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USI. Report No. 761

Surface-to-Surface and Subsurface-to-Aiu PropagationOf Electromagnetic Waves.

* TIlE DERIVATION OF ELECTRIC AND MAGNETIC FIELD COMPONENTS

FOR "THE. QUASI-STATIC, QUASI-NEAR, AND NEAR-FIELD RANGES

O PETER R. BANNISTER

S~E/,M Systems Planning Branch

Radio Communication Sy.Ntrms DiUision

0

17 February 1967 -.i . .. .. 4_ j

Distribution of this document is unlimited.

1U. S. Navy Underwater Sound LaboratoryFort TrumbulL New London. Connecticut

5:,,U,.LUOL L•'• U ""r

ABSTRACT

The electric and magnetic field components produced by vertical and horizontal dipoles(both electric and magnetic) are derived and presented for the quasi-static, quasi-near, andnear-field ranges. The depth, h, of the transmitting dipole is less than or equal to zero; theheight, z, of the receiving antenna above the plane, conducting, homogeneous earth variesfrom zero to some height, z, that is much less than the ionospheric reflecting height(ionospheric effects are neglected). The horizontal separation, p, between the transmittingand receiving antennas is comparable to the receiving antenna height, z. The derivationsare based upon the quasi-static and near-field approximations to the vector potentials forthe vertical and horizontal dipoles and upon application of the reciprocity theorem. Thesurface-to-surface propagation equations reduce to well-known expressions when I Y P I 1and I y, pI << 1, as do the subsurface-to-air equations when p >> z.

ADMINISTRATIVE INFORMATION

The work presented in this report was performed under USL Project No. 1-901-00-00as a general theoretical propagation study. The corresponding Navy Subproject and TaskNo. is SF 106 01 02-7077.

The report is based on a paper presented by the author at the symposium on "Sub.Surface Communications" sponsored by the Electromagnetic Wave Propagation Committeeof the Avionics Panel of the NATO Advisory Group for Aerospace Research andDevelopment (AGARD/NATO), held in Paris, France, from 25 through 29 April 1966.

REVIEWED AND APPROVED: 17 February 1967

W. A. VonWinkle R.L. Corkran, Jr., Capa N

Associate Technical Director Commanding Officer and Director

for Research

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS iii

LIST OF TABLES "i

DEFINITIONS OF SYMBOLS AND ABBREVIATIONS v

INTRODUCTION

SURFACE-TO-SURFACE PROPAGATION IN THE QUASI-STATIC RANGE 2The General Range 2Subrange 'yp 1 <>ii 4Some Values of the Field-Component Functions 4

SUBSURFACE-TO-AIR PROPAGATION 6The Quasi-Near Range 6

The Near-Field Range 7

SUMMARY 9

INITIAL DISTRIBUTION LIST Inside Back Cover

i/i

LiST OF ILLUSTRATIONS

Figur! Page

1 Dipole Orientations whev, 11 0+ 2

2 111K,1 versus IyFp/ 21 5

3 IWI versus 1yIp/2i1

4 I TI versus lylp,/21 6

LIST OF TABLES

Tables

I Surface-to-Surface Propagation Formulas for the General Quasi-Static

Range .10-11

2 Surface-to-Surface Propagation Formulas for the Quasi-Static

Subrange lyopi < <I< « y« p • 12

3 Surface-to-Surface Propagation Formulas for the Quasi-Static

Subrange I 0 pI <<1 >> »yjP• 13

4 Subsurface-to-Air Propagation Formulas for the Quasi-Near Range 14-15

5 Subsurface-to-Air Propagation Formulas for the Near-Field Range 16-17

6 Subsurface-to-Air Propagation Formulas for the Near-Field Range

with p >> z . 18-19

iiiliv

DEFINITIONS OF SYMBOLS AND ABBREVIATIONS

c The velocity of propagation in the upper half-space (free space); 2 3 ý 10"(meters/sec)

d| fThe infinitesimal dipole length (meters)

dA The infinitesimal dipole area (meters 2)

ei't The time factor assumed

EP The horizontal electric field component in the p direction 'volts/meter)

E IThe horizontal electric field component in the 4 direction (volts/meter)

E z The 7ertical electric field component (volts/meter)

G, Wait's height gain factor for vertical polarization (valid for p >- z);-- 2 Z/yl

The depth of burial of the transmitting antenna (h 0) (meters)

H The height of the vertical loop antenna above the earth; - VyI

ti- PThe horizontal magnetic field component in the p direction (amperes/meter)

The horizontal magnetic field component in the 0 direction (amperes/meter)

11z The vertical magnetic field component (amperes/meter)

HED The horizontal electric dipole

HMD The horizontal magnetic dipole

HGF The height gain factor; equal to the field strength at height z divided bythe field strength at height z = 0*

I0 (yIp/2) The modified Bessel function of the first kind, order zero, and argument y 1p/2

I I (Ylp/2) The modified Bessel function of the first kind, order one, and argument yIP/ 2

J0 (Ap) The Bessel function of the first kind, order zero, and argument Ap

Ko(ylp/2) The modified Bessel hunction of the second kind, order zero, and argument ypi 2

K I(yjpi2) The modified Bessel function of the second kind, order one, and argument yp/2

inks Meter-kilogram-seconds, the unit employed

R The radial distance in a spherical coordinate system; - (p 2 + z2)0

T 161IK, + 4yp(I IK° - ioKI) + y2,p 2 (g1 K I Ko)

uo0 (A2 + yo2)' (meters")(A2 + y2)1, (meters-1)

VED The vertical electric dipole

N'MD The vertical magnetic dipol •

W 31I lKI - (yjp/2)(IoKI - I Ko)

z The height of the transmitting antenna above the plane conducting earth(z > 0) (meters)

V

Yo The upper half-space (free space) propagation constant (meters"); - (_EoIoI2)%

1 IlThe lower half-space (the earth) propagation constant (the displacementcurrents in the earth are assumed to be negligible); 0 (i w&41o)0 (meters I)

85 The skin depth in the lower half-space (the earth); = (2/1o 1p)½

E 0 The permittivity of free space; T 10"°/36 n (farads/meter)

A The dummy integration variable

Aair The wavelength in the upper half-space (free space); c c/f

Aearth The wavelength in the lower half-space (the earth); - 2 r8

A - Ao The permeability of free space; - 4 v x 10'" (henries/meter)

p The radial distance in a cylindrical coordinate system; - (x2 + y2)'1

The conductivity of the lower half-space (the earth) (mhos/meter)

The azimuth angle in a cylindrical coordinate system; - tan* (y/s)

CU The angular frequency; - 2 if (radians/sec)

0+ ÷The infinitesimal distance above the surface of the earth (meters)

0" The infinitesimal distance below the surface of the earth (meters)

vi

SURFACE -TO-SURFACE AND SUBSURFACE-TO-AIRPROPAGATION OF ELEC f'RIOMAGNETIC WAVES

'rhe Derivation of Electric and Magnetic Field Componentsfor the Quasi-Static, Quasi-Near, and Near-Field Ranges

.!"T"ODUCTION

Rqdiation from electric and magnetic dipole antennas in the air above aplane, conducting, homogeneous earth has been -or.sidered by many writers,beginning with Sommerfeld. ' Unfortunately, relatively little attention has beenpaid to surface-to-surface propagation in the quasi-static range i . I )when -::P is allowed to be any value. (Definitions of the symbols appear in the

introductory pages at the front of the report.)In this report the theoretical work

that has been accomnlished for this range is summarized, and th.L electric and

magnetic field components that have not been derived previously (to the author'sknowledge) are derived for the case in which it o . Surface-to-air propa-gation in the near-field range has been considered by Norton,' who states, how-ever, that some of his formulas are valid only for distances down to a free-space wavelength i.e.. R - ._). Subsurface-to-air propagation in the quasi-nearand near-field ranges has been treated by Moore, ' Wait,' Babos and Wesley,"and Ba~os` (among others) with the restriction that , -- -- The field compo-

I A. Soutmerfeld., "•n the Propagation of lave. in tireless Telepraph'."

Annalen tier Phy ik. vnl. 81. no. 25. 11 leceml-er 1926. pp. 1135-1153.

2 k.A. \or*nn. "The Proparation of Hadio lavev Over the Surface of the Larth

and in the Upper Atmosphere." Proceeding% of the Institute of Radio Enginpers. Vol.

25. no. 4. 'eptember 1437. pp. 1203.-1236.SH.K. Wlore. "The ilteor-, of 4adtLo (Communirat ion between Submerged sub.

&4rine.-, Ph. 1). 1ho-,in . Cornell InivPrxit., 1"61. (Revis0-d in 1961 bl u.k. Mooreand IFL. Blair. "Di°.olr Radiation in a Conducting Half-.pare." M.i Journal of

Rpscarrh-l). Radin Propagation. vol. CJID). ho. 6. \ovpaber . e,-ember 1961.

pp. S'd-Sbl.)

SJ.W. wait. "the flectroasanetis •ieldlL -f a Ilorisontal Dipole in the

Presence of a (londtrting Ilalf-spa•'." CanatIlaso J-urnal of Phtsics. vol 14. 1041.pp. 11I-102h.

A. Ra"•ins. Jr.. a nd J.R. Ses I.. The tlorisontal 'lorttr, Dipole in a Un.-

dtttne Itlf.-pare. l'art. I and It. Krport, \o,. 11. 3 1 and S-.31. marine Ph 'Sia1l.aboroitor%. U'rtsrratt% of (asonli, a.n 11411. I•St4.

. BVRa'n. Jr., Diap.ic Rad,.a';,,n in the Pr•eaece of a C.*oaducart Ialf-Spar..

Porgamon )ores-. ('Aford. Inglani. 13't

Z Z

(oro)

II

VED HED HMD VMD

FiH. I - Dipole Orientation% when h = 0"

nents pr(duced by subsurface dipole antennas that are valid for the quasi-near( I....... - R . .,_ ) and near-field (11 comparable to ý., ) ranges are pre-sented in this report without the above restriction". Ionospheric effects areneglected.

Four types of dipole antennas will bC examined: the vertical electric dipole(VED), vertical magnetic dipole (VMD), horizontal electric dipole (WIED),and horizontal magnetic dipole (IIMD). The four antennas are situated at theorigin of a cylindrical coordinate system ,,.n and are assumed t! -carry aconstant current, I. The VED and lIED are oriented in the z and x direc-tions, respectively; the axes of the VMD and HMD are oriented in the z and

_y directions, respectively. The dipole orientations when h -• 0+ are shown inFig. 1. The earth occupies the lower half-space (z < 0); and the air, the upperhalf-space (z > 0). The units employed are meter-kilogram-seconds (mks); atime factor of " . is assumed.

SURFACE-TO-SURFACE PROPAGATION IN THEQUASI-STATIC RANGE

TilE GENERAL RANGE

For the general quasi-static range (,, < < .,,) and z = h= 0+, the approxima-tion that the propagation constant in air (',,) is equal to zero can be utilized inthe derivation of the field components. This is called the quasi-static approxi-mation and was developed by Lien. - It is valid for observation distances thatare very small with respect to an air wavelength (distances s }. /20) and fordepths, h, much less than the observation distance.

7 iv I,.iwn, ''lld.it inin from a Hforizontul I)ipole4 ira a Semi-Infminit lMiasi-

;'nt avo Med ium, Journnl of Applierd Phvic-. vol. 24, January Iq53, pp. 1-4.

2

Several electric ano magnetic field-colnponeiit e j)rs 'Lolls for th", g.n:..:.. !

quasi-static r'uIg( have been deteVrlmined previously. The IE - and IIf., comp)o-nents for the VED have been deri.ed by Norton;' the Ep, comp(.nent has beenderived by Wait and Campbell. " All e!ectric and magnetic components for theVMD have been dlerived by Wait "' and Gordon. " The I ITF) IE,, |..,and IIcomponents also lhave been derived by Wait. '2 Martin has extended Wait'sresults and has evaluate,! the lIED 1I,1, 1I ,,, and E%, components. ý Further-more, Wait has (letermimed the ITMI) magnelic fiheld components." 'rheseexpressions for the general quasi-staitie range are summ:arized in Table i.

The reciprocity theorem (which apl))lies to dipoles in the presence of any

linear medium) statesthiat the voltage, V., , induced in antenna 2 by the cur-rent, I,, of antenna 1 is the same as the voltage, V, , induced in antenna 1by an identical current, I , flowing in antenna 2. Applying the reciprocitytheorem, we can then determine the remaining field components for the general

quasi-static range. The IIMD) E , and E,,, components can be determinedfrom the IlI:D II[,, and IIH, components; and the IIIND E . component, fromthe VED IIf,, coaponcnt. Epressions for these field components also are inl-eluded in Table 1. Note that ,iP- P and dA - A when P and A are muchsmaller than ,..... and the measurement distance, ,.

Norton. op. Cit. (see footnote 2, ahlove).

1.1 . Wiail. tnd 1.L.. Cempl,.ll, 'Thle Yielt. of an Electric Dipole in a Semi-

1nfinite' Conducting Medium,'" .Journal of Gnojh'.sical Research. vol. 58, no. 1, 1953,

pp. 21-28.10 J.l. wait, "The IPropl•gation of Ele-ctromagne'tic Wave. Along the' Earth's

.urface," Elec'trom.ngnetie Waves., edited ibv 1. [anger, University of WisconsinP'ress, l462, pp. 2t3-290.

11 AN. Gu)rdi,, -"rhe Field Induced bv ,n Oscillatory Magnetic. Dipole Outside

a .emi -e ti- i ifinit t Conductor,'" Qunrter•y .Jourondl of Mechanical and Applied %lathemat -

.. s, vol. 1, no. 1, 1951, pp. 105-115.12 Wait, op. ,it. (stee f,,otnote .;, eal...ve).

13 C.A. Martin, It(\A I.,lorntories., Princeton, N..I., private communieation, 1963.

14 .1.11. %nit, ''lenhietn 'i" a iloriruontal Oscillating Magnetic Dipole Over a

Condtecting Homogeneous Enrth,' Transnctions of the American Geophysical Union, vol.

34, n,,o. 2, April 10.53, pp. 185-188; Atnd ''Th Fields of an Oscili ting •IagneticDipole Immersed in a Semi-Infinite Conducting Medium," .Journal of GeophysicalHli.-s4p ch. vot, l. 58, nio. 2, ittle I11,53, pp. 1 ,7-178.

3Y

SUBRANGE <..,, ' < I . YiP'

For the quasi-static subrange it, which ', I <<I<< y,P (i.e.,<.,,,r,,, <.. <, < k.,, ), which is actually the quasi-near range, the modified Bessel

functions of Table 1 can be replaced by the first one or two terms of theirasymptotic expansions and the e- ""' terms approach zero. The resulting field-component expressions are presented in Table 2.

For an HED antenna there is a diffused return current in the earth corre-sponding to the current in the horizontal wire. For this reason a horizontalwire above the earth with the ends of the wire grounded is called a "ground re-turn antenna." The current in the horizontal wire of length I and the groundreturn current act as an HMD (vertical loop) antenna of height H = 1/y, abovethe earth. This can be observed easily by comparing the HED and HMD field-component equations in Table 2. That is, the magnitude of the effective area,A, of this equivalent loop antenna is

A - _ _ (1)

where h is the skin depth in the earth. As a matter of interest, a "ground re-turn antenna," either buried or on the surface of a semi-infinite conductingmedium, is equivalent to a rectangular one-turn loop of length I and heightH I1/y, as long as P >>b.

SUBRANGE ,,,. < > P

For the quasi-static subrange in which ,< Y>,Ip ' (i.e.,"..> > < < ) ). the exponential and modified Bessel functions in Table 1

can be replaced by the first two or three terms of their series expansions. Theresulting field-component expressions are given in Table 3.

SOME VALUES OF THE FIELD-COMPONENT FUNCTIONS

Many of the equations in Table 1 contain modified Bessel functions of orderzero or one and argument yip 2. The magnitude of the function I, K, versus"• 2 is plotted in Fig. 2. For small values of the argument the function ap-

proaches the value of 1/2; for large values I, K, is approximately equal to

1/.,,,, This asymptotic expansion may be employed for values of yp/2 > 5The magnitude of the function W versus ),•, '2 is plotted in Fig. 3. For

4

Is

05

04-

03-

02-

01-

0 LLfL _ LL01 0.2 05 1 2 5 10

Fig. 2-- IlK versus jylyp2

0,6--

05

0,4

0 2

0 -

0

01 0,2 05 2 5 ýo

Fig. 3 - j Wl versus iy p /2,

1 4

120-

I08-

06-

o,2---

0.1 0.2 05 1 2 5 10

Fig. 4- T versus Iy, 1 21

small arguments this function also approaches 1/2; for large arguments it isapproximately equal to 2/,',P. The magnitude of the function T versus 1 y,p/21is plotted in Fig. 4. For small arguments T equals approximately y, 2p2 /4 ; forlarge arguments ( > 78 ) the asymptotic expansion T • 6 /ywp may be employed.

SUBSURFACE -TO-AIR PROPAGATION

THE QUASI-NEAR RANGE

For the quasi-near range (i.. ,, << R << i.,, ) with hO0- and zŽ-0+1the Lien quasi-static approximation applies as long as the observation distance,R, is less than t.,,jr/20 and the depth, h, of the transmitting dipole is muchless than R. If the earth is a conductor and IyR >> I(R >> ), thenit, _: ( ý,-+ yj,' '-- - , in the exact integral expressions, since the impor-tant values of i. are of the order of . Therefore, the exponential attenua-tion-with-depth term, e'y'h , may be removed from under the integral sign (inthe exact formulas for the field-component functions). By utilizing the aboveapproximations and Lhe integral ""

Is A. Erdelyi (editor), Tables of Integral Transforms, McGraw-Hill Book Com-

pany, Inc., New York, N.Y., vol. 2, 1954, p. 9.

6

"f .",e I- J,,(". , ) d'. P" ! , ( • (2)

(where the P, (z/R) are the Legendre polynomials), we have calculated theVED, VMD, and HED field components for subsurface-to-air propagation inthe quasi-static range. They are listed in Table 4.

The HMD field components can be obtained with the reciprocity theorem orby a synthesis of the HED field components. They can be found simply bydifferentiating the HED field components with respect to the depth, h. ForI yjR I>> 1 ( R > > s ) the depth factor is simply e Therefore, the HMDcomponents can be obtained by replacing d I with yjdA in the HED equations.The results of this method agree with those obtained with the somewhat differ-ent explanation presented for surface-to-surface propagation in the quasi-staticsubrange yp '! < < I < < yp . The HIVD field components also are listed inTable 4.

An examination of the equations presented in Table 4 reveals that the EP,E 0, and H, components have substantial height gain factors. The height gainfactor is defined as the field strength at height z divided by the field strengthat height z = 0+. However, the E , Hp, and Hb components are decreasedin magnitude when z >0. In fact, when .7= I' \ 2, the VED E, component isessentially zero (to a first-order a,'proximation). Similarly, when Z p -the HED and HMD H P components approach zero; and, when z p = 1/2, theVMD H P component is essentially zero (to a first-order approximation).

We note also that when h = 0- and z = 0+, the VMD, HED, and HMDfield-component expressions in Table 4 reduce to the expressions given in Table 3(which are valid for the quasi-near range with z = h = 0+). The VED com-ponents in Table 4 will be compatible also with those Ln Table 3 if they are mul-tiplied by the factor y' /:' (this is due to the shift from h = 0- to h = 0+).

THE NEAR-FIELD RANGE

For the near-field range (R comparable to i.,,, ) with h V0" and z - 0+,the assumptions that the earth is a conductor ( ol > > o F, ) that ,,,R > > I(R > > ),andthat R >> h still apply. The restriction that ( y )" ,,p <.,, » Iheight gain factor for vertical polarization,

16 Norton, op. cit. (see footnote 2, above).

7

G,. = I + ( y,` Yj ) z, (3)

is approximately equal to 1. The VED, VMD, and HED field componentsfor this range were evaluated on the basis of the above approximations and with

Sommerfeld's integral:

e__ e II J., •p ) X d , e (4

SU.- R

The components are listed in Table 5. The HMD field components (see Table 5)were obtained from the HED field components by setting d ! = Y, dA (as wasdone for the quasi-near range).

When y,.,R < < I, the near-field components (Table 5) reduce to the quasi-static field components (Table 4). If the VED antenna is placed at the earth'ssurface (h = 0+), the field components will be identical with those previouslyderived by Norton. " When P > > z. the near-field components reduce towell-known expressions; these are listed in Table 6. For example, the HIEDequations are identical with those previously derived by Wait " except for thefollowing differences:

a. Wait assumed that z = 0 when he derived the E and E • components.

b. Wait's height gain factor for the E, component [I + (yo-'y1 ) :1 is neg-ligible for the near-field range (p comparable to •..,tr); therefore, it

was not included in Table 6.

When , <K< 1, the horizontally polarized componenis (E., H , and H,)also are identical with Wait's. Therefore, the restriction that I ( Y'-' Y, ) p I < <is not required for these components.

17 Sommerfeld, op. cit. (see footnote Labove); and Erdflyi, op. cit. (see

footnote 14, above).

18 Norton, op. cit. (see footnote 2, above).

19 Wait, op. cit. (see footnote 4, above).

8

SUMMARY

The electric and magnetic field components produced by vertical andhorizontal dipoles (both electric and magnetic types) were derived and pre-sented for:

a. Surface-to-surface propagation in th.. quasi-static range,

b. Subsurface-to-air propagation in the quasi-near range, and

c. Subsurface-to-air propagation in the near-field range.

When I yip > > I or I yipI < z. Also, when I y.R I < < I , the near-field equationsreduce to the quasi-near field formulas. For additional information on thederivation of the field components, see USL Reports Nos. 698, 701, 719, 720,and 729.20

20 P.R. Bannister, The Quasi-Static Fields of a Horizontal Magnetic Dipole,

USL Report No. 698. 1 November 1965; P.R. Bannister, The Quasi-Static Fields ofDipole Antennas, Part 1. IISL Report No. 701. 3 January 1966; P.R. Bannister andW.C. Hart. The Quasi-Static Fields of Dipole Antennas. Parts 11 and Ill. USL Re-ports Nos. 719 and 720. 8 February 1966 and 23 February 1966; P.R. Bannister andW.C. Hart, The Near Fields of Subsurface Electric Dipole Antennas, USL Report No.728, 4 Mereh 1966; and I.C. Hart and P.R. Bannister, The Near Fields of SubsurfaceMagnetic Dipole Antennas, USL Report No. 729. 7 March 1966.

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UNCLASSIFIEDSecurity Classification

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U. S. Navy Underwater Sound Laboratory UNCLASSIFIEDFort Trumbull, New London, Connecticut 21) GROUP

3 REPORT TITLE

k, SURFACE- TO-SURFAC E AND SUBSURFACE-TO-AIR PROPAGATION OF ELECTRO-MAGNETIC WAVES- The Derivation of Electric and Magnetic Field Components for theQuasi-Static, Quasi-Near, and Near-Field Ranges

4 OESCRIPTIVE NOTES (T7me af report end Inclusiv'e daeO.)

Research report* AUTHOR(S) (Long none. horet name, initial)

Bannister, Peter R.

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17 February 1967 2 6 13je. CONTRACT ON GRANT ,jO. 9e ORIGINATOR'S RUPORNT iumosews)

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1S. ABSTRACT

The electric and magnetic field components produced by vertical and horizontaldipoles (both electric and magnetic) are b'-rived and presented for the quasi-static, quasi-near, and near-field ranges. The depth, h, of the transmitting dipole is less than or equalto zero; the height, z. of the receiving antenna above the plane, conducting, homogeneousearth varies from zero to some height, z, that is much less than the ionospheric reflectingheight (ionospheric effects are neglected). The horizontal separation, P.* between thetransmitting and receiving antennas is comparable to the receiving antenna height, z. Thederivations are based upon the quasi-static and near-field approximations to the vectorpotentials for the vertical and horizonta-l dipoles and upon application of the reciprocitytheorem. The surface-to-surface propagation equations rechice to well-known expressionswhen >>1p I and P <<c1. as do the subsurface-to-ai r equations when # >>z.

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thme report. report from DDC. "2a. REPORT SECURITY CLASSIFICATION: Enter the over- (2) "Foreign announcement and dissemination of thisall security classifiaction of the report. Indicate whether reotby DDC is rnot authorized.""Restricted Date" is included. Marking is to be in accord- eltance with appropriate security regulations. (3) "U. S. Government agencices may obtain copies of

this report directly ftom DDC. Other qualified DDC2b. GROUP: Automatic downgrading to specified in DOD Di- users shall request throughrective S200. 10 and Atrnied Fortnees Industrial Manual. Enterthe group number. Alsio, when applicable. show that optionalmarkings have been used fur Group 3 and Group 4 as author- (4) "*U. S. military agencies may obtain copies of thisized. report directly from DMC Other qualified users.3. REPORT TITLE: Enter the convlete report title in all shall request throughcapital letters. Titles in all cases should be unclassified.1f a meaningful title caroot be selected without classifice.lion, show title classification in all capitals in parenthesis (S) "All distribution of this report is conttrolled. Qual-immediately following the bile. if ied DDC users shall requmest through

4. DESCRIPTIVE NOTES If appropriate. enter the type of________________report. e.g.. Interim, progress. summary, annual, or find. lIfthe repoft has& beren furmished to the Office of TiechnicalGave the inclusive dates when a specific reporting period is Se'icePs. r-DWoarmen Of Commerce. for sale to the? public. SM-icovered. cater tise fact and enter the price, if knoumlo

S.AUTHDRIS) Enter the nome(s) of authog(s) as shown on IL, SUPPLEIIIENTARY NOTE& Use for additional irsplemna.or in the report. Enter last name, first nme. middole Initial. tory notte..If military, show raok an" brsnch of service. The name ofthe principal &Alltho as an ahaolute minimum requrement. 12. SPONSDRIt4G MILTARY ACTIVITY: "atr the mawme 0

6. RPOR DAL Eterthedat th reortas ay, the departmental project office or laboratory sponsornag (par6. RPOR DAT Enair he ate: th reort s dy, rrrg for) the research and dievelopmermt. Include address.

month. year. or month. year. If more than one date appearson the report, use date cl publication. 1.1 ABTRACT: Enter an abstract giving a belief and fachmal

7a TTALNUMBR O PAES Trioelpatecurd sumnairy of the document indlicative ofthegi rpo rtvesethoullhsh.l T0oTA nUrmaE FPGSTetl paiaintieue.6-e.conteth it miey a~so appear elsewhere is the body of the toesical Me.

shoud L~ow orma pagnaton pt..edues. ie..enteott If additional sapce io required. a continuation sheet shallnumber t'l pages containing Inlornatioi be attached'76 NUMWER OF REFERENCE& Enter the total numbqr of It is highily desirable that the abstraci of cloassified importsref~In'n #4 Citled In the rot.fOl be unclassifierd Each paragraph of ther abstract sheall e"d withG& CONTRACT OR GRA%-T NtUIIRt If opproloriate. enter on iadicalion of thI ilt" security classification of the M.ieo appjl, able numbwerm' the tontract #r grent under whoih formsatiae in the paragraph. represested as ITSo ers (Ca at (U)the irp.-on was Wiltten, There is no limitation On the Iveirth of the ebstract Now-&b. 4k. & so PROJECT NUJMBER. Entort the approgoriate ever, the suggeste l"Irh is frmM ISO I-% 22 WOWdS,

"mltry deprtnmbent adentafis numbonsu taas proitbee.et . 14 KEY WORDS: Key woeds.a s ore eten.ally meaningful teressukpoem .r~mbe. sstemnumerslas nuibee rts. r short phrases that rharacotenre as rPoor and mow be used 0s

9. ORIG.INATOR'S REPORT MUIEUNDtS. Cnter the of I*- made.i entries for cataloging ther report Key words most becool tppott numt-e- 1ty whirh Itie duocument wilt be identified ad,. ta'd so thoat so sereartt clessificatao. is o~reqed IftetAand. unatrolld bow the originotmltg at.% itiV. TinietrmUt lrSuch e-i equipmeest model desipatio. tied. same, militarttiybe uaqmiue I flths rfor-t. lot-sert Irode name. georaphgim I scoltif.. way he usted We kely

96 OTII~a. kFPoRT NII~%)It tI" rep.r- hon been 5*-e5 but will he tloll,di by an andrsit~on of oteclaictal con.asma1guoqmya oither repor tW-tt (.6brs ov teeh tho otta. roanabol test The 0oteftigmormt Of tiubs. rules. and weigtsiis pti onaelsi

tor tor .w..i also eadte thist uam-oers),th

IM. MA%'lAIIILITY LIMTAMM~ 91OTICKS Eateor sany lie611ittoas .0 lathero 4asumaca the rryio.rt. 01the' than I

U NC LASIFIEDSecurity Ctamfiadktice

Surface-to-Surface and Subsurface-to-Aiu Propagation Of … · 2018-11-08 · USI. Report No. 761...

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