs only in a few carbonatite rocks; it is conceivable that NaNbO3 could be more common on Venus than Earth if Venus‟ canali represent flows of

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carbonatite magma (Komatsu et al., 1992; Kargel et al., 1994; Treiman, 1995). The other

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ferroelectric compounds suggested by Shepard et al. (1994) and Brackett et al. (1995) are geochemical chimera – unlikely because natural processes rarely combine their constituent

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elements under suitable circumstances. Chlorapatite, Ca5(PO4)3Cl, is perhaps the only relatively common mineral that is

ferroelectric and becomes paraelectric at temperatures achieved on the Venus surface; thus, we suggest that it is the ferroelectric substance on Ovda Regio and other highlands on Venus. Chlorapatite is polar (Mackie et al., 1972; Rausch, 1976; Bauer and Klee, 1993) because its Cl–

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anions are displaced from symmetric sites in the crystal structure (Hughes and Rakovan, 2002; Hughes et al., 2014; Hughes, 2015). Thus, chlorapatite crystals can be fully polar or contain polar domains (Ferraris et al., 2005; Baikie et al., 2012), see Figure 4 of Hughes and Rakovan (2002). The electrical polarity of chlorapatite crystals (or domains within them) can be reversed

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under an applied electrical field (Rausch, 1976), so chlorapatite is truly ferroelectric. The

temperature for chlorapatite‟s ferro- to paraelectric transition has not been measured directly, but is estimated to be between 675 and 775K (Rausch, 1976), and may be at ~695±4K (Hitmi et al., 1984). This is consistent with the transition in radar backscatter coefficient on the Ovda

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highlands (Fig. 3). The difference between the transition temperatures in Ovda and on Tepev can be rationalized as representing slightly different temperatures or chlorapatite compositions at the two sites; differences could include anion composition (proportions of F- and OH- in place of

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Cl-) or cation composition (substitution of Sr or rare earth elements for Ca). Chlorapatite could be abundant enough to produce the observed radar behavior. Typical

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Earth basalts contain 0.3 – 1% P2O5, which would be accommodated by ~0.5 – 2% apatite (chlor- or otherwise) and/or merrillite. The abundances of P2O5 and apatite in Venus basalts are

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not known (Treiman, 2007), but other planetary basalts (eucrite, martian, lunar) contain

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comparable proportions of P2O5 and thus potentially of apatite, e.g. (Barrat et al., 2007; Hallis et al., 2014; Treiman and Filiberto, 2015). Chlorine-rich apatite is present in some of these

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planetary basalts (Patiño Douce and Roden, 2006; Boyce et al., 2015). Thus, it is reasonable to hypothesize that similar proportions of P2O5 and chlorapatite could be present in Venus‟ rocks. It is clear, however, that the ferroelectric substance inferred for the Ovda tessera and the

Tepev Montes volcanoes is not globally distributed – at least three volcanoes (Maat, Ozza, and Sif) are tall enough to cross the critical elevation of 4-5 km but do not show a precipitous decline

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in radar backscatter at that elevation. The differences among these sites cannot be solely rock compositions, because all of the volcanoes (including Tepev Montes) are inferred to be basaltic. A likely explanation is that these surfaces are of different ages – that formation of the ferroelectric substance requires a significant time, and that surfaces lacking its signature are

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young (Klose et al., 1992; Robinson and Wood, 1993; Wood, 1997; Fegley, 2003; Basilevsky et al., 2012).

Our suggestion that the ferroelectric substance is chlorapatite appears to be consistent with this scenario. The primary phosphate mineral in terrestrial, martian, and lunar igneous rocks

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is generally fluorapatite (Piccoli and Candela, 2002), in part because Cl and H2O are readily lost to volatile phases (Aiuppa et al., 2009; Ustunisik et al., 2011; Ustunisik et al., 2015), and because F is partitioned more strongly into apatite from melt than is Cl or OH (McCubbin et al., 2015).

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Original F-rich igneous apatite could then react with HCl in the Venus atmosphere to yield chlorapatite (see Supplemental Material), either as full crystals or as Cl-rich domains in mixed

al., 2014; Hughes, 2015).

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apatite crystals (Hughes and Rakovan, 2002; Ferraris et al., 2005; Baikie et al., 2012; Hughes et

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Maxwell: Atmosphere-Surface Chemistry?

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In contrast to Ovda Regio, Maxwell Montes and other mountain belts around Ishtar Terra show a “snow line,” across which radar backscatter coefficients increase sharply (and

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emissivities drop sharply) with increasing elevation (Fig. 5). This “snow line” is at relatively constant elevation and thus temperature and pressure, and has generally been interpreted as representing the equilibrium position of a chemical reaction involving the Venusian atmosphere. Suggested chemical reactions include sulfidation or oxidation of iron in surface rock to produce minerals with relatively high electrical conductivities (Pettengill et al., 1988; Klose et al., 1992;

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Wood, 1997), and precipitation from the atmosphere of semiconductor „frosts‟ like Te, PbS, Bi2S3, and HgTe (Brackett et al., 1995; Pettengill et al., 1996; Schaefer and Fegley, 2004; Kohler et al., 2015). Although Maxwell Montes is extremely rough, that roughness alone is not sufficient to cause the observed high radar backscatter coefficients (Campbell et al., 1999;

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Campbell, 2012).

The presence of electrically conductive or semiconductive materials on Maxwell is

consistent with bistatic radar observations from both the Magellan and Venus Express spacecraft. In both experiments, radar beams were transmitted from the spacecraft to the Venus surface, and

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the reflected beams were received on Earth (Pettengill et al., 1996; Simpson et al., 2009). Both bistatic experiments both found that radar returns from Maxwell Montes were consistent with a material of high relative permittivity || ≈ 100, i.e. a semiconductor (Pettengill et al., 1996;

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Campbell et al., 1999; Simpson et al., 2009; Campbell et al., 2012). For example, the semiconductor compound pyrite, FeS2, at 730K has || ≈ 100 (Peng et al., 2014). The same

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bistatic experiments gave || ≈ 4 for Venus‟ lowlands, which is typical of dry silicate rock like

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basalt (Campbell and Ulrichs, 1969; Pettengill et al., 1996; Simpson et al., 2009). It is noteworthy that the average radar backscatter coefficient decreases significantly

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toward the highest elevations of Maxwell Montes (Fig. 4a, 4b, 6), see Campbell et al. (1999) and Carter et al. (2006b); a change which is echoed by small increases in radar emissivity (Fig. 6),

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see Klose et al. (1992). Campbell et al. (1999) evaluated several possible causes of this change, including rock compositions (Basilevsky and Head, 1995), mass wasting, differences in temperature or atmosphere composition, and elevation errors, but did not identify a specific cause. An interesting suggestion is that surface temperatures across Maxwell are significantly greater than those on Ovda, such that the transition from high to low radar backscatter occurs at

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~5 km elevation on Ovda but at ~9 km on Maxwell (Fig. 6). If the temperature estimate for the transition on Ovda is correct, ~700K (Seiff et al., 1980), and the transition is at the same temperature on Maxwell, then Maxwell‟s surface is ~ 30K warmer than predicted (Seiff et al., 1980).

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Our new data about Maxwell (Fig. 6) are consistent with those of Campbell et al. (1999), but do not resolve a specific cause for the decreasing radar backscatter at its highest elevations. However, we can offer two other possible explanations. If the high backscatter material on

Maxwell is a result of vapor-phase transfer of volatile elements from the lowlands (Brackett et

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al., 1995), then it is possible that an element moving uphill could be depleted nearly

quantitatively (by deposition or reaction) at intermediate elevations (~4-8 km; Fig. 6), and no longer be abundant enough at the highest elevations to form high-backscatter surfaces. On the

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other hand, if the high-backscatter material is a product of atmosphere-surface chemical reactions, that product could be unstable at the highest altitudes on Maxwell. For example it is

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conceivable that atmosphere-rock chemistry yields magnetite at the lowest elevations, pyrite at intermediate elevations (~4-8 km; Fig. 6), and then hematite at the highest elevations. This is

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from Venus.

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obviously an area for further thermochemical modeling, and acquisition of additional hard data

IMPLICATIONS

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The cause of high radar backscatter at Venus‟ high elevations has been confusing and controversial; explanations have included high porosity, semiconductor „frosts‟ deposited from the atmosphere, and ferro-electric or semiconductor materials (either inherent to the rock or from atmosphere-surface chemical reactions). Here, using higher-resolution altimetry from SAR stereo, we have shown that a single explanation is not adequate – that the patterns of radar

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backscatter coefficients in Ovda Regio (and other near-equatorial sites) are different from those on Maxwell Montes (and nearby sites), and cannot both arise from the same mechanism. The radar backscatter returns from Ovda Regio are consistent with the presence of a substance that experiences a phase transition from ferroelectric to paraelectric, as proposed by

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Shepard et al. (1994) and Arvidson et al. (1994). We suggest that the substance is the mineral chlorapatite, which could be abundant enough in planetary basalts to produce the observed radar signatures. Geologic relations on Ovda are not consistent with the presence of highly porous material only at high elevations (Campbell et al., 1999). It seems most likely that the ferro-

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electric phase, i.e. chlorapatite, is not intrinsic to Venusian rocks, but is a weathering product that required significant time to form. Possibly, original igneous fluorapatite is altered to chlorapatite by chemical reaction with HCl from the atmosphere.

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Radar backscatter returns from Maxwell Montes are consistent with the presence of a semiconducting material (i.e., with high permittivity) above a critical altitude of ~4.5 km, and

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continuing up to nearly the highest peaks (~8-9 km). This pattern is consistent with the concepts of chemical reactions controlled by temperature or pressure, like vapor-deposition as proposed

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by Brackett et al. (1995) and Schaefer and Fegley (2004), or chemical reaction between the

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atmosphere and surface rock as proposed by Klose et al. (1992) and Wood (1997). Geographic and geologic relations on Maxwell are not consistent with a proposed presence of intense

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roughness only above its critical elevation, see Figure 4c (Campbell et al., 1999). So, the radar backscatter patterns at Ovda (etc.) and at Maxwell must arise from different

causes, and are most consistent with differing compositions of atmosphere or rock at the two locales. If the rock on Maxwell Montes contains a ferroelectric compound (like chlorapatite), its presence could be obscured by a coating or reaction zone of semiconductor material; in that

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respect, Maxwell and Ovda could be composed of the same kind of rock, be it basaltic or granitic (Ivanov, 2001; Shellnutt, 2013). However, the absence of a semiconductor material on Ovda (and other near-equatorial sites) is more difficult to explain. If the composition and temperature profiles of the Venus atmosphere are the same above Maxwell and Ovda, both should show the

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same atmospheric deposits, i.e. “heavy metal frost.” So, if the semiconductor material on

Maxwell is an atmospheric precipitate, then the atmospheres above Maxwell and Ovda must be significantly different (Haus et al., 2015). On the other hand, if Venus‟ atmosphere is similar across the whole planet, then the absence of a semiconductor coating on Ovda is problematic

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unless the semiconductor material on Maxwell is a chemical reaction product between

atmosphere and rock, and the rock on Ovda is not similar to that on Maxwell. In this case, if the semiconductor reaction product is pyrite, FeS2 (Klose et al., 1992; Wood, 1997), Ovda cannot be

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made of typical basalt, which is rich in iron. It may be that lander missions with geochemical

Acknowledgments

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analysis capabilities will be required to understand the radar properties of Venus‟ highlands.

This work was started in a LPI Summer Internship by Harrington, mentored by Treiman

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and Sharpton, which was supported by the LPI‟s Cooperative Agreement with NASA. We are grateful to R. Herrick for producing the DEM on which this work is based, for making it

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publically available, and for assistance with its interpretation. The LPI IT staff supported our GIS work with the DEM. Access to Magellan data (SAR, altimetry, emissivity) was via the U.S.G.S. „Map-a-Planet‟ websites, both original and beta. This work has benefitted from helpful

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Figure 1. Global view of Venus showing radar-bright highlands, with boxes denoting areas of

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detailed studies in Ovda Regio and Maxwell Montes.

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Figure 2. Altimetry artifacts in areas of low radar backscatter (Howington-Kraus et al., 2006) . A. Diagram of geometry of Magellan altimetry observations, modified after Ford (1993),

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See text for explanation.

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showing how strong contrasts in radar backscatter can spoof to give false low elevations.

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B. Magellan SAR image of a portion of Ovda Region (see Fig. 3). The area of low SAR

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backscatter to right (east) is at the highest elevation in the scene, based on SAR stereo altimetry.

C. Magellan smoothed altimetry for this area (GTDR mosaic); lower elevations are darker colors. The area of apparent low elevation on the right (east) of the altimetry map corresponds to the area of low radar backscatter in image 2B. See also Arvidson et al. (1994). Red zone at east (right) of image does not have stereo coverage.

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Figure 3. Areas studied in Ovda Regio.

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A. Overview of Ovda Regio, from Magellan MIDR. Note continuous increase in radar brightness

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from the plains surrounding Ovda into its highlands. Boxes show areas studied here; arrow points to “festoon lava flow” area (Schenk and Moore, 1992; Permenter and Nusbaum,

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1994), studied in detail by Arvidson et al. (1994).

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B. The “Ramp” sample area in Ovda Regio, centered at -7.0°,89.5° (see also Fig. 2B).

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From lower right to center top smooth ramp surface from lowland plains (outside image, to lower right) with a continuous gradation from low to high radar reflectivity. On both sides of this ramp

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are highland plateaux, which have very low radar backscatter at their highest elevations.

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C. The “Ramp” area of Figure 3b, annotated. Each polygon is an area of relatively constant brightness (radar DN, or backscatter coefficient) and elevation; data on each polygon were collected as input to Figure 5. Violet shading shows elevation from smoothed Magellan radar altimetry (from the GTDR mosaic), with darker purple representing ower elevations. Note that the dark plateau at the upper right of the image shows the lowest elevation from radar

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altimetry. That plateau is actually at high elevation (shown by stereogrammetry), and the radar

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altimetry here is incorrect, see Figure 2 and Howington-Kraus et al. (2006)

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D. Golf area. E. Golf area with polygons.

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Figure 4.

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Base image c/o LPI.

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A. Magellan SAR image of Ishtar Terra, centered at ~65°N 340°E, with features cited in text.

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B. Maxwell Montes, showing polygons along the three analyzed SAR swaths, or “noodles.” See

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part A for context, note Cleopatra Crater.

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C. “Snow Line,” northern flank of Maxwell Montes, from Magellan SAR FMIDR mosaic; scene centre at ~68°N 6°E. Here, the boundary between low-backscatter and high-backscatter areas is perpendicular to geological structures (fault scarps, valleys), showing that the boundary is caused by surface roughness alone.

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D. Digital elevation model for a portion of Maxwell Montes, including the Cleopatra impact

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crater (Herrick et al., 2012); north is to top (see Figures 4A, B). Elevations in meters relative to 6051.0 km radius, lower elevations shaded darker. Contour interval is 200 meters,

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selected contours labeled. Apparent scarps running north-south (as in the pair north of Cleopatra, and that near left side of image) are not real changes in elevation (Herrick and

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Rumpf, 2011), but arise from misregistrations of Magellan BIDR „noodles‟ in generation of

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FMIDR images.

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Figure 5. Radar properties of Ovda Regio. Red symbols and legend are Magellan SAR radar

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reflectance coefficients and elevations for the „ramp‟ and „golf‟ areas studied here (Fig. 3). Black symbols and legend are Magellan emissivity for all of Ovda from Arvidson et al.

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(1994); small dots are elevation by Magellan altimetry; large symbols are for elevation by

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SAR stereogrammetry (Arvidson et al., 1994).

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Figure 6. Radar properties of Maxwell Montes. Red symbols and legend are Magellan SAR radar

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reflectance coefficients and elevations for the three noodles studied here (Fig. 4). The huge range of radar backscatter values above ~4 km represents (in part) the intense roughness of

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the topotraphy on Maxwell. Black symbols and legend are Magellan emissivity for all of Maxwell Montes, from Klose et al. (1992).

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Figure 7. Tepev Montes. Top frame is SAR image, showing low-backscatter regions at the summits of both its shield volcanoes (28.91-30.35 °N; 43.76-46.65°E). White line shows

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location of elevation traverse in bottom frame from Magellan altimetry (Campbell and Rogers, 1994; Carter et al., 2006). Elevation is in km relative to the 6051 km datum. The altimetry shows that neither shield has a depression or caldera (at least at the resolution of the altimetry. The transition in backscatter coefficient is at elevation ~5.4 km above datum (thin dark line).

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Figure 8. Electrical Behavior of a Ferro-electric Material. Hysteresis curves of electrical

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polarization (P, in charge per unit area) of a hypothetical ferroelectric material versus applied voltage gradient (E, in voltage per distance). Hysteresis loops represent cycling of applied voltage from low E to high E. The permittivity of the material is the slope of the

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curve at E=0.

The black curve is for a temperature far below the critical temperature TC. Following that

curve counter-clockwise counter-clockwise from very negative E, P begins strongly negative (the material is polarized one direction), and remains negative as E increases until some positive value. Then, following the arrowhead, P increases rapidly to a positive value (the material is polarized in the other direction). As E then becomes more negative, the

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polarization P remains positive until some negative value of E is reached. At that point, the material becomes polarized in the original direction again; this is the hysteresis loop. The permittivity at this temperature, the slope of the black curve at E=0, is low. The purple curve is for a higher T, but still below TC; the permittivity remains low. The blue curve is for T equals TC; the hysteresis loop has closed, and the slope of the

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curve at E=0 is near-infinity, i.e., the permittivity is very high; this curve corresponds to the transition on Ovda Regio from SAR dark (at low temperature & high elevation) to SAR bright (at higher T and lower elevation).

Finally, the green curve is for T>TC. There is no hysteresis loop, as the material is no longer ferroelectric. The permittivity remains high but is rotating toward lower values as T

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increases.