06943-1-.F UNIVERSITY OF MICHIGAN College of Engineering Department of Aeronautical and Astronautical Engineein ng High Altitude Engineering Laboratory Final Technical Report LUNAR SUBSURFACE ELECTROMAGNETIC PROBING H. F. Schulte E. K. Miller * A. Olte * * Radiation Laboratory Electrical Engineering Dept. 6943-1-F = RL-2145 Under Contract with: Bendix Systems Division Bendix Corporation Ann Arbor, Michigan Administered through: Office of Research Administration February, 1965

Lunar Subsurface Electromagnetic Probing I. Introduction By deploying an electrically short dipole antenna on the lunar surface and mneasuring the antenna electrical impedance at selected frequencies, potentially useful information about the surface and subsurface materials of the moon can be obtained. During, the imipedance measurement at a particular frequency, a portion of the electro-lmagnetin field radiated by the antenna will penetrate the lunar surface, interact with tthe lunar material, and thereby change the antenna impedance from its free-space value. The field penetration is determined by antenna length, operating frequency, and the local lunar conductivity ( cr ) permittivity ( E ) and permeability (L ). The presence of a low-altitude lunar ionosphere migtht also interact with the antenna, Ibut for the purposes of this discussion, the effect will be considered negligible. It should be noted here that this technique hias auo been viborously pursued on tlhe earth because of the availability of irmore direct 1methods. Furtlermore, the relatively high water content of much of the earth's surface layers results in high soil conductivity and thus penetration of radio frequency energy is limited by the skin-effect. It will be assumed henceforth that the lunar material has a relatively low conductivity. If the lunar conductivity is high however, the field penetration will be limited, but the discovery of higlhly conductive lunar material will be of prime geological interest in it,; own righlt. \'llile. the above technique is simple in concept, interpretation of the ilmpedalnce versus frequency measurements in terms of absolute values of a-, E,., and material density with respect to depth is difficult. This results.rom) the potentially infinite 1nmber of combinations of subsurface charaecteristics and possible material variations with respect to frequency. Also, there is not as vet a satisfactory solution for the problemn of the impedance of an antenna located at the interface between free space and a lossy medium.

-9 - In spite of these difficulties in obtailing an unambiguous absolute inter - pretation of the subsurface make-up, the proposed technique appears to be very useful in nianned and unmanned exploration of the moon because of its ability to detect changes in lunar subsurface conditions from one place to another. If, for instance, a series of inlpedance nmeasuremenrts are made at one location, and this same series is repeated at another site, the following conclusions can be drarwn from the results: 1. If the nmeasurements at one site differ from those at the other, then at least some of the subsurface conditions at the two sites must be different. 2. I' the measuremenets at both sites are the same, or essentially so, then the probability is high (but not absolute) thiat the subsurface conditions are likely to be similar. Even the limited amount of inlformation implicit in the above two conditions is of value for instance, in site selection for lunar core drilling. If the object of the drilling is to obtain (if possible) a series of cores of differilg characteristics, then whenever criterion numbner one above is satisfied, the objective will be achieved. It niight also be feasible to detect the presence of crevasses, particularly if they are not deeply buried. To investigate the sensitivity of the antenna impedance to material variations it wVill be assumed that the antenna is immnersed in a homnogeneous medium which has either the properties of the material medium or free space'. Then it will be recognized that when the antenna is at the material-space inte.rface, its behavior will be somewhere between these two extremes. The impedance of anu antenna plnced inl an itnfinite., homogeneous lossy miledtinm which rmay }lave a conlplex permeabilit-, permittivity and colnductivity is considered in the following section.

-3 - II. DIPOLE IMPEDANCE IN AN INFINITE HOIVIOGENEOUS MEDIUM According to King (1956), solutions which apply to free spacu are correct for the material mediumL if the values for the electrical constants of the material lmedium are substituted for those of free space. Thus, an expression for the impedance of an antenna in free space may be transformed into the correct forni for the material medium with the appropriate substitution of electric al cInstants. Attention here will be limited to the electric: dipole antenna, and due to the frequencyC range which is of interest and the practical limitations on the lenlgtll of the antenna, as well as the theoretical simplification which arises, the antenna will b)e assumed to be short compared with the wavelength. With this restriction, an expression for the impedance in a material medium of an electric dipole antenna with zero base separation, obtained froml the enlf mlethod and a first-order solution for the antenna current, is (King, 1956, p. 184): j ( —2) Z =2h 2 7rh (. 2 a -2 +j '- (w 1.-" h): R +jX (1) Q-2 + 2 ln 2+j I (Co.. h)3 where 2h a Ee e = antenna length = antenna radius = 2 f = 27rx frequency = 2 In (2h/a) (7e = Ee- - w: E -cI/OW I. II = E' - J = E- j E L -:l - -j/.

-4 - This expression produces values within 10 percent of those obtained from a second-order solution for antenna lengths in the range 2Iklh = 2h1ulU < 1.0 and wvithin 20 percent in the range 1.0 < 21klh < 2. 0. \We have allowed for a conm-plex permeability and permittivity while considering only a real conductivity, since nost materials can be represented in this way. It should be noted that these electrical properties of the material may be functions of the frequency, but it will be assumed here that they are constant in valtue over the frequency interval under investigation. Thiis expression was programnled for solution on an IBM 7090 computer. A frequenrcy interval of 5 x 10 to 5 x 10 cps was investigated for an antenna length 21h of 20 meters and a radius a of 1 millimeter. The center frequency f about which the frequency f is incremented is f - 5x10 cps ( w = 2 rf ). C C ( ' Typical results for the resistance and reactance as the electric constants of the medium are varied are given in Figs. 2. 1 to 2. 8. Figures 2. 1 and 2. 2 show tlhe results where,u and E are real and separatelyx have values which are 4 times those for free space. The result is to increase the resistance in proportion to the 3/2 power of the increase in permeiability and to the square root of the increase in permittivity. The reactance decreases in proportion to the increase in the permittivity and is unaffected by changes in the permeability. In Figs. 2. 3 and 2. 4 are shown the results for various real conductivities when Ul =.' = /o and E = El - 2 E o There is a very large increase in the resistance of 4 to 6 orders of magnitude at the lower end of the frequenc-y interval, whiile at the higher end thle vallues are. close to those for zero conductivity. A corresponding decrease of the same order of magnitude is observed in the reactance. Figs. 2. 5 and 2.. present the impedance when cr= 0, p. = p' -- /L o and = e ' -j " - 2 E -jE " for various ratios of e "/ E'. Again a large increase in 0

-5 - resistance is seen, but there is relatively little decrease in reactance. It is especially interesting to observe in the frequency interval where dR/df < 0, tlat -2 -1 R. cr f for the conducting medium and R 0[ f for the medium with a complex pernlittivity. This characteristic, as well as the great difference in their respective reactance curves for the larger values of conductivitS, indicate that frequency swept measurements may provide a method for discriminatinlg between a real conductivity and a complex permittivity. Finally, Figs. 2. 7 and 2. 8 show the results obtained for the case where o - 0, - E ' = 2 E and pL = pL' -j/" = 2 L o - j " for various values of the ratio of L "/ p'L. There is relatively little change in either the resistance or reactance due to the complex permeability. On the lbasis of some radar scattering measurenments of the moon, Urunschwig et ail (1960) conclude that E' 1. 08 E and cr'/c E' 11.2 ( c' = 3. 36 x 10 MHOS/IMETER) if.' = /. A study of lunar surface radio comrnunicatiotn recently concluded by Vogler (19b4) uses E' = 2 E and -4 a - 10 4 MHOS/MITER as the values for the top layer of the lunar surface. Another study of lunar communication by Smith (1 964) used E' - 4 and oa' = -4 4 x 0 MHOS/AMETER. The values which are employed for the calculations here are thus representative of those which are currently considered reasonable for the electrical properties of the moon's surface. More recently, King (1961) followed a new: approach to find the inmpedance of thie electric dipole antennia. It involved rearranging tile integral equation which w\as formerly used for the antenna current. The new form of the equation is again solved by an iterative procedLure, but it las the advantage that the zeroth order.solution pIroduces results whose accur acy lies somewhere between the first- alnd sec:old-order solutions of tile original equation. King pLesents some results for the impedance of a short dipoule antenna immlersed in a dissipative mediumll), obttained fromn this approach. Solne calculations were performied with (1) for somrne of the parameter values used by Kinu, with the result that ilmpedance values

-6 — obtained by th}e two methods agreed to within 10 percent. It should be noted that the limnit 21klh < 2. 0 is satisfied over the entire frequency range when the free space electrical properties are used. When, Iowe Ier, e' Eor = 2 JL then 21klh exceeds this limit for frequencies of f > 4 x 10 cps, which could result in errors larger than 20 percent in the calculated impedances. This is a small portion of the total frequency interval however, and does not invalidate the results. The dashed portion of the curves indicates the range where the above limit does not hold. There is an additional manifestation of the approximnate character of (1). When a complex permeability is used, the resistance can be shown to become negative when the imaginary part of the permeability sufficiently exc eeds the real part. It is unlikely that any real medium would possess such a permn e ability. In Figs. 2. 9 and 2.10 the results are rearranged to illustrate the changes in resistance and reactance as r- and E vary at selected frequencies. These curves demonstrate that adequate sensitivity to material parameter variations exists, even when allowance is made for the fact that these data are for the completely immersed antenna. III. DIPOLE IMPEDANCE NEAR A FREE SPACE-MATERIAL MEDIUA1 INTERFACE The original study of the dipole antenna over an infinite conducting half-space was carried out by Sommerfeld (1909). There have been various treatments of this problem by many authors since then. Sommerfeld and Renner (1942) extended Sommerfeld's original study to a half-space of arbitrary properties and found the radiation resistance from the enmf method for horizontal (HED) and vertical electric Hertzian dipoles (VED) as a function of height above the interface. The surprising result is that when the half-space has finite conductivity, the radiation resistance of both antennas becomes infinite when their height above the interface decreases to zero. When, however,

- I - their half-space is infinitcly conducting or non-conducting, the radiation resistance is finite at thie interface. This is a somewhat perplexing double limit process which King (1956) sidesteps by noting that since a physical antenna has a non-zero thickness the linmit of the antenna heigtht decreasing to zero is meaningless. There is an interesting comparison which can be made between the HED at the free space boundary and the same antenna im1mersed in an infiflite material nedium which haLs tile properties of the half-space. In both cases, the antenna radiation resistance becomes zero when tilhe conductivity of the material mnedium goes to infinity. On the other hand, when the material medium has a finite conductivity and then the frequency is alluwed to approach zero, which is equivalent to letting the antenna height above the interface become zero, different results for radiation resistance arc obtainfed. The radiation resistance of the antenna in the infinite imedium becomes a constant inversely proportional to the conductivity, while that of the HED, as mentioned above, becomes infinite. It seems intuitively obvious that the antenna impedance would be most affected by the material medium when it is surrounded by it, and when the antenna is at the interface between the material medium and free space, the effect should be smaller. Also, since an infinite radiation resistance is not acceptable on physical grounds, it is apparent that the present solution to the interface problem fails when the antenna is at, or near, the interface. Some experimental measurements by Proctor (1950) indicate that the theory is quite good in predicting the actual radiation resistance for an antenna height down to 6 x 10-4 wavelengths. The theory must fail for heights less than this for a lossy medium however. With this limitation in mind, curves have been derived from results recently given by Vogler (1964) for the HED as a function of frequency. His results were obtained using the emf method for calculating the impedance of the Hertzian dipole. Fig. 3. 1 shows the radiation resistance over the same

- - frequency interval for a Hertzian HED with same length, 2h - 20 METERS, as was used for the antenna in the previous calculations. For the parameters considered, 50 meters is as close as we can approach the interface and still read the Vogler's curves. Two curves are presented for finite conductivities, and an antenna height of 50 meters, both of which resemble those obtained for the infinite medium except that the increase in resistance is not so pronounced. Also shown is the resistance when tile conductivity of tile half-space is zero and the antenna is at the interface. The increase in resistance then is not quite equal to the square r oot of the increase in perllittivity as was the case for the infinite medium. No curve is shown for tile reactance at the 50 meter height since it is relatively unaffected by the half-space. When the antenna height is zero, the reactance is infinite according to this theory. FiCgure 3. 2 shows the resistance as a function of height above a halfspace with oc' = 0, L' = Mo and E = 4 o, and a frequency of 5 x 10 cps. Sincea, for the infinite medium of zero conductivity and real permittivity e and permneability pj R F(h l, a, ) v (2) where F is a function of antenna length and radius and of frequency, it is reasonable to write for the same antenna in free space near the half-space R = F(h, a, w ) G (I, E, tL )o E (3) where G is a function of the antenna height H and shows the results of the half-space properties on the antenna resistance. This form is correct for the half-space problem and G(H) is given by, (Sommerfeld, 1949).

lhia 2k 1-1 I-) 0 I L ( ( I I ):- -,, -L ) -I - I 1 I . I L 0 s Ii 2k H - 2 k H c os 2 k H f-0 () 0 rj (2 i~ Iiy) (1) I L -I-..{Rif t-7; --- R O 2 i] XdX}] e (2ver w -iii 1 thle Prop)ag at'ion constant, of free- space nud K ~is the propag~ationl conStanit. Of he" LiUatCliaI. medium hailf space. 'vuici as giveni an aIsym, 1ptotiC form for G inthe limit II 0 I < 1, F E(E -1F1 G(JI, E L) I ( 1 ()+ 2 (~ ~ dLnl is Sceili to F1 (x jF2 (x be indlependenat of H. F and F. are given by x + x ( + x)] d ~ ( + X) (I - ~2 d2 X +x(1 - d)c+I - (I+ -N - x)A1 J~ i+ x (1- x) (2 x2) d 3 I(I X) (1-x22d4 EIE -1 D0 with Fi-gure 3. 3 showis (C safnto of 1777. It is apparent thiat G is slii:4tly leSS thanl 1P /TE but thiat. as CIEIE inrae,0approacheis IEI rt resistance thou app-roaches ttle inlfinlite mnedium value. Thus, thc theoretical indicuationl is that the antenna radiation re~Sitanjce for thle HED locatedl at thec-.interface between free spacc aniid a material medium half-space applroaches thiat

-10 - v-ailue wlich -,.'OLld resullt V.hlen the same anteniia is inmerscd in the mlateriLl LediLum iL the pernitliviLy of the material medium is greater than about 10 timILs tlhat of' free space. It should 1)C recalled, however, that the treatment follfowed by Vogler iidiclates an ilnfiite reactance for tle same antitenna whlen at the intcrface, Cven1 f.)ur' a lussless utledium. It nay be of interecst to injclude somLe experimental results obtained by Proctor (1950), lizuka (1U34) and beeCey et LU (1964) for impedance measurements of lilnear aLntLerrLa near thie interface between free space arid a material medium hiall space. Thle wvork of Sceley (19G64) et al is cspecially interesting, in that imiieasurcimenits 'were made on a dipolc antenna 3. 23 miles long laid across an island, at frequencies bctweenl 3 NKc anld 45 Kc. The experiment was carried out to determine vhiethecr an island couLId be made to radiate as a slot radiator. Table I presents tlec 'results of some of these nmeasurements. ThlCe smaller valiues uf /11 X for Iizluka's and Secley's work represent t'ie case Vwhenl the antenna.as actually touching the interface. It is interesting to observe that the resistance and reactance, in all cases but one, exhibit a decrease in magnlitude \ihcn the antenna is brought into contact with the interface with respect to the values just above the interface, contrary to the theoretical calculations from the -Icertzian dipole theor>. These results do sho,', tilhe possibility for a large increase in resistance over thlat free space. At the sane time, they indicate the limiitations of thle available theory which predict infinitely largeu impedances ill such[ situations. IV. FURT1HER TIEORETICAL \\WORK In a uniform materiaul medium we may calculate the impedance of electrically shuort dipole anteniima itlhi relative casc and reasonably good acecurac y lXargely uecause of tlhe theoretical wvork of Kting and his students. The 1mediuml- may be loss-frec or lossy. The conmplexity of computations in the lossy medium are greater than in the loss-free niedium but as shown above, they are still miantagable). The expressions for the impedance rest on a solution

-11 - of aninntegral cquatiol] for the ciurrent fl tle line ara aitenia. The liin.ar; anlteltna consists of perfcc'tly cotducleing c.ylinders joined }by an ileal voltage getierator. \\ lhe the space conSists of a material half-space arnd the rest vacluum (or air ), then the only calculations for the dipole impedance v.liichl exist are based on the E1A\iF nmctllod ald the Hlertzian dipole fields. This procedture was firsL forutl lated by Sommerfeld at thic turn of the century and since then extenlded by lhimtself, Ils students alnd ot}er workers. Experience indicates that tiis miiethod gives uscable results whien the half-space is either loss-less and the mediulm clectromagnetic paraneters finite, or when it is of infinite conductivi.ty. tWhn tthe half-spac is lossy, then tlhe impedance results are of sufficient accuracy onljy as long as tihe dipole does not approach too close to the loss)' ilterface. Wlien the separation distance becomes less than one-half v'avelengtl, it is clear tliat the error is bound to increase and, for example, as tl tlhorizontal -l'ertzian dipole approaches the lossy interface the real part of the dipole imipclance beconmes iinfinite: a result that is completely tronig. How tiis comi-es about is easy to sec. The Hertzia.n dipole is an oscillatilg point current. The electric field of this sourcu becomles infinite at the rate of d-3 for d << X where d is thte distance of tlie observer fror the source. As we let the horizontal Hertzian dipole approachl the lossy interface, we impress on the finitely conducting interface an intfinitely la-rg electric field which gives rise to non-iltegrable singularity in tlhe power absorption by tlic 1Jediu1i. Such a situation will never arisc if one cUonlsiders a lillear allntenna as discussed in tlhe first paragraph of tilis section. \\ec are forced to coInclude that tlU method of computing tle dipole impedaanlce whicht rests on thie EMnF method and the Iertzian dipole fields leads to incorrect results Tlthen tlie dipole is clhose to thc material interface. Thus tlhere is a rieed to formulate all integral equation for the cuLxIrrent of a linear antenna tlhat is horizontal to a lossy interface, as shoxiin beloxw, as wnas done by King for the hom'1ogelneous lossy medium.

-12 - H FREE SPACE MATERIAL MEDIUM Feomll a solution of this integral equation one can obtain antenna currents that will lead to useful dipole antenna impedances close to the interface. Tiis problem is iinvolved and tedious m emlematically, but the present need for a 0good solultion and availability of highl speed CO11mpUterS should comlbine to solve! this problenl. Both of thecse factors were missing in the earlier studies. V. CONCLUSIONS AND RECOMMENDATIONS The precceding sections have dcnmonstrated that the proposed method for lunar subsurface electronagnetic probing should provide useful resLults, particularly whei advantage is taken of tlie ability to make relative Ineasurenments fr-oml one lunar site to another. Variations in both permittivity and conductivity can be detcteted readily. Permeability changes have only minor effects on the electric dipole. An investigation of the loop antenna mlight be undtertaken in futlure wo rkl if sensitivity to permeability change is desired. In order to obtain the maxinmum amount of informnation from Lhe meas — uremlients, it \ill be necessary to carry out the analysis of an antennla at a -iaterial-free space boundary and then experimentally verify the theoretical predictions. It will then be possible to conduct an error analysis of the effect of lack of contact of the antennra with the interface at all points along its length. Thlis wvill assist in specifying the care Nwith 'which the antenna must be deployed

-1 3 - prior to nicasurerniet. It will also alluwf an estim-iate of the fea~sibl~iity of mo1u t itili an antenna on- a tra~xver.sec. veh -icle to obtain continuous readings during), rehi'cle operationl. A's j)I7SCUiLIV, cnirisionedl, thle inst1rumen,1t w~oulld consist of a bo(x conltainlingl springa-loaded reels for antenna storage and all the electronics neceIssa-ry- to tacke bohrsitvJndratve LflCLLSiriftts of the antentna at a m-inimumof three frequecjicsi-,. Instr.umentC volumeI shoul1d be less than 112 cubic foot and it should wecighI less than U pounds. Duringr operation, less than 2 watts of powe%7r would be cqirel.Time data output wvould be in the formn of analog voltages which w,~ould di~spl Iayed on self-contained voltmeters and also would be properly conditioned for tape recorde —r or telemecteringr inputs.

2500-312-M FIG. 2. 1. 1iesistance versuisFrequtency for Dipole Antenna of Length2h. 2O0Meters, fladlus a=lIvm and a'0. 102 5 -4 -2 -IU1 6 5 -4 -3 -2 1 0 8 7 -6 X: 4 3 10 -6 5 4 3 2 Ec i0o2 6 -5 - E 4EO 4 -p1 3 - 2 E = 0 Ap %Xl 2 Frequencv', cps

Reactance,, Ohms Q 0 PT] 1 1 I I Il i 1 1 1 1 -1 U C 0 rI -4 C) N: N: f4 N: II (t ci) . - II 0 F-A L 0

9500-3'~'12-Mf "IG. 2. 3. Resistance versus,- Frequencv, for Dipole Antenna af Length 2h= 20 Meters; 1-,adlius:z -1. mm; and p =-go c2%~ 1 0 I 111 iir 6 5 4 3 2 4 _ _ _ _ _ 10 8 6 5 4 3 2 W E 3 C. 10 4 6 0 4 2 102 6 5 Example 3 -4 0 a IO xLu 2~ E 2.78x IU MHOS/METER Co0 2 4:3 0 A I I I I I I I I I I I I1 I I I I I I I I I Frequency, eps

2,0 C n- 3 1> FTC. 2. 4. Rleactance ve rsus Frequ e ncv for Dipole Antenna of L.enrth 2h=z20 M\eters, Radius awl mm arnd, p 0 ___________ __________ I I 11 11 T111 2 3 ~ 3 - ~ -4 10. 0 (ax 2.7'8 x1U M /F R 5 8 -101 2 3 4 5 6 10 2 3 4 0 51.0 3 2 3 4 5 2 0. 1 3 -4 - 0. 0 5 -8 0i 1J I I I I I1 1 I t il I I III I 9 ' — I R7Q P.2 I~~ F'reauencv. cp~s

FIG. 2. '.Resistance versus VFrequiercv 'Ior Dipole of Length 2h='.f) Mter-, Radius a=1 mmn and j=() Li -j', '2 0 104 Sks, 1 I i 3 2 - 1 6 0 5 4 3 2 9 6 4 - 3 X. E c (1) u rCd.6-i w vi 4) Pf4..01 or#' 2 -101. 8 -7 -6 -5 -4 -3 -2 -100 1 i Fr eqiuenlc, cp)s

R~eact~ance, ohms I I I 0 rT1 CI - - c )

Resistance, Ohms 0 1-" 0 1 0 0) b-A 'O. I CA) I~ 11146 04%b %% qb *-A t 0 -— l I I I A%%4

Reactance, Ohms 0A I -A I w Ir 0 - I I.- j i 11 1II I I I I I l I I I I II i I I I I I A 0 7j -C It -0 S= eD m (".11 I'< 0 10 71 q (C~ 0 jc: r 'I, -1 'I. - r - t I I - I I I I I I I I - I I ---- I 0 III I I I II I I I I II II II II CA II II I I I I I I I I I I I I I I.......... I...... I -.........

Fig. 2. 9 Resistance & Reactance versus Permittivity DIPOLE ANTENNA, LENGTH 2h = 20 METERS RADIUS a = mm, -=O, =M o -- RESISTANCE f = 1X10 --- REACTANCE f =5x105.-104 () 0 LJ C) z -- Iz 102 Cr) 103 0 F — 102 I f= 2.5x105 f = |xiO5 f =lx105 f =5x 05 f= Ixi06 B=:/e 10 100

io5 -- RESISTA f 0- REACTAF v> I x loO a I mm 0 2 E0 LU 0 0 LId f =I x 106 LJ 103 ILl I 0 2 I0-4 I- I0-2 10 100 A - FC D Fig. 2. 10 Resistance & Reactance versus Conductivity, Dipole Antenna, Length 2h= 20 meters NCE NCE I 01

T!IC>:.i3.I Resistance o-)I Dipole Antentna of Length 2h t-u M.)UAeters and radius axi rrim in Free Space Near Material Medium Half Space. 10 2 101) 0 10( (71 l-. X, C. 11 Li r_: '51 00.PTj C) Ix 10- 1 io-2 10o3 in 4 I C) in Frequency, cps

2-n-.- i32-MA FIG. 3.2. Resistance of Dipole Antenna ot Length 2h=20 Meters, Radius a = 1 mm in Free Space as Function of Height H Above Material Medium with c = 4e -= a, a = H and Frequency = ).;1x5 cps. 2.0 r R r Free Space Resistance O p 0 q0 R 0 1. n i I I I I 0 10 20 30 40 50 II, meters

K")0 C 0 0 r. U 'A 0 'a) C 0) CNJ C-4 'I-, c c c~l C) (0?fBaO) L,)

L' 5 00 - 3 1 2 - NM' -r w~r - -- Calculated 1 'I ec Space Measured | -- — r _ _ _ _ ___I____I Source Freqt ency ' 0 O /, E( kh 0 R jxo R jx o Iizuka 114 Mc 2.97x10- | 78 (1.(88 0.178 7. 192 -726 68. - 6 11.() (E'lonopole).,,,, I. I -10n 71 ()6 ii5 -1, ]20,0 1.43x10 73 0. (088 6.1 - 9.9 77 1. - 1. 0 -i I I 1i )6I, -5 6 Seelev Etal 3Kc 1.52x10 ' 1.88x10 0.164 0.54 -8,010 325.0 -2800.0 (Dipole) 1.8x 6 - 4.4x10 1.88x10 0.164 0.54 -8,010 100.0 - 970.0 5r10 lc 5..07xlO 5..64-105 0.548 6. 25 -,400 101(. 0 - '700. 0 1.37x10 1 5.x (4x10) 60.0n- 140.0 20 c I1. 0x10 2.82x1 1.096 27.7 -1,09) l.0 40. -7 2.74x) 2.82x10 1.0i 27.7 1310. () 425.0 P'roctor 5:.4 Me 6.:3x10 -4 6.. 0 o1 i.( 0 I I 3.0 0 (:Dipole) "1. 001.-10 70. 0 * i',o dielectric constant iven. Island consisted of sandy soil TABL I

BIBLIOGRAPHY Lunar Subsurface Electromagnetic Probing King, R. W., Harrison, C. W., "Half-Wave Cylindrical Antenna in a Dispersive Medium: Current and Impedance", J. Res., NBS, 64D, July-August, 1960, pp. 365-380. Iizuka, K., "An Experimental Investigation on the Behavior of the Dipole Antenna Near the Interface Between the Conducting Medium and Free Space", I.E.E.E. Trans., A. & P., AP-12, January, 1964. Wait, J. R. "Electromagnetic Fields of a Horizontal Dipole in the Presence of a Conducting Half Sphere", Can. J. of Physics, 39, 1961, pp. 1017-1028. Bhattacharyya, B. K., "Input Resistances of Horizontal Electric and Magnetic Dipoles Over a Homogeneous Ground", I. E. E. E. Trans., A. & P., AP-11, 3, May 1963. Keller, G. V., "Electrical Properties of the Deep Crust", I. E. E. E. Trans., A. &P., AP-11, 3 May 1963. Pritchett, W. C., "Attenuation of Radio Frequency Waves Through the Earth", Geophysics, 17, No. 2, pp. 193-217. Horton, C. W., "On the Use of Electromagnetic Waves in Geophysical Prospecting", Geophysics, 11, 505, 1946. Fritsch, V., "Propagation of Radio Frequency Electromagnetic Fields in Geological Conductors", J. Res. NBS, 67D, 2, March -April, 1963. Wheeler, H. A., "Radio-Wave Propagation in the Earth's Crust", J. Res., NBS, 65D, March-April, 1961. Wait, J. R., "Electromagnetic Waves in Stratified Media", Pergamon Press, 1962. Tozer, D. C., "Physics and Chemistry of the Earth", Pergamon Press, Vol. 3, 1959. Wait, J. R., "On Anomalous Propagation of Radio Waves in Earth Strata", Geophysics, 19, April 1954. Stratton, J. A., "Electromagnetic Theory", McGraw-Hill, New York, 1941. Wheeler, H. A., "Fundamental Limitations of Small Antennas", Proc. IRE, 35, December, 1947. Wheeler, H. A., "Useful Radiation From an Underground Antenna", J. Res., NBS, 65D, January-February, 1961. -------- "Electromagnetic Waves in the Earth", (Selected Topics), I. E. E. E. Trans., A. & P., AP-11, 3, May, 1963.

Brunschwig, M., Ahrens, T. J., et. al., "Estimation of the Physical Constants of the Lunar Surface", University of Michigan Radiation Laboratory Report No. 3544-1-F, Nov. 1960. Zdanekhopal, "The Moon", I. A. U. Symposium, Lenningrad, 1960, Academic Press. Troitskiy, V. S., "Lunar Radio Emission-The Physical State and Nature of The Moon's Surface", from Izvdstiya Komissii po Fiziki Planet, No. 3, 1961, NASA Technical Translation, NASA TT F-172, July 1964. Burks & Hart, "Progress in Dielectrics", John Wiley, New York, 1961. Von Hipple, A. R., "Dielectric Materials and Applications", John Wiley, New York, 1954. Keller, G. V., and Licastro, P. H., "Dielectric Constant and Electrical Resistivity of Natural Cores", Geological Survey Bull., 1052-H (Washington: G. P. O. 1959). Negi, Janardan G., "Radiation Resistance of a Vertical Magnetic Dipole over an Inhomogeneous Earth", Geophysics, Vol. 26, No. 5, October, 1961, pp. 636-642. Proctor, R. F., "Input Impedance of Horizontal Dipole Aerials at Low Heights Above the Ground", Proc. IEE (Br), Vol. 97, PT 3, #47, May, 1950. King, R. W. P., "Dipoles in Dissipative Media", Electromagnetic Waves Symposium, Edited by R. E. Langer, University of Wisconsin Press, 1962. Wait, J. R., "Radiation Resistance of a Small Circular Loop in the Presence of a Conducting Ground", Jour. of Applied Phys., Vol. 24, No. 5, May, 1953. Wait, J. R., "The Magnetic Dipole Over the Horizontally Stratified Earth", Can. Jour. of Phys., Vol. 29, 1951. Iizuka, K. and R. W. P. King, "An Experimental Study of the Insulated Dipole Antenna Immersed in a Conducting Medium, " IEEE Trans on Antennas and Propagation, Vol. AP-11, September, 1963. Iizuka, K. and R. W. P. King, "An Experimental Study of the Half-Wave Dipole Antenna Immersed in a Stratified Conducting Medium", IRE Trans. on Antennas and Propagation, Vol. AP-10, July, 1962. Iizuka, K. and R. W. P. King, "The Dipole Antenna Immersed in a Homogeneous Conducting Medium.', IRE Trans. on Antennas and Propagation, Vol. AP-10, July, 1962. Iizuka, K. and R. W. P. King, "The Dipole Antenna as a Probe for Determining the Electric Properties of a Stratified Medium", IRE Trans. on Ant. & Prop., Vol. AP-10, November, 1962.

King, R. W. P., "Theory of Linear Antennas", Harvard University Press, Cambridge, Mass., 1956. Vogler, L. E. and J. L. Noble, Curves of Input Impedance Change Due to Ground For Dipole Antennas, NBS Monograph 72, January, 1964. Vogler, L. E., A Study of Lunar Surface Radio Communication, NBS Monograph 85, September, 1964. Vogler, L. E., and J. L. Noble, Curves of Ground Proximity Loss for Dipole Antennas, NBS Technical Note 175, May, 1963. King, R. W. P. (1961). "Dipoles in Dissipative Media, " Cruft Laboratory, Harvard University Tech. Tept. 336. Seeley, E. W., P. E. Tallant and I. Rainwater (1964). "An Experimental VLF Dipole Traversing an Island, " Quarterly Report, Foundational Res. Projects April-June, Naval Ordinance Lab., Corona, NAVWEPS Rept. 8197. Smith, N. (1964). "The Effect of a Lunar Ionosphere on Lunar Surface Radio Communications, " University of Michigan Radio Astronomy Observatory, Report No. 64-7, June 1964. Sommerfeld, A. (1909). "Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie, " Ann. Phsik, Voq. 28, p. 665. Sommerfeld, A. (1949), Partial Differential Equations in Physics, Academic Press. Sommerfeld, A. and F. Renner (1942), Radiation Energy and Earth Absorption, English Translation. Wireless Engineer, Vol. 19, pp. 351, 409, 457.