A radar image of Venus

i c a r u s 17, 699-703 (1972)

A Radar Image of V e n u s ~ R. M. G O L D S T E I N AND H. C. R U M S E Y

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91103 R e c e i v e d J u n e 7, 1972 Radar scans of Venus, performed at the Jet Propulsion Laboratory's Goldstone Tracking Station, have yielded a brightness map (attached) of a large portion of the surface. The bright area in the south (c¢) and the twin such areas in the north (/3 and 8) were first discovered by spectral analysis of radar echos. When range-gating is also applied, their shapes are revealed, and they are seen to be roundish and about 1000 km across. Although radar brightness can be the result of either intrinsic reflectivity or surfieial roughness, polarization studies show these features to be rough (to the scale of the wavelength, 12.5era). Dark, circular areas can also be seen, many with bright central spots. The dark areas are probably smooth. The blurring of the equatorial strip is an artifact of the range-Doppler geometry ; all resolution disappears at the equator. Another artifact of the method is the "ghost," in the south, of the images of fi and ~. Such ghosts appear only at the eastern and western extremes of the map. Data for this radar map were taken during the close approaches of spring, 1969, and fall, 1970. Another opportunity occurs in June of 1972. Venus will present the same aspect then, except that the spin axis will be inclined slightly toward Earth. W~e hope to take advantage of this opportunity to fill in the blurred equatorial zone and to remove the ghost images. INTRODUCTION

We present here the latest results in our continuing effort to map the surface of Venus by radar. Data was taken during the November 1970 opportunity with the newly increased capability of the J e t Propulsion Laboratory's Goldstone Tracking Station. See Table I for these radar parameters. TABLE I Antenna gain (two-way) 124dB

When this data is combined with that of 1969, a much improved radar image results. This improvement is not due simply to the larger store of data, b u t rather to the different points of view which were available during the two opportunities. Although Venus presents the same longitudes to Earth at each time of closest approach (because of its peculiar synchronous spin), the latitudes can change significantly. SIGNAL PROCESSING

System temperature 25°K

Radiated power 400kW

Wavelength 12.5cm

The basis of planetary radar imaging is signal processing in order to extract the echo power as a two-dimensional function of time-delay and Doppler frequency shift. Time-delay contours on the surface consist of a set of circles concentric to the subradar point. For the Venus experiments, the contours were spaced 37.5km in range, and

1 T h i s p a p e r p r e s e n t s t h e r e s u l t s of one p h a s e of research carried out at the Jet Propulsion L a b o r a t o r y , California I n s t i t u t e of T e c h n o l o g y , u n d e r C o n t r a c t No. N A S 7-100, s p o n s o r e d b y t h e National Aeronautics and Space Administration. the Copyright © 1972by Academic Press, Inc. 699 All rights o f reproduction in any form reserved.

signal processing system had a response

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at half-power of a b o u t the same width. Doppler f r e q u e n c y shift, the second dimension, is caused b y the r o t a t i o n of Venus. Seen edgewise b y the radar, the Doppler contours are also concentric circles which are parallel to the effective axis of rotation. Our resolution in this dimension was a p p r o x i m a t e l y the same. E v e r y 8 sec, during the time echo power is received, an a r r a y of 32 t i m e - d e l a y b y 256 Doppler cells is recorded. Such d a t a sets form the raw material for the radar image. Figure 1 is a sample set, averaged over about 4hr. Each curve is the response of one time-delay ring. Power density is plotted as a function of Doppler frequency shift. The curves peak at the edges because of the oblique intersection there between time-delay and Doppler rings. A larger surface area is contained within those time-Doppler cells. Other peaks which can be seen in Fig. l correspond to features

on the surface of Venus. Some of t h e m have high brightness contrast with respect to the surrounding areas. THE NORT14--SouTH AMBIGUITY There is an essential a m b i g u i t y in this imaging system. T h a t is, points s y m m e t r i cally placed n o r t h and south have the same t i m e - D o p p l e r coordinates. I t is n o t possible, for example, to tell solely from the d a t a in Fig. 1, w h e t h e r the features are in the n o r t h e r n or s o u t h e r n hemisphere of Venus. There are presently two m e t h o d s which have been used to separate this n o r t h south ambiguity. One is the use of two antennas, spaced a large n u m b e r of wavelengths apart, as an interferometer. The slightly different angle of view allows the separation to be performed. B o t h the H a y s t a c k and Arecibo Observatories h a v e

/% .jjx.

FIG. 1. Raw data set. Each point represents the received power in one time-delay-Doppler cell. Doppler is along the abscissa ; power the ordinate. Each curve represents one time-delay ring.

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R A D A R I M A G E OF V E N U S

successfully used this m e t h o d . The resulting r a d a r images, along w i t h our p r e v i o u s one, h a v e b e e n r e p r o d u c e d in Sky and Telescope (The Staff, 1970). W e h a v e chosen the second m e t h o d which m a k e s use of t h e relative m o t i o n of Venus to effect t h e separation. As Venus swings b y E a r t h in its orbit, the effective axis of r o t a t i o n nods, so t h a t t h e line of n o r t h - s o u t h s y m m e t r y shifts. T h u s the s o u t h e r n " g h o s t " of a n object in t h e n o r t h would shift its position, a n d it is t h e n possible to d e t e r m i n e t h a t the object is, indeed, in the north. A m u c h larger effect occurs w h e n d a t a f r o m t w o inferior conjunctions are combined. T h e line of s y m m e t r y can t h e n change l a t i t u d e b y o v e r 13 ° , a n d the n o r t h - s o u t h s e p a r a t i o n becomes m u c h e~sier.

THE GRADIENT METHOD

I n order to t r a n s f o r m the d a t a sets into an image, we h a v e used the principle of " P r e s e r v e the D a t a . " T h a t is, we e s t i m a t e the i m a g e in such a w a y t h a t if Venus a c t u a l l y h a d t h a t brightness distribution, t h e n we would h a v e o b t a i n e d e x a c t l y t h e same data. To illustrate this principle, let d i be the data measured in the ith time-Doppler cell. Then

= f f i(O,¢)J,(O,¢)dA +

n,,

where M is t h e u n k n o w n brightness distribution to be e s t i m a t e d a n d A~ is t h e r a d a r response. I t is essentially zero outside of the i t h t i m e - D o p p l e r cell, b u t it has a c o m p o n e n t in b o t h the n o r t h a n d the south. T h e i n t e g r a t i o n is o v e r the surface of Venus; n i r e p r e s e n t s noise in the measurement. L e t our e s t i m a t e of M be 21I ;

.~(0, ¢) =

E ms Gs(O, ¢), J

where the mj are coefficients to be determ i n e d a n d the Gj r e p r e s e n t t h e half-tone dots of printing, or the " p i x e l s " of television. I f Venus really h a d t h e distribution 211, then the reconstructed data ~i would be

,nj f f aj(o, lA,Io, ldA ~- E Aisms • J

T h e n we choose the m s to minimize t h e s u m S, where

S ~ Z (~i - di)-'. i

This a p p e a r s to be a s t r a i g h t f o r w a r d p r o b l e m in linear least squares. T h e answer involves t h e inverse of the m a t r i x A r A where A is t h e m a t r i x of the Aij defined above. T h e classic a p p r o a c h is n o t possible in our case because the m a t r i x is necessarily singular. T h e r e are portions of the surface of Venus seen on t h e first d a y of t h e e x p e r i m e n t t h a t are n o t seen again because t h e y r o t a t e out of view. The s a m e is t r u e for the last day. Differing points of view are n o t o b t a i n e d for these areas, hence t h e n o r t h - s o u t h s e p a r a t i o n is n o t possible. W e h a v e applied a g r a d i e n t m e t h o d to minimizing the s u m S. S t a r t i n g w i t h an initial set of the coefficients ms, we a d d a correction p r o p o r t i o n a l to the g r a d i e n t in an i t e r a t i v e process. I n v e c t o r n o t a t i o n

where mo is the initial coefficient set, ~ is the g r a d i e n t v e c t o r aS gk -~ am k , a n d the s i are the step sizes. I t can be shown t h a t a t the n t h i t e r a t i o n

m, =too + al 2 + a 2 ( A T A ) 2 + a3(ArA) 22 +... + an(ATA) "-1 2, where Z ~ A T A ~ o - AT-d a n d the a i are s u m s of p r o d u c t s of the step size s i. W e c o m p u t e the n - 1 v e c t o r s above, a n d t h e n minimize S b y a s t a n d a r d least-squares on the al. T h e o p t i m a l ai d e p e n d only on t h e lengths of the v e c t o r s Z, A Z , A r A Z , A ( A T A ) Z , etc. This m e t h o d p e r m i t s the solution to be carried o u t on a m e d i u m scale c o m p u t e r , t h e e n o r m o u s size of the m a t r i c e s n o t -

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R . M. G O L D S T E I ~

withstanding. The A m a t r i x for the Venus d a t a has dimension 120 000 b y 40 000. The i t e r a t i v e process converges a f t e r a half-dozen tries, a n d the solution is stable. T h a t is, if t h e solution is p e r t u r b e d , f u r t h e r iterations restore it. F o r areas which c a n n o t be s e p a r a t e d as to h e m i s p h e r e (first or last d a y data), the g r a d i e n t m e t h o d leaves the original e s t i m a t e unchanged. THE RADAR IMAGE Figure 2 is a r e p r o d u c t i o n of our result-

A~D

H . C. R U M S E Y

ing r a d a r image. T h e 20 ° s e g m e n t s of longitude of the e a s t e r n a n d western edges are n o t well s e p a r a t e d as to n o r t h a n d s o u t h for the reasons m e n t i o n e d . All of the rest of the image, however, is well separated. T i m e - D o p p l e r processing has its poorest resolution along the s u b - E a r t h track. The distance, along the p l a n e t a r y surface, across the first t i m e - d e l a y ring is m u c h g r e a t e r t h a n across t h e l a t e r rings. This effect can be seen in Fig. 2 as a b l u r r e d b a n d r u n n i n g east a n d w e s t t h r o u g h the

FIG. 2. l~adar image of Venus. The grid is 10° in latitude and longitude. The zero meridian runs through a, the bright area in the southeast. Top is north.

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RADAR IMAGE OF VENUS

center of the image. This artifact is diminished over the western half of the map because of the separation of the subE a r t h tracks during the two inferior conjunctions. The two tracks crossed each other over the eastern section, however. The remainder of the image is a good representation, within our resolution capability, of the radar brightness of the surface of Venus. Although the dielectric constant and conductivity of the material affects the echo strength, we feel t h a t most of the brightness contrast shown here is the result of variation of surface roughness. The very bright spots a (0 ° long, 25°S lat) and fi (85°E, 25°N) have, from previous investigations (Goldstein, 1965), been found to depolarize microwaves strongly. We conclude t h a t these areas are very rough to the scale of our wavelength, 12.5cm. The other bright spots are probably also rough.

The very dark areas are likely to be quite smooth. Even though a surface m a y be a good reflector of microwaves, if it is smooth and located away from the subE a r t h point, reflected waves would be directed away from Earth and little power would be received. I t is tempting to identify the dark circular areas with maria, as on the Moon, but there is insufficient evidence for this. Many of these areas have bright central spots, near the limit of our resolution. We note t h a t Fig. 2 is a radar brightness map, and gives no direct measurement of elevations or depressions. REFERENCES GOLDSTEIN, R . M. (1965). P r e l i m i n a r y V e n u s r a d a r results. Radio Sci. 69D, No. 12, 16231625. S t a f f o f Sky and Telescope (1970). N e w r a d a r m a p s of Venus. Sky and Telescope 40, 274-275.

DISCUSSION HAGFORS : W h a t is t h e r a n g e of a s p e c t angles for t h e m a p , a n d w h a t a b o u t t h e v a r i a t i o n o f reflectivity w i t h a s p e c t angle ? GOLDSTEI~: T h e effect o f t h e a v e r a g e s c a t t e r i n g law is r e m o v e d f r o m t h e d a t a . T h e m a x i m u m v a r i a t i o n in t h e a s p e c t angle is 90 ° f r o m t h e r o t a t i o n . Also, as seen f r o m t h e E a r t h , t h e axis o f r o t a t i o n n o d s b y only a b o u t 6 ° . F i n a l l y , in t w o y e a r s a s u b - e a r t h t r a c k is displaced b y a b o u t 12 °, h e l p i n g us to resolve t h e n o r t h / s o u t h a m b i g u i t y . A. S~APmO : W h a t is y o u r f r e q u e n c y ? GOLDSTEIN : 2388 M H z . KUZMt~ : W h a t is y o u r surface resolution? GOLDSTEIN : 250 ~ sec in d e p t h . T h e lateral r e s o l u t i o n is a b o u t 50 miles. KUZMIN: HOW do y o u a v o i d t h e n o r t h / s o u t h a m b i g u i t y ? GOLDSTEIN : B y a l e a s t - s q u a r e s solution. I f a p o i n t is seen f r o m different p o i n t s o f view it is resolved if n o t too close t o t h e e q u a t o r . W e d e t e r m i n e a b r i g h t n e s s d i s t r i b u t i o n w h i c h b e s t fits all t h e d a t a . SAGAS: IS t h e r e a n y v a r i a t i o n w i t h earlier m a p s ? GOLDSTEIN : NO, it is j u s t t h e s a m e e x c e p t for one d a r k area a b s e n t on o t h e r m a p s . I h a v e no idea a b o u t t h e origin o f t h i s difference. A. SHAPIRO : H a v e y o u allowed for a t m o s p h e r i c a b s o r p t i o n ? GOLDSTEIX : T h e r e is n o t v e r y m u c h a b s o r p t i o n a t 12.5 cm. KVZMI~ : I f t h e difference b e t w e e n b r i g h t a n d d a r k areas is due only t o dielectric c o n s t a n t , w h a t difference is dielectric c o n s t a n t implied? GOLDSTEIN: I ' m n o t s u r e ; t h e difference o f r a d a r reflectivity is a f a c t o r o f a b o u t 15 to 20. PETTENGILL : T h e p o l a r i z a t i o n results rule out a t t r i b u t i n g this difference to dielectric c o n s t a n t v a r i a b i l i t y . GOLDSTEI~q : Yes, I believe t h e surface t e x t u r e d o m i n a t e s t h e dielectric c o n s t a n t variations.