photometric properties of phobos surface materials from viking images

ICARUS 131, 52–77 (1998)ARTICLE NO. IS975800

Photometric Properties of Phobos Surface MaterialsFrom Viking Images

Damon P. Simonelli, Michael Wisz, Andrew Switala, Daniel Adinolfi, Joseph Veverka, Peter C. Thomas,and Paul Helfenstein

Center for Radiophysics and Space Research, Space Sciences Building, Cornell University, Ithaca, New York 14853E-mail: [email protected]

Received February 19, 1996; revised June 13, 1997

modified by discrete cratering events and is not mixed horizon-tally by extensive downslope creep as is apparently the case onClear-filter Viking images, and an accurate numerical modelDeimos. 1998 Academic Pressof the shape of Phobos, have been used to determine this satel-

lite’s photometric properties. A global-average Hapke functionderived from disk-resolved data confirms previous indications

I. INTRODUCTIONthat Phobos has a strong opposition surge. Photometricallycorrected images were mosaicked into an albedo map; most of

Because scattered light from Mars makes it difficult tothe resulting normal reflectances are in the range 0.06–0.10,observe Phobos from Earth, disk-resolved images fromand the brightest region on Phobos is the northeast rim ofMariner 9, Phobos 2, and especially Viking provide thethe crater Stickney, the portion of that rim with the highestonly real opportunity to study the photometric behaviorconcentration of grooves. Globally, there are three albedo

classes, reasonably separated geographically: (1) Bright mate- of this martian moon. However, such studies have beenrial is to the east and south of Stickney, corresponding approxi- hampered to date by the lack of an accurate model for themately to the locations on Phobos having the highest, ‘‘bluest’’ shape of the satellite. Without the accurate incidence andvisible/near-IR ratio (Murchie et al. 1991). (2) The darkest emission angles that such a model provides, photometricmaterial is to Stickney’s west, correlating with material having investigation of the spacecraft images of Phobos has beenan intermediate visible/NIR ratio (Murchie et al.’s ‘‘bluish limited to the following: (1) Deriving the global-averagegray’’ unit). (3) Intermediate-albedo material dominates the photometric function from the disk-integrated phase curve,anti-Stickney hemisphere, corresponding to material with a

with the associated problems of projected-area correction,lower visible/NIR ratio (Murchie et al.’s ‘‘reddish gray’’ unit).uniqueness of solution, etc. (Efford 1989; see also PangA search for variations in phase behavior across Phobos’et al. 1983). (2) Estimating the global photometric behaviorsurface shows few such effects overall, limited to isolated areas:from disk-resolved measurements using a triaxial-ellipsoid(1) Stickney’s floor darkens with increasing phase faster thanshape model and simplified photometric function (Klaasenaverage Phobos. This crater floor is both slightly more backscat-et al. 1979). (3) Making qualitative statements about, ortering and significantly rougher than the global average; the

latter effect may be related to the slumping hinted at in low- approximate measurements of, the phase-angle depen-resolution images of Stickney. (2) We confirm that in many dence of albedo contrasts, including the contrast betweencases, the contrast between the bright rims of small craters and the ‘‘typical’’ Phobos surface and bright crater and groovegrooves and their surroundings drops noticeably with increas- rims (e.g., Thomas 1979, Avanesov et al. 1991, Shkuratoving phase (phase angles in use 5 108–508). However, these et al. 1991) and the contrast between the typical Phobosbright rims, overall, display a diversity of photometric behavior surface and dark crater-floor deposits (Goguen et al. 1978).and are the most heterogeneous areas on Phobos in terms of We now have an accurate numerical model for the irreg-regolith properties. (3) We confirm that dark deposits in the ular shape of Phobos (Thomas 1993, Simonelli et al. 1993).floors of smaller craters darken faster with increasing phase

Also available is Cornell’s Spud irregular-object softwarethan their surroundings (cf., Goguen et al. 1978) and find that(Simonelli et al. 1993), which allows us to determine accu-these deposits are more backscattering than average Phobos.rate incidence and emission angles from the shape modelIsolated regions with unusual phase behavior occur onand analyze the resulting disk-resolved brightness mea-Phobos but not on Deimos (Thomas et al. 1996). The variablesurements using modern photometric functions such as thephotometric properties of Phobos’ isolated craters and grooves,Hapke function (cf., the Gaspra, Ida, and Deimos work inand the association of global albedo features with Stickney,

reinforce interpretations that Phobos’ regolith is emplaced and Helfenstein et al. 1994, 1996 and Thomas et al. 1996). These

520019-1035/98 $25.00Copyright 1998 by Academic PressAll rights of reproduction in any form reserved.

VIKING PHOTOMETRY OF PHOBOS 53

TABLE Iimprovements make it worthwhile to reexamine the disk-Viking Clear-Filter Images Used in Photometric-Functionresolved photometric data present in the Viking images of

Determination and Albedo MapPhobos. This reexamination is also useful because we cansearch for correlations between the visible-light photomet-ric behavior observed by Viking and the visible/near-IRcolor units that have been identified in Phobos 2 imagesof the satellite (Murchie et al. 1991).

In Section II, we use a subset of the clear-filter Vikingimages to determine a globally averaged Hapke photomet-ric function for Phobos. This photometric function is usedto generate a clear-filter albedo map of the satellite; weshow that the major albedo patterns correlate well withthe color patterns identified by Murchie et al. (Section III).Finally, in Section IV we carry out a refined examinationof the phase-angle behavior of selected regions on Phobos,including bright crater and groove rims as well as darkdeposits in crater floors.

II. GLOBAL PHOTOMETRIC FUNCTION

We begin by determining an improved global-averagephotometric function for the surface of Phobos. We limitthis work to data obtained with the Viking Orbiter cam-eras’ wide-band clear filter (effective wavelength 0.54 em)for two reasons: (1) The great majority of the Viking im-ages of Phobos are taken with this filter; accordingly, itprovides coverage over a much wider range of geometriesthan any other Viking filter, including the only imageswithin the opposition surge and the only images at ex-tremely high phase angles. (2) Previous examination ofthe limited data in the Viking narrow-band color filters(violet 5 0.45 em, green 5 0.53 em, and red 5 0.59 em)indicated almost no visible-light color variations acrossthe surface of the satellite (Duxbury and Veverka 1977,Veverka and Duxbury 1977, Klaasen et al. 1979). We havenow applied improved color-ratio techniques, includingsubpixel registration, to color imaging sequences from Vik-ing orbits 115a, 413a, and 143b, which emphasize the rangeof longitudes where the Phobos 2 spacecraft detected only images available show Phobos filling the field of view.

All images were calibrated radiometrically and geometri-visible/near-IR color variations (Murchie et al. 1991). Weconfirm that even with more rigorous analysis, there are cally using U.S. Geological Survey Planetary Image Car-

tography System (PICS) software. The absolute and rela-no significant color variations across the surface of Phobosin the limited wavelength range of the Viking cameras. tive calibration of the Viking Orbiter cameras is expected

to be good to about 610%.To determine the clear-filter photometric function, weselected 22 Phobos images covering the entire available The numerical shape model developed for Phobos

(Thomas 1993, Simonelli et al. 1993) gives the radius ofrange of solar phase angle a (Table I), in many cases usingthe same images as Klaasen et al. (1979). We included all the satellite every 28 in latitude and longitude. However, in

photometry the important quantity is surface slope—andthree available images within the opposition surge andselected a significant number of high-phase images in order based on our experience with the accuracy of model slopes,

it made sense to be conservative and use a version of theto average-out the large uncertainties expected at suchgeometries. To sample the full range of available incidence shape model whose resolution was reduced to 48 in lat/lon.

The wire-grid model was overlayed on each image usingand emission angles, we used moderate-resolution, full-disk images wherever possible; however, the opposition- the known lighting-and-viewing geometry (subspacecraft

and subsolar points, range, and direction of north) andsurge images are low resolution, and at 108–208 phase the

54 SIMONELLI ET AL.

TABLE IIGlobal-Average Photometric Functions

Deimos Gaspra IdaPhobosa Viking Galileo Galileo Moon

Hapke parameter Viking clear filter clear filter GRN filter GRN filter V filter

Regolith single-scattering 0.070 6 0.020 0.079 0.36 0.218 0.21albedo w

Opposition surge angular 0.055 6 0.025 0.068 0.06 0.020 0.07width h

Opposition surge ampli- 4.0 1621

b 1.65 1.63 1.53 2.01tude B0

Phase function of regolith g1 5 20.20 6 0.04 g 5 20.29 g 5 20.18 g 5 20.33 g 5 20.18particlesc g2 5 0.66 fixed

f 5 0.13 6 0.09geff 5 20.08

Macroscopic roughness 228 6 28 16.48 298 188 208

mean slope angle uReference This paper Thomas et al. Helfenstein Helfenstein Helfenstein

1996 et al. 1994 et al. 1996 et al. 1994

a The best Phobos fit achieved with a 1-term Henyey–Greenstein function (not as good a fit as the 2-term function shown above) has w 5 0.054,h 5 0.072, B0 5 5.7, g 5 20.13, and u 5 218.

b The limited data put little or no upper limit on the amplitude of Phobos’ surge, but do constrain it to be stronger than the surges of the otherlisted objects.

c In a 1-term Henyey–Greenstein phase function, g is the asymmetry factor determined by integrating the phase function over all phase angleswith cos(1808 2 a) weighting; a negative value signifies backscattering particles and a positive value signifies forward-scattering particles. In a 2-term Henyey–Greenstein phase function, g1 and g2 are the respective asymmetry factors of separate backscattering and forward-scattering terms,f is a partition coefficient describing how to linearly combine the two terms, and geff is the effective asymmetry factor of the overall 2-term function.

guided by the positions of stereogrammetric control points quoted there for each parameter was estimated by cyclingthat parameter through a series of values, performing aand the satellite’s limb. (See Fig. 2 in Simonelli et al. 1993

for examples of the Phobos shape model overlayed on gradient search at each step to optimize the other Hapkeparameters, and examining whether the resulting opti-Viking images.) At each sunlit pixel, we interpolated along

the shape model to determine photometric incidence, emis- mized rms residuals show a deep minimum, or only a shal-low one, at the overall best fit. Figure 1 shows the goodnesssion, and phase angles, and measured the calibrated re-

flectance (usually referred to as I/F, where I is the reflected of the fit as a function of the incidence, emission, and phaseangles, and in Table III the best-fit Hapke function is usedintensity and fF is the plane-parallel solar flux incident on

Phobos in the Viking clear filter). At high solar incidence to generate useful global quantities such as the geometricalbedo and mean normal reflectance.angles, even small errors in surface slope can cause large

errors in the photometric data; accordingly, data at inci- Because Viking provides one Phobos image at a 5 1.58and two at a 5 38, but no other photometrically usefuldence angles $858 were excluded. We also excluded satu-

rated data (one area on the bright rim of Stickney in image images (near-global views) until phase angles beyond 108(cf., Table I), the best-fit opposition surge amplitude B073b03). Each image’s final photometric data file was pro-

duced by binning and averaging its data in 58 bins of photo- and width h have large uncertainties. However, even withthe large error bars, B0 is constrained to be $3. Such ametric latitude and longitude.

The data from the 22 images were fit with a Hapke high value is surprising; the original derivation by Hapke(1986) stipulated B0 # 1, and while this requirement hasphotometric function; see Hapke (1981, 1984, 1986), and

Table II, for definitions of this function’s available free been relaxed during the current debate about the surge’scause (hiding of interparticle shadows vs a coherent-back-parameters. The fitting procedure, inherited from Hel-

fenstein et al. (1994, 1996), uses a combination of grid scatter interference effect; e.g., Bowell et al. 1989, Hapkeet al. 1993), values $3 are still considered abnormally high.searches and gradient searches to find the Hapke parame-

ters which minimize the rms residual between observed We are confident that the Viking Phobos data, taken atface value, require such a high B0 for several reasons: (1)and theoretical disk-resolved reflectances. The resulting

best-fit parameters are shown in Table II. The uncertainty We tried an alternate fit where B0 and h were fixed at


FIG. 1. The goodness-of-fit for modeling Viking Phobos data with a global-average Hapke photometric function. Panel (a) shows, as a functionof phase angle, the best fit that is possible using the B0 and h determined for Gaspra by Helfenstein et al. (1994) and a 1-term Henyey–Greensteinparticle phase function; (b), (c), and (d) show the best fit overall, corresponding to the Phobos Hapke parameters in Table II, plotted vs the phase,incidence, and emission angles, respectively. Disk-resolved reflectances I/Fobs sampled from across the surface of Phobos in 22 clear-filter imagesare ratioed to reflectances I/FHapke predicted for the same viewing geometries; the resulting ratios have been binned and averaged in 18 bins of eachphotometric angle. Error bars are standard deviations indicating the scatter among the ratio values in each bin; the horizontal line on each plotrepresents a perfect fit between observation and prediction. Note the opposition-surge misfit, and the overall concave-upward trend, in panel (a),as compared to the much-improved fit (flatter trend) in panel (b).

values previously determined for Gaspra (Helfenstein et al. be explained as an artifact if the three opposition-surgeimages are brighter than they should be, relative to images1994), an irregularly shaped object whose opposition surge

is well constrained and whose B0 value of 1.63 is typical at other phases, by only 10–20% (cf., Fig. 1a). A brightnessdifference of this size is possible if these three imagesof recent Hapke fits to inner-Solar-System objects (cf.,

Table II). The resulting fit was much poorer than the nomi- see an unusually high-albedo side of the satellite or havecalibration problems relative to the rest of the data setnal, high-B0 fit (compare the opposition-surge portions of

Figs. 1a and 1b). (2) B0 stays high whether we use a 2- (although the map generated in the next section suggeststhat the albedo of the side of Phobos seen in these imagesterm or 1-term Henyey–Greenstein particle phase function

(see the footnotes to Table II). (3) Efford (1989) derived is only slightly higher than average, by much less than 10–20%).a similarly high B0 in a disk-integrated analysis of the

Viking Phobos images. Note, however, that it would not Other details regarding the Hapke fit are worth noting:(1) Phase function of regolith particles: We achieved atake much of a change in the data to produce a significant

change in B0: B0’s departure from ‘‘normal’’ values could significantly better fit with a 2-term Henyey–Greenstein

56 SIMONELLI ET AL.

TABLE III state that our results confirm the strong opposition surgeBasic Photometric Quantities for Phobosa present in the Viking Orbiter data for this satellite, as

originally reported by Klaasen et al. (1979) and reiteratedGeometric albedo p 0.071 6 0.012b

by Efford (1989). (3) The surface of Phobos has a macro-Phase integral q 0.30 6 0.04b

scopic roughness only marginally greater than those ofSpherical albedo A 5 pq 0.021 6 0.005b

Phase coefficient b 0.033 6 0.004c Deimos, Ida, and the Moon (u slightly above 208 for theNormal reflectance rn 0.071 6 0.012b former, vs 208 or slightly below 208 for the other three

bodies) and is somewhat smoother than the surface ofa Calculated from the global clear-filter photo-

Gaspra.metric function, integrating over a sphere whereFigure 2d in Thomas et al. (1996) presents a more de-necessary. The error bars quoted for p and rn are

so large because of the large uncertainties in the tailed comparison of the relative phase behaviors of theopposition surge amplitude B0. surfaces of Phobos and Deimos. Over a 5 10–818 these

b Consistent, within the uncertainties, with values moons have similarly shaped phase functions, with thedetermined by Klaasen et al. (1979) and Pang

surface of Phobos being 20–30% darker than that ofet al. (1983).Deimos; but thanks to the former’s stronger oppositionc Evaluated over phase angles 158–308. Units are

magnitudes/degree. surge, the near-opposition reflectances of the two bodiesare virtually identical.

III. ALBEDO MAPfunction than with a 1-term Henyey–Greenstein (e.g., com-pare Figs. 1a and 1b at moderate-to-high a); but with no A. Generation of the MapPhobos data at phase angles beyond 1238, it is difficult

The generation of a global albedo map requires its ownto constrain the value of the 2-term function’s forward-distinct set of clear-filter Viking images. The images mustscattering parameter g2. Accordingly, we chose to holdcover as much of Phobos as possible, and since we are nog2 fixed at 0.66, the value determined for the Moon inlonger required to sample a wide range of incidence andHelfenstein et al. (1997).1 (2) Macroscopic roughness of theemission angles, we are free to use images where the satel-surface: The roughness parameter u is by far the best-lite fills the frame. Low-phase images are preferred becauseconstrained parameter; the plot of optimized residual vsthey can be extrapolated to zero phase with less uncertaintyu has a deeper, more U-shaped minimum than the corre-and are freer of shadows, but the three images within thesponding plots for other Hapke parameters. (3) Emission-opposition surge should be avoided because they representangle trend: The data set’s incidence-angle and emission-a distinctly different regime of photometric behavior fromangle trends cannot both be fit by the same Hapke function,other phase angles and because they have poor spatiala sign that the data are being biased slightly by albedoresolution. Accordingly, we used images from a limitedvariations and/or shape-model uncertainties. The compro-range of relatively low phase angles, specifically a 5mise that best fits the important phase-angle trend, and108–508.minimizes residuals, is one that models the incidence data

The 18 images included in the albedo map are listed inwell at the expense of a poorer emission-angle fit (see theTable I. Note that more than half of these images havesloping trend in Fig. 1d).subspacecraft longitudes clustered at 2208–2608W, domi-In addition to presenting the Phobos results, Table IInated by two high-resolution imaging sequences at a 5lists analogous Hapke fits derived elsewhere for Deimos,108–158. Elsewhere on the satellite, longitude coverage isGaspra, Ida, and the Moon. This comparison reveals threesparser and phase coverage not quite so favorable. For atrends: (1) As expected from the darkness of the martiansmall part of Phobos there are no usable Viking imagesmoons, Phobos’ single-scattering albedo is comparable toin the required phase-angle range; these areas appear blankthat of Deimos and smaller than those of Gaspra, Ida, andin the final albedo map.the Moon. (2) If we emphasize B0’s role as a tracer of the

The images were calibrated and aligned with the Phobosrelative amplitude of the opposition surge, we concludeshape model. If we assume that all parts of the satellite havethat Phobos may well have a larger surge than any of thethe limb-darkening and phase-angle behavior predicted byother bodies listed. Given the possible reservations aboutthe global Hapke function (see further comments on thisour best-fit B0 value, however, it may be safest to simplybelow), we can use the function to correct for these photo-metric effects. In particular, the I/F of each pixel was con-

1 This value of g2 appeared in the originally submitted version of Hel- verted into a normal reflectance rn, the reflectance that thefenstein et al. (1997). In the final published version of that paper, the

surface would have if incidence, emission, and phase anglesMoon’s g2 had changed slightly to 0.64. This change is small enough thatwere all equal to 08. The images were then transformedit was not deemed to be worth altering the value of g2 being adopted

for Phobos. into sinusoidal map projections (cf., Simonelli et al. 1993),


FIG. 3. Histogram showing the distribution of clear-filter normal reflectances in the Phobos albedo map. Note the ‘‘shoulder’’ produced by thelow-albedo material to the west of Stickney.

trimmed to remove the most obvious artifacts of the photo- mainly to the immediate east and south of Stickney. (2)Dark material (rn P 0.05–0.07), located mainly to the westmetric-correction process (near terminators, or where the

shape model’s longitude lines converge at the poles), and of, and also on the floor of, Stickney. (3) Intermediate-albedo material (rn P 0.07–0.08), which is less spatiallypieced together using a seamless mosaicking procedure

that employs spatially variable weighting of data in overlap confined than the other classes, occupying almost the entireeastern half of the map (i.e., the anti-Stickney hemisphere).areas (a procedure developed by Helfenstein et al. 1989).

Finally, the resulting sinusoidal albedo map was trans- It is conceivable that image-to-image calibration uncer-tainties, or unaccounted-for regional variations in phaseformed into the normal-cylindrical projection shown in

Fig. 2 (scale 5 pixels/degree at the equator); a histogram behavior, could be causing some of the observed albedocontrasts. Accordingly, we have examined whether theof the associated normal reflectances is shown in Fig. 3.

Although the sinusoidal and normal-cylindrical projections most important of these albedo boundaries appear in otherphotometrically corrected Viking images not included inare equal-area only when mapping a sphere, the histogram

has been generated with radius-squared weighting so as to the albedo map. This examination verifies that the albedopatterns in Fig. 2 are real, but also indicates the magnituderepresent accurately the relative fraction of the surface

area that has various albedos. of possible errors in the albedo map: (1) Images that showthe same region at similar photometric geometries wereMost of the normal reflectances are in the range 0.06–

0.10. The highest-albedo feature on the satellite is the seen to differ in reflectance by up to P10% (e.g., a differ-ence of up to P0.007 out of a reflectance of 0.07), confirm-northeast rim of the large crater Stickney, corresponding

to the portion of the rim that has the highest concentration ing that calibration uncertainties are as large as anticipated.(2) We show in Section IV that Stickney’s floor, and to aof grooves (see Fig. 4 and also the groove mapping by

Murchie et al. 1991). This bright feature is largely within lesser degree the dark material west of Stickney, havephase behaviors that differ slightly from the global average.the area of hummocky topography that Thomas (1979)

interpreted as Stickney ejecta and may be the part of the Given the direction and size of these differences, and thefact that our albedo map is extrapolated from a . 108ejecta that has been most heavily disturbed, recycled, gar-

dened, or otherwise kept ‘‘fresh.’’ Globally, the map can using a global photometric function, we estimate that themap exaggerates how dark Stickney’s floor appears bybe divided into three albedo classes, which are reasonably

separated geographically and which are color-coded in Fig. P10% (and may be causing a similar, but smaller, exaggera-tion for the material to Stickney’s west).2b: (1) Bright material (clear-filter rn P 0.08–0.12), located

58 SIMONELLI ET AL.

B. Comparison with the Locations of the Murchie et al. ally consistent with the color/albedo relationship noted inthe VSK data by Murchie et al. (see those authors’ Fig. 7,Color Unitsand Fig. 5 of Murchie and Erard) with the exception, once

Although visible-light Viking Orbiter data fail to show again, of Stickney’s floor. Note that the new correlationscolor patterns on Phobos, Murchie et al. (1991) discovered go farther than the original Murchie et al. color/albedocolor variations across the leading and anti-Mars hemi- relationship in two ways: (1) The visible-light ‘‘albedos’’spheres of the satellite using wide-band visible and near- used by Murchie et al. were reflectances taken directly frominfrared images from Phobos 2’s VSK camera (wavelength a single (low-phase) VSK image without photometric cor-ranges 0.40–0.56 and 0.78–1.10 em, respectively). It is of rection; and even in the updated VSK work by Murchieinterest to see to what extent these color units can be and Erard, albedos were extrapolated to zero phase with-correlated with the albedo patterns in Fig. 2. out any correction for limb-darkening (incidence and emis-

The most prominent color units identified by Murchie sion angle) behavior. It is an improvement to compare theet al. were: (1) A spectrally ‘‘blue’’ material (ratio between colors with normal reflectances that have been correctedwide-band visible and near-IR reflectances as high as 1.4) for both phase and limb-darkening effects. (2) Our color/on the walls and floor of, and to the immediate southwest albedo systematics cover a larger area than just the oneof, Stickney. (2) A ‘‘bluish gray’’ material (visible/NIR side of the satellite considered in Murchie et al.’s Fig. 7ratio slightly above 1), covering a broad area to Stickney’s and Murchie and Erard’s Fig. 5, suggesting that the color/immediate west. (3) ‘‘Reddish gray’’ material (visible/NIR albedo relationship reported by those authors for one sideratio slightly below 1) dominating the anti-Stickney hemi- of Phobos extends to other parts of the satellite as well.sphere. Note, however, that the absolute calibration of Murchie et al. interpreted the observed color variationsthese color-ratio values as originally published in Murchie as compositional differences: based on the placement ofet al. is now thought to be incorrect. Specifically, Murchie, the color units, they proposed that the Stickney-formingpersonal communication (and also Murchie and Zellner impact penetrated far enough below the satellite’s surface1994) recommends multiplying the Murchie et al. visible/ layer to excavate and emplace around Stickney, a bluish,NIR ratios by 0.84, on the basis of the HST spectrum of possibly mafic, material. Our data indirectly support suchPhobos (Zellner and Wells 1994) and improved ground- an interpretation. In laboratory measurements of carbona-based observations of the martian surface region that was ceous chondritic meteorites, which are as dark as Phobos,used to calibrate the VSK images. This revised color cali- the samples become both brighter and redder as particlebration is used in the updated VSK data analysis presented size decreases (e.g., Johnson and Fanale 1973). Accord-by Murchie and Erard (1996). We reproduce two of Mur- ingly, the fact that Phobos’ high-albedo regions are actuallychie et al.’s VSK images in Fig. 5a, using the new color- among the bluest on the satellite, rather than the reddest,ratio values from Murchie and Erard. suggests that the color and albedo patterns are not domi-

With the help of the Phobos shape model, we have nantly due to particle-size differences and must be pro-synthesized what the albedo patterns of our Viking map duced by some other effect, such as compositional varia-look like at the viewing geometries of these two VSK tions. (Application of these laboratory results to Phobos

should still remain valid in spite of the HST determinationimages. The resulting synthetic ‘‘albedo images’’ are in-that the satellite’s leading hemisphere is not spectrally simi-cluded in Fig. 5a for comparison. We find strong correla-lar to C asteroids; Zellner and Wells 1994.)2tions between our three visible-light albedo classes and the

Murchie et al. color units. Our high-albedo class tends tooccur in the same locations as the Murchie et al. ‘‘blue’’ 2 According to Murchie and Erard (1996), the ‘‘bluer’’ areas on

Phobos—the materials thought to be associated with Stickney ejecta—unit; in particular, the bright feature at Stickney’s NE rimlack bright circular crater rims and bright arcuate rim segments. Usingcorrelates approximately with the spectrally ‘‘bluest’’ re-the albedo map in Fig. 2, we can make a more complete tabulation ofgion on Phobos (these two regions overlap only slightly, the occurrence of such rims and test the hypothesis that they are missing

but this may just reflect the large uncertainties involved in regions dominated by Stickney ejecta. We find that the only longitudeson the map that lack bright rims are to the immediate west of Stickneyin trying to overlay a Viking-based shape model on the(from 608W westward to the gap near the map’s left-hand edge), an areaVSK images). Similarly, our low-albedo materials tend towhich should indeed contain the majority of this crater’s ejecta blanketcorrelate with the ‘‘bluish gray’’ unit, and our intermediate-(Dobrovolskis and Burns 1980). However, the observed presence of bright

albedo materials tend to match up with the ‘‘reddish gray’’ rims in the longitudes immediately east of Stickney poses a significantunit. The most significant exception to these color/albedo problem for the hypothesis: while there is indeed expected to be less

Stickney ejecta in this area (Dobrovolskis and Burns 1980), ejecta shouldcorrelations is Stickney’s floor, a ‘‘blue’’ area that is darkby no means be absent even as far as 508 east of Stickney, depending onrather than bright.Phobos’ orbital position at the time of this crater’s formation (ThomasBy co-registering the VSK images and the ‘‘albedo im- 1997). We conclude that there is an imperfect association between bright

ages,’’ we have quantified these color/albedo systematics. circular rims/bright rim segments and areas lacking in Stickney ejecta,at least when judged using the albedo map in Fig. 2.The resulting trends, plotted in Figs. 5b and 5c, are gener-


The strong correlations between the albedo and color imaging sequences were compared visually; we also ratioeddata, and the close association of our map’s albedo patterns the images from each of the five lowest-phase sequenceswith Stickney, support the dominant role the formation of to 242a21, an image from the highest-phase sequence. Athis crater has played in the evolution of the surface of representative example of the ratioing results, using nu-Phobos. Stickney’s role in global patterns, and the associa- merator images from the lowest-phase imaging sequence,tion of many of Phobos’ smaller albedo features with is shown in Fig. 6.grooves and small craters, place this satellite in sharp con- Some isolated bright rims in the area under consider-trast to its sister moon Deimos. Although the mean normal ation do exhibit unique phase behavior. However, thesereflectance and range of normal reflectances are similar crater and groove rims are so narrow and difficult to regis-on both satellites, the albedo patterns on Deimos are domi- ter that they are not well served by image-ratio techniques,nated not by discrete cratering events a la Stickney but by and must be studied using specialized contrast measure-horizontal mixing of the regolith, manifested primarily by ments (see part C below). The emphasis of the image-albedo ‘‘streamers’’ running downslope from ridge crests ratio work is to provide an overview of phase-behavior(Thomas et al. 1996). variations, especially on regional scales.

In Fig. 6, and in the data set as a whole, the ratio mapsare bland over most of the region of Phobos under consid-IV. VARIATIONS IN PHASE-ANGLE BEHAVIOReration, indicating that the albedo pattern remains constantACROSS THE SURFACEfrom one photometrically corrected image to the next. The

Because there are so few Viking images within the oppo- only significant albedo changes occur in the southwesternsition surge, and those images are low resolution, little can and northeastern corners of the region (these are unusuallybe said about variations in the opposition effect across the dark areas on the ratio images) and in crater floors (thesesurface of Phobos. Accordingly, when investigating region- are unusually bright in the ratios); we believe that noneto-region differences in photometric behavior our empha- of these effects can be interpreted as evidence of unusualsis is on phase behavior at phase angles outside the surge. phase behavior. The change in the northeastern cornerWe search for these variations with the same basic ‘‘tool’’ represents the effects of small uncertainties in the Phobosused in albedo mapping: clear-filter images that have been shape model, made visible because this region is close tophotometrically corrected with the global Hapke function the terminator in the higher-phase image in use (242a21).and map-projected. If all parts of the surface have the same Regarding the southwestern corner, the boundary betweenlimb-darkening and phase-angle behavior as the global- this feature and the rest of the mapped area correspondsaverage function, the photometric-correction process will to a major boundary in Phobos’ shape, specifically therecover the normal reflectances of all regions accurately gentle ridge separating the equatorial region from the satel-no matter what phase angle the image originally came lite’s south-polar ‘‘facet.’’ At all phase angles under consid-from, and the albedo pattern will be the same from one eration, incidence and emission angles are more glancingphotometrically corrected image to the next. Conversely, in the south-polar facet than in the equatorial region. Thusif the albedo pattern changes significantly between photo- the polar region is always subject to more of a limb-darken-metrically corrected images from different phase angles, ing correction than regions to the north, a situation thatthis indicates that there are local deviations from the global will again exaggerate the effects of small shape-model un-phase behavior. certainties. Finally, as to the craters in question, they are

so small that their shapes are not included in the PhobosA. General Search for Deviations from the shape model, making incidence and emission angles for

Global Phase Behavior the crater floors inaccurate. In particular, slightly differentparts of the crater floors are visible to the spacecraft atWe begin with a data set which provides an overviewdifferent phase angles, and the parts that are visible haveof a significant portion of Phobos with both good phasemore glancing Sun angles in the higher-phase images thancoverage and reasonable spatial resolution. This data setin the lower-phase images; but because the craters are notinvolves six moderately high-resolution imaging sequencesin the shape model, the photometric-correction processfrom Viking orbits 242a, 246a, 250a, and 252a, which coverdoes not remove these changing effects. Thus the craterlongitudes 2008–3008W at a range of different phase anglesfloors appear bright in the ratio maps because of uncor-between 108 and 508. Because these images cover only arected Sun-angle effects rather than unique phase be-portion of the satellite, we opted for simple-cylindricalhavior.projections and an increased scale of 10 pixels/degree,

Since this excellent data set for longitudes 2008–3008Wwhich comes within a factor of two or better of preservingshows no clear evidence of deviations from global-averagethe intrinsic resolutions of the images. The albedo patterns

in mapped, photometrically corrected images from the six phase behavior, we conclude that the surface of Phobos,


overall, is reasonably homogeneous in this regard, with behavior. Conversely, Stickney’s floor shows a tilted trend,indicating that unique phase behavior for the crater floorunusual phase behavior limited to isolated areas.is the source of the contrast change with phase angle.

B. Stickney Figure 7 suggests that the contrast between Stickney’srim and the dark material immediately to Stickney’s westWhen looking for anomalous phase behavior among iso-may also vary somewhat with phase. Measurements verifylated features of special interest, the obvious starting pointthat the latter material, like Stickney’s floor, darkens withis Stickney, with its dominant role in the satellite’s colorincreasing phase faster than ‘‘typical Phobos,’’ but indicateand albedo patterns. The shape of Stickney is moderatelythat this phase behavior is more poorly defined than, andwell constrained by stereo data. Accordingly, the Phobosdeviates from the global behavior less than, the behaviorshape model does include a viable representation of thisof Stickney’s floor.large crater, and this is one case where we can include a

To understand better the unusual phase behavior ofcrater floor in our search for phase-behavior variations.Stickney’s floor, we fit its photometric data with a HapkeThe images that were used in Section II to determinefunction. The limited range of incidence, emission, andthe global-average photometric function provide good cov-phase angles available for this region precludes a com-erage of Stickney at six different phase angles in the rangepletely independent fit, so we fixed some of the Hapke1.58–478. Photometrically corrected images from this dataparameters at their global-average values. The exceptionsset are shown in Fig. 7 in the same sinusoidal, 5 pixels/were (1) we let the single-scattering albedo w vary (todegree format which was used when mosaicking togetheradjust for any albedo difference between Stickney’s floorthe global albedo map. This format preserves the resolu-and ‘‘typical Phobos’’) and (2) we let the particle phasetion of the images used.function’s backscattering parameter g1 , and the macro-In Fig. 7, the albedo contrast between Stickney’s brightscopic roughness u , vary (to model the floor’s unique phasenortheast rim and darker floor increases systematically to-behavior). The new fit, shown in Fig. 8c, suggests that theward higher phase angles.3 This trend indicates the pres-material in the floor of Stickney is slightly darker thanence of local deviations from the global-average phasetypical Phobos material (w values are 0.06 and 0.07, respec-behavior. To determine whether the unique behavior oc-tively), slightly more backscattering (g1 values are 20.25curs on the rim, the floor, or a combination of the two, weand 20.20, respectively), and significantly rougher (u val-went back to the original, photometrically ‘‘uncorrected’’ues are 318 and 228, respectively). The macroscopic-version of each image in Fig. 7 and measured photometricroughness effects could be related to the massive slumpingangles and calibrated reflectances from each pixel insidethat is hinted at in the Viking images of Stickney’s floor;two carefully chosen polygonal regions, one on the north-the low resolution of the Stickney images makes it difficulteast rim and one on the crater floor (Fig. 8a). As usual, weto be more specific.binned and averaged in photometric latitude and longitude

and excluded the saturated part of the rim in image 73b03.C. Bright Rims of Smaller Craters and Grooves

Figure 8b shows how well the global-average photometricfunction fits the resulting data as a function of phase angle. It has been reported that small bright albedo features

on Phobos, especially bright rims on grooves and on cratersStickney’s bright northeast rim shows a flat trend to withinthe uncertainties; this means that the rim’s only deviation smaller than Stickney, stand out in great contrast to the

surrounding surface at low phase (typically a 5 78–158)from the global function is an albedo difference, with noevidence of any deviation from the global-average phase and get much harder to see as the phase angle increases.

Unfortunately, the published descriptions have beenpurely qualitative (e.g., Thomas 1979) or, at best, semi-3 Since the lower-phase images in Fig. 7 have poorer spatial resolutions,quantitative; for example, Avanesov et al. (1991) andand since camera modulation transfer function (MTF) effects tend to

reduce the contrast at scales near the limit of resolution, MTF effects Shkuratov et al. (1991) quote the amount of contrast exhib-may be contributing to the visual impression that the contrast between ited by the rims at low phase (20–30% brighter than theirStickney’s rim and floor is lowest at lower phase. However, MTF effects surroundings) but do not provide similarly quantitativeshould not be influencing significantly the reflectance measurements

statements for higher phase angles, saying only that theshown in Fig. 8, since these measurements involve averaging data overcontrast ‘‘disappears’’ at the latter geometries. The mate-polygonal areas of pixels and thus are never made near the limit of

spatial resolution. rial responsible for this unusual phase behavior has been

FIG. 4. Outline showing the location of the brightest albedo feature on Phobos, on the northeast rim of Stickney (cf., Fig. 8a), superimposedon a high-pass-filtered mosaic produced from Viking images 854a81, a82, and a83. The albedo feature is located on the portion of the rim that hasthe highest concentration of grooves.

62 SIMONELLI ET AL.

FIG. 2. Normal-cylindrical map of Phobos showing the distribution of clear-filter albedos. Panel (a) shows the original b/w map, pieced togetherfrom 18 photometrically corrected images and stretched so that pure black and pure white represent normal reflectances of 0.05 and 0.12, respectively.In (b), the same map has been color-coded; green, orange, and blue hues emphasize the three albedo classes discussed in the text. Unexpectedlybright areas at high latitudes and at the western edge of the map (the most extreme of which are coded as white in (b)) are artifacts due to smalluncertainties in the Phobos shape model, which become exaggeratedly visible in photometrically corrected images near terminators and near thepoles. The map scale is 5 pixels/degree at the equator, which does not always preserve the images’ intrinsic spatial resolutions but acceptably discernsregional albedo patterns.

interpreted to either have a different (more porous? The images used in the general phase-behavior searchin part A of this section form an excellent data set forrougher?) texture than its surroundings (e.g., Thomas

1979) or have a greater abundance of a fresher, transparent, addressing quantitatively the phase behavior of bright rims.In particular, a trio of prominent bright-rimmed cratershigher-albedo regolith component (Avanesov et al. 1991,

Shkuratov et al. 1991). just north of the equator near longitude 2608W can be

FIG. 5. (a) Correlations between the locations of Phobos’ visible-light albedo classes and visible/near-IR color units. In all cases, the intensityis provided by visible-light images from the VSK camera on Phobos 2; subspacecraft points are 18S, 2098W (left-hand images) and 18S, 1128W (right),and north is up. In the top row, the hue represents the normal reflectances from our Viking clear-filter albedo map (cf., Fig. 2b), which has been‘‘wrapped around’’ our Phobos shape model using those same subspacecraft points and registered as well as possible to the VSK images. (At gapsin the albedo map, the intensity image is shown uncolored.) In the bottom row, which is adapted from Plate 1b of Murchie et al. (1991), the huerepresents visible/NIR ratios determined from VSK images. (The numbers on the associated color bar reflect a new, improved calibration of thevisible/NIR ratios from Murchie and Erard 1996.) Areas coded with an orange hue occur in approximately the same locations in each of the left-hand images; areas coded with green occur in the same locations in each of the right-hand images; and areas coded blue occur in the same locationsin each of the right-hand images, at least to Stickney’s southwest and at that crater’s northeast rim. The most significant deviation from thesecorrelations is the floor of Stickney, which is coded green in one row of images and blue in the other.

63

FIG. 5—Continued. (b, c) Color/albedo trends derived from the images in (a). In (b), data have been sampled from all parts of Phobos in view;the number of pixels falling on different locations on the plot is represented by variations in the ‘‘density’’ or ‘‘darkness’’ of the plot. In (c), datahave been limited to five selected polygonal areas on the images, to identify the color/albedo relationships of specific parts of the satellite.

64

66 SIMONELLI ET AL.

FIG. 6. An example of the results from our general search for regional variations in phase behavior. (a) A simple-cylindrical map producedby mosaicking five photometrically corrected clear-filter images from orbit 250a (images a12 through a16, original phase angles 108–148), stretchedso that pure black represents a normal reflectance of 0.03 and pure white is a normal reflectance of 0.13. (b) A similarly stretched, photometricallycorrected map produced from the single clear-filter image 242a21 (P508 phase). White areas around the boundaries are caused by small uncertaintiesin the shape model becoming exaggeratedly visible near the terminator and the pole (see text). (c) The ratio of (a) and (b). This is the ratio of theoriginal, unstretched versions of these maps, i.e., a direct ratio of normal reflectances; pure black represents a ratio of zero, middling gray is a ratioof 1, and pure white represents a ratio of 2. Most of the ratio map is bland, indicating little variation in phase behavior across the mapped area.Crater floors, and the corners of the map (latitudes south of 2408 and longitudes east of about 2208W), should be ignored due to artifacts, asexplained in the text.

followed through this data set’s six different phase angles rims, and then used these profiles to measure the contrastbetween the rims and their surroundings at each available(108–508), and a set of bright-rimmed grooves farther to

the east, near longitude 2208W, can be seen at five of these phase angle. That figure also shows the results of similarcontrast measurements for two small ‘‘bright spots’’ thatphase angles.

In Fig. 9 we return to the photometrically corrected lie immediately south of the craters, spots which couldthemselves be related to tiny, unresolved craters. Finally,simple-cylindrical projections used in part A and zoom-in

on the portion of these maps that contains the trio of Figs. 11 and 12 present a comparable suite of photometri-cally corrected images, and the associated contrast mea-craters. As in part A, the changes in crater floors from one

image to the next are merely uncorrected Sun-angle effects surements, for the bright-rimmed grooves that lie to thesecraters’ east. Note that we use a separate set of slightlyrelated to these craters’ absence from the shape model;

accordingly, our examination of Fig. 9 focuses instead on higher-resolution map projections (scale 15 pixels/degree)for the groove study, because the albedo features on groovethe contrast between the bright rims and the surrounding

inter-crater regions. In Fig. 10 we have made normal- rims are smaller and narrower than those on the crater rims.The results of these various contrast measurements arereflectance profiles across the images in Fig. 9 along a line

through the two craters with the most prominent bright as follows: (1) We can only partly confirm the statements


FIG. 7. Montage of photometrically corrected clear-filter images of Stickney, showing that the contrast between its bright rim and darker floorincreases noticeably toward higher phase. Picture numbers and phase angles are indicated; note that the data shown for 38 phase represent averagingthe results from two different images. The images have been cropped from sinusoidal map projections (north is up), and are stretched so that pureblack represents a normal reflectance of 0.03 and pure white is a normal reflectance of 0.15. At two of the three highest phase angles there is anunusually bright feature in the middle of the right edge of the image; this is an artifact produced by a small uncertainty in the shape model, madevisible because it is close to the terminator in the images in question.

by Avanesov et al. (1991) and Shkuratov et al. (1991) that by one of the two bright spots in Fig. 10d and one of thesix groove rims in Fig. 12b. (Another of the crater rims,crater and groove rims are 20–30% brighter than their

surroundings at low phase. Specifically, we confirm that the eastern rim of crater B, actually shows an increase incontrast with increasing phase, although measurements ofsuch a contrast is typical of Phobos’ bright crater rims and

spots (Figs. 10c and 10d), but find that the bright groove this rim are complicated by the fact that it abuts a largedegraded crater whose shape may be imperfectly realizedrims seen by Viking are much subtler features (less than

10% contrast even at their most visible; Fig. 12b). This by our Phobos shape model.) Furthermore, even amongthose rims that are harder to see at higher phase there isdiscrepancy may reflect the fact that our low-phase Viking

images examine a different set of grooves, at a slightly no fixed rule about the strength or details of the effect;for example, the crater rims and bright spots that behavedifferent phase angle, than the low-phase Phobos 2 images

used by the earlier authors. (2) Our measurements confirm in this fashion are still reasonably visible even at a 5508, whereas many of the bright groove rims have trulythat many of the bright rims do become harder to see at

higher phase, in the sense that the contrast with their inter- disappeared by this phase angle.Among the different bright rims examined, only onecrater surroundings drops noticeably with increasing phase

angle. However, not all bright rims exhibit this expected contrast behavior exhibits enough self-consistency to war-rant special attention: five of the six groove rims darkenbehavior: one of the four investigated crater-rim segments,

the western rim of ‘‘crater B,’’ shows little or no contrast with increasing phase faster than the average Phobos sur-face, starting out P7–8% brighter than their surroundingschange with phase (Fig. 10c), a constancy that is shared

68 SIMONELLI ET AL.


FIG. 8. Phase-behavior measurements of Stickney materials. (a) Outlines showing the parts of Stickney’s floor and bright northeast rim thatunderwent separate photometric sampling. The underlying image is the lower-right image in Fig. 7. (b) As a function of phase angle, we show howwell the global-average Hapke function from Table II fits photometric data taken separately from Stickney’s rim and floor. The data were sampledfrom the seven images whose photometrically corrected versions are shown in Fig. 7; ratios between observed and predicted reflectances I/F werebinned and averaged in 18 bins of phase angle, producing the usual standard-deviation error bars. The horizontal dashed line, which is the meanvalue of the open circles, passes through all those points’ error bars, indicating that the phase behavior of the bright rim is not discernably differentfrom that of the global function. The slope exhibited by the solid circles, however, shows that Stickney’s floor darkens with increasing phase fasterthan ‘‘typical Phobos’’ (compare these points with the solid line, which represents a perfect fit to the global function). (c) Goodness-of-fit plotsshowing the best fit achieved for the Stickney-floor data upon letting some of the Hapke parameters vary from their global-average values. Whichparameters were varied, and their final best-fit values, are described in the text; reflectance ratios are again binned and averaged in 18 bins.

at 138 phase and dropping to zero contrast, or close to it, (i.e., the required perturbation in g1 would be even smallerif paired with a plausible increase in u ), and thus cannotat 508 phase (Fig. 12b). Incidence and emission angles doresolve whether the bright groove rims are caused primar-not vary much from groove-to-groove or from one phaseily by differences in surface texture or differences in rego-angle to the next; incidence angles are always 248–428 andlith transparency.emission angles are 138–338. With such a limited range of

low-to-moderate incidence, emission, and phase angles, aD. Dark Deposits in the Floors of Smaller Craterschange in macroscopic roughness does not have enough

leverage to explain the groove rims’ contrast behavior by Goguen et al. (1978) reported that dark deposits visibleitself (i.e., approximate Hapke calculations suggest that in the floors of some small craters on Phobos drop inthese rims would require an implausibly high roughness brightness with increasing phase more rapidly than theof u . 408). A viable alternative is to make the bright average surface of the satellite. This conclusion was basedgroove rims slightly more backscattering than typical on profiles across images and the associated measurementsPhobos; we estimate that g1 would only have to be per- of the contrast between the dark material and its surround-turbed to P20.26 from its global value of 20.20. Note, ings. Goguen et al. did not fit a photometric function tohowever, that the contrast data also allow for the possibility their observations, but did propose that the crater-floor

deposits are rougher than ‘‘typical Phobos’’ and could beof a combination of roughness and backscattering effects

70 SIMONELLI ET AL.

FIG. 9. Appearance of crater rims as a function of phase angle, focusing on a trio of bright-rimmed craters just north of the equator nearlongitude 2608W. These are photometrically corrected clear-filter images in simple-cylindrical projection (north is up), stretched so that pure blackrepresents a normal reflectance of 0.03 and pure white is a normal reflectance of 0.11. Changes in the appearance of crater floors from image toimage should be ignored, as these areas contain uncorrected photometric effects (see text); the important relationship is the contrast between thebright rims and the surrounding inter-crater areas, and how this contrast changes with phase (see the associated measurements in Fig. 10).

vesicular impact melts. We now reexamine the phase be- This is the only instance in this paper where such an alter-nate shape model is used.havior of these deposits using the Hapke function and

newly calibrated, photometrically corrected images. The resulting images are displayed in Fig. 13 and shownot only the crater we are focusing on but also smaller darkFollowing Goguen et al., we focus on the crater that

has the most extensive dark crater-floor deposits on the deposits in neighboring craters. The visual appearance fitsthe trend noted by Goguen et al. (1978): all dark depositssatellite, located at latitude 58S, longitude 2958W. This

crater was seen unsmeared by Viking in only a few clear- are much easier to see at high phase than at low phase,consistent with the fact that they darken faster with increas-filter images around 108 phase and a few clear-filter images

around 808 phase. We photometrically corrected the best ing phase than the rest of the satellite surface.Since we do not have an accurate shape or accurateimage from each of these sets and then transformed into

simple-cylindrical projections at 30 pixels/degree; this large photometric angles for the interior of the crater with themost extensive deposits, we cannot sample photometricscale fully preserves the intrinsic resolution of both images,

which is important given the small size of the dark deposits. data from it directly and must ‘‘bootstrap’’ our way asfollows. We made profiles across the images in Fig. 13 thatNote, however, that the crater in question is just large

enough to be included in the Phobos shape model, but cut across the two most prominent dark deposits on thiscrater’s floor (see Figs. 14a and 14b). These profiles allowedsmall enough not to be modeled well by the latter’s wire

grid. The crudeness of the crater model would lead to us to measure the contrast that each deposit makes withthe area between the two deposits, where the latter areaartifacts in the photometric-correction process (false new

contrast boundaries, etc.), especially in the higher-phase was assumed to be average Phobos material. At each phaseangle we averaged the contrast measurements for the twoimage. Accordingly, we chose to create a new version of

the 48-resolution Phobos shape model in which the crater deposits, to get our best estimate of the typical contrastbehavior of the dark material. Next, using the shape modelhas been removed. For consistency, we use this alternate

shape model for photometrically correcting and map-pro- where the crater has been removed, we went back to eachof the original unmapped images and measured photomet-jecting both the crater’s high-phase and low-phase images.


FIG. 10. Measurements of the contrast behavior of bright crater rims and bright spots. (a) The upper-right image from Fig. 9, annotated toshow the location of the profiles in the next panel and identify the craters and bright spots under study. (b) Profiles across the photometricallycorrected images in Fig. 9, using the profile location in (a). Between the two lowest-phase images, which have similar phase angles, the ‘‘background’’normal reflectance of the intercrater areas changes by almost 10% (i.e., a change of almost 0.007 out of a reflectance of 0.07); this discrepancyillustrates the maximum size of Viking-image calibration uncertainties.

FIG. 10—Continued. (c) The contrast between bright crater rims and the surrounding intercrater areas, illustrating that some of the rims dobecome harder to see at higher phase (crater A) but some do not (crater B). Contrast is measured from the profiles in (b) and is expressed as aratio between the normal reflectances of the rim and the intercrater background. For the solid circles, the background was determined by averagingthe reflectances of all the intercrater areas in a profile; in the highest-phase image, where the intercrater profile is far from flat, an alternate set ofcontrasts (open circles) was produced using background measurements that fit a sloping line to the parts of the profile immediately surroundingeach crater. Error bars (solid points only) reflect estimated uncertainties in the measurements of rim and background reflectances. (d) Contrastmeasurements for the bright spots, derived, in similar fashion, from profiles across the images in Fig. 9 (profiles not shown). Only one of the twospots becomes significantly harder to see at higher phase (spot D). The ‘‘interspot’’ areas of the associated profiles show significant structure, sothis time all backgrounds were measured using sloping lines.


FIG. 11. Photometrically corrected clear-filter images of a set of grooves near longitude 2208W, tracking how their bright rims (arrows) disappearwith increasing phase. These are simple-cylindrical projections (north is up), stretched so that pure black and pure white represent normal reflectancesof 0.05 and 0.10, respectively. The overall brightness of the scene appears to vary with phase angle because the strong stretch needed to make thesubtle groove-rims visible is exaggerating small deviations from the global photometric function. Changes in the appearance of crater floors fromone image to the next should be ignored, as these areas contain uncorrected photometric effects (see text).

ric angles from the point that lies at the center of the ellipse Unfortunately, however, the allowed range of solutionsdoes not provide useful constraints on the macroscopicdefined by the crater’s rim. Evaluating the global-average

Hapke function at these geometries gave us the reflectance roughness u , so we cannot corroborate Goguen et al.’sproposal that the dark deposits are unusually rough.I/F of average Phobos material at each phase angle. Finally,

by combining each of these ‘‘average Phobos’’ reflectanceswith the contrast measurement from the corresponding

E. Comparison with Deimosphase, we estimated the I/F that the dark-deposit materialwould have at each of the two measured photometric Thomas et al. (1996) found no evidence for significant

variations in phase-angle behavior across the surface ofgeometries. We have fit the resulting photometric measure-ments with a Hapke function, once again allowing only w, Deimos. Thus the two martian moons are similar in the

sense that each body is reasonably uniform overall withg1, and u to vary from the global-average values. Thereare three unknowns but only two data points, allowing a regard to phase behavior, but the moons differ in the sense

that isolated regions with unusual phase behavior do occurrange of possible solutions rather than a single best fit.The resulting parameter constraints (Fig. 14c) indicate on Phobos but not on Deimos. The occurrence of localized

photometric variations on one body but not on the otherthat the dark deposits have a lower single-scattering albedothan anything else measured on Phobos and are almost makes sense, given that Phobos’ albedo patterns are gov-

erned by discrete cratering events while Deimos’ albedocertainly more backscattering than the typical surface ofthe satellite (a more negative g1 value). These attributes are patterns are modified by creep-induced horizontal mixing

of the regolith (Thomas et al. 1996).consistent with a regolith made of dark, opaque particles.

74 SIMONELLI ET AL.

FIG. 12. (a) The upper-left image from Fig. 11, annotated to identify the groove rims whose contrast behavior has been measured. The verticallines delineate the western and eastern boundaries of the specific groove-rim segments under study. (b) Contrast behavior of the groove rims in(a), measured from the photometrically corrected images in Fig. 11. Each image was reprojected slightly so that a particular bright rim was alonga horizontal line of pixels, and by averaging reflectances along such a line we measured the mean normal reflectance of each rim segment; theseresults were then ratioed to the mean normal reflectances of visually bland polygonal areas immediately outside the grooves. Error bars werecalculated from the standard deviations on the measured mean reflectances. The contrast drops significantly toward higher phase for two of thethree northern rims and all of the southern rims, indicating a material that darkens with increasing phase slightly faster than the average Phobos surface.

V. CONCLUSIONS with a lower visible/NIR ratio (Murchie et al.’s ‘‘reddishgray’’ unit).

Our reexamination of the photometric data in Viking A search for phase-behavior variations on Phobos’ sur-images of Phobos confirms previous indications that the face shows that such effects are limited to isolated areas:satellite has a strong opposition surge and indicates that (1) Stickney’s floor darkens with increasing phase fasterthe brightest region on Phobos is the northeast rim of the than ‘‘typical Phobos,’’ as a result of being both slightlycrater Stickney, the portion of that rim with the highest more backscattering and significantly rougher than theconcentration of grooves. The Viking data also reveal the global average. The unusual roughness may be related topresence of three global albedo classes, reasonably sepa- the slumping hinted at in low-resolution images ofrated geographically: (1) Bright material is to the east and Stickney. (2) We confirm that in many cases the contrastsouth of Stickney, corresponding approximately to the lo- between bright crater and groove rims and their surround-cations on Phobos having the highest, ‘‘bluest’’ visible/ ings drops noticeably with increasing phase. However, notnear-IR ratio (Murchie et al. 1991). (2) The darkest mate- all bright rims exhibit this expected behavior—and overall,rial is to Stickney’s west, correlating with material having we must conclude that the photometric behavior, and byan intermediate visible/NIR ratio (Murchie et al.’s ‘‘bluish inference regolith characteristics, of bright rims on Phobosgray’’ unit). (3) Intermediate-albedo material dominates are quite heterogeneous. (3) We confirm that dark deposits

in the floors of smaller craters darken faster with increasingthe anti-Stickney hemisphere, corresponding to material


FIG. 13. Photometrically corrected clear-filter images from two different phase angles, showing several craters whose floors contain dark deposits.All such deposits are much easier to see at high phase, confirming that they darken faster with increasing phase than the average Phobos surface(cf., Goguen et al. 1978). These simple-cylindrical projections straddle the equator and cover the region from P3058W (left edge) to 2608W (rightedge); in both images, pure black and pure white represent normal reflectances of zero and 0.11, respectively. These images were produced with aspecial version of the Phobos shape model that does not include the shape of the largest crater shown (see text). Accordingly, the floors of allcraters, including the largest, vary in brightness between images due to uncorrected photometric effects.

phase than their surroundings and find that they are almost survey of the phase behavior of bright crater and grooverims would be useful; it would more clearly define thecertainly more backscattering than the average surface

of Phobos. typical phase curve of such materials, the degree to whichdifferent bright rims have different behaviors, and the geo-The association of global albedo features with Stickney,

and the variable photometric properties of isolated craters logical causes of both the typical behavior and the observeddifferences. Finally, it is important to expand our extremelyand grooves, reinforce interpretations that Phobos’ rego-

lith is emplaced and modified by discrete cratering events limited phase coverage of the dark crater-floor deposits,because only then will we be able to constrain the macro-and is not mixed horizontally by extensive downslope creep

as is apparently the case on Deimos. scopic roughness of these intriguing features.Most of the gaps in our photometric knowledge of

Phobos can be filled only by obtaining new observations ACKNOWLEDGMENTSwith Mars-orbiting spacecraft and, in some limited cases,

This research was supported by the NASA Planetary Geology andEarth-orbiting telescopes. This satellite’s underobservedGeophysics Program under Grant NAGW-2186. We thank R. Kline andopposition surge is a fruitful target for future studies, givenB. Carcich for image-calibration programming support and Spud software

the current indications of a strong surge and the hope that support, respectively. We appreciate thoughtful reviews by K. Klaasensome of the region-to-region variations in phase behavior and S. Murchie. We also thank S. Murchie for providing both slide and

digital versions of his specially processed VSK images.seen at a $ 78 may extend to lower phase angles. A global

FIG. 14. Measurements of the contrast behavior of dark deposits. (a) Close-ups of the images in Fig. 13, showing the locations of profiles acrossthe largest crater in those images. Profiles A and B each go through the two darkest deposits on the crater floor (a circular feature and a triangularfeature); the deposits appear at slightly different positions in these two map projections because the latter were produced with a shape model thatdoes not include the shape of this crater. To increase the deposits’ visibility, the left-hand image has been stretched relative to how it appeared inFig. 13—meaning that the left and right images no longer have comparable brightness scales. (b) Profiles across the photometrically correctedimages in (a), using the profile locations shown in that panel. Arrows point toward the two darkest deposits; the associated numbers indicate thecontrast between each deposit and the average Phobos surface, estimated by ratioing the deposit’s reflectance to the mean reflectance of the arealabeled ‘‘Average.’’ (c) Hapke-parameter constraints for the dark deposits based on the contrast measurements in (b), compared with the photometricfunctions derived for other Phobos materials elsewhere in this paper. The solid line shows the range of physically viable solutions that perfectly fitthe deposits’ two available data points (see text). u , 128 is excluded because it cannot fit the data; u . 408 fits the data, but is nominally excluded(dashed line) because such a large roughness is not considered physically plausible. The dotted lines indicate the uncertainty in the range of solutions,based on our best estimate of the uncertainty in the contrast measurements in (b).

76 SIMONELLI ET AL.


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