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AD-A146 518 AN INDIRECT MEASURE OF BELOW-GROUND ELECTRIC FIELD i/i CONDUCTIVITY AND DIELECTRIC CONSTANT(U) HARRY DIAMOND LABS ADELPHI MD R P MANRIQUEZ ET AL. SEP 84 UNCLASSIFIED HDL-TR-2852 MIPR-HC1881-3-40i F/G 20/2 NL IlU fIlflIIIIIIIlf I IIlllllllll

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Page 1: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

AD-A146 518 AN INDIRECT MEASURE OF BELOW-GROUND ELECTRIC FIELD i/iCONDUCTIVITY AND DIELECTRIC CONSTANT(U) HARRY DIAMONDLABS ADELPHI MD R P MANRIQUEZ ET AL. SEP 84

UNCLASSIFIED HDL-TR-2852 MIPR-HC1881-3-40i F/G 20/2 NLIlU fIlflIIIIIIIlfI IIlllllllll

Page 2: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

,,"..

iii1.0 M~I n

*° ,I1 3

L'I

111,1 11.

1111.25 11.4 "1.6

MICROCOPY RESOLUTION TEST CHART"NATIONAL BUREAU OF STANDARDS-193-A

S..

4N

Page 3: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

coLO

Page 4: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

. ..

360

300

240

t.120

Page 5: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE 0MI.I Dee. Ente,e.I)__________________

READ INSTRUCTIONS -REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

1. REPORT N4UMBER 2.OVY ACCESSION NO. 3. CIPIENT'S CATALOG NUMBER

4. TITLE (ad Subtitle) S. TYPE OF REPORT & PERIOD COVERED

An Indirect Measure of Below-Ground Electric Field, Technical ReportConductivity, and Dielectric Constant_________________

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(&) S. CONTRACT OR GRANT NUMBER(&)

V Rolando P. Manriquez PRON: WS3-8301WSA9John F. Sweton MIPR: HC1001-3-401

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA & WORK UNIT NUMBERS

Harry Diamond Laboratories2800 Powder Mill Road Program Ele: 33126KAdelphi, MD 20783-1197

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

National Communications System September 1984vOffice of the Manager1.HUGROPAE

Washington, DC 20305 3814. MONITORING AGENCY NAME A AOORESS(If differetm trom Controlling Office) IS. SECURITY CLASS. (of tisl repot)

IS*. OECL ASSIFICATION/ DOWNGRADING ISCH EDULE

IS. DISTRIBUTION STATEMENT (ot mu. Repor)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (ot Mhe abstract entered in Block 20. if dlifeet from Report)

5 1 038

HDlwProuect E3fie

IX. KEY WORD (Cutbus m reverse 6111 II mec.v and Identify by block n,,bw)

Ground condrutiit andeienlect costaind Pnabrecodcigarallel-plateE-ed sensor toeaue

* the electric field beneath the air/ground interface. The sensor is described with a simple equivalent cir-cuit, and the characteristic response is evaluated both in time and frequency. The agreement between

.* *the calculated and measured transmitted electric f ield is qulite good for reasonable values of constant andfrequency-dependent electrical conductivity and dielectric permittivity of the ground. The electrical prop-erties of the ground were the only parameters that needed to be adjusted to provide agreement between-4theory and experiment. Those values taken were considered within reasonablebons

* O ~ 43 mioJANOSSSSSLT UNCLASSIFIED1 SECUITY CLASSFICAT FOR OF TIlS PAGE (fm~ 3Zta nteooQ

qw' -4 'v 1.

Page 6: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

VP'

FOREWORDV.

The National Communications System (NCS) in response to PresidentialDirective/NSC-53, "National Security Telecommunications Policy," is funding acomprehensive program on the effects of nuclear weapons on selected telecom-

- munications systems. A portion of this effort is directed at determining thehigh-altitude electromagnetic pulse (EMP) vulnerability of the commercial BellTelephone TI Carrier systems, and at developing a TI Carrier system specifi-cally engineered to be EMP hard. The work described in this report was per-formed in support of these efforts.

11 1 ..y od

9.. :.9

r r .. ;.

I4 ... .. L .... ...... ........, ... A " ,' L I l , ,

% IL

9.' . ___ _____ ___%

Page 7: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

L-TV• ..- 7

CONTENTS

Page

FOREWORD ........ ....................... .................. **............... 3

1. INTRODUCTION .................. ...... . .. . ..................... . . 9

2. ANALYTICAL CALCULATION OF TRANSMITTED E FIELD ........................ 10

3. EXPERIMENTALLY MEASURED FIELDS ...... . .............................. 0. 12

4. EFFECTS OF CONSTANT GROUND PARAMETERS--SENSOR CHARACTERIZATION ........ 15

5. EFFECTS OF FREQUENCY-DEPENDENT GROUND PARAETERS--SENSORCALIBRATITON ........................................................ 21

6. CONCLUSION AND RECOMMENDATIONS .............. o......s..............o...... 29 t

LITERATURE CITED ..... *............................ ....... ... 32

SELECTED BIBLIOGRAPHY .................................... **...... ***..... 33

DISTRIBUTION ............ .... ............... ..... ... ...... 35 5

FIGURES 6..-

1. Flow chart of an indirect measure of below-ground E field, 1

conductivity, and dielectric constant ............................. 10 or

2. Waves and fields ..................................................... 11

3. Isometric view of buried E-field sensor, measuring instruments,and REPS .. . . . . . . . . . . . . . .. . . . . . . .. . . . . .. 13 "

4. Measured Hx(t) fields at TP1 and TP4 ................................. 14

5. Measured sensor voltage Vo(t) at TP1 and TP4 ...................... 0 14

6. Equivalent circuit of E-field sensor ................................. 15

7. Results of first term and second term of equation (8) at TPI

with a - 0.007 aho/m and r = 15 .................................... 16 06

8. Results of first term and second term of equation (8) at TP4with a - 0.007 mho/m and Cr = 15 .................................... 17

9. Comparison between calculated and measured transmitted electric

fields at TP4, with a = 0.001 mho/m and cr = 15 ..................... 18

.

or.'V I

Page 8: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

FIGURES (Cont'd)

Page

10. Comparison between calculated and measured transmitted electricfields at TP4, with a = 0.007 mho/m and Cr = 15 ..................... 18

11. Comparison between calculated and measured transmitted electricfields at TP4, with o = 0.02 mho/m and Er = 15 ...................... 19

12. Comparison between calculated and measured transmitted electricfields at TP4, with a = 0.007 mho/m and Cr = 1 ...................... 19

13. Comparison between calculated and measured transmitted electricfields at TP4, with a = 0.007 mho/m and Cr = 80 .................... 20

14. Comparison between calculated and measured transmitted electricfields at TPI, with a = 0.007 mho/m and Cr = 15 ................... 20 .

15. Magnitude of transfer function A(w), measured sensor voltage

Vo0 (), and "unfolded" sensor voltage V(w) at TP4, witha = 0.007 mho/m and Cr = 15 22

16. Phase shift function O(w) response of sensor at TP4, witha = 0.007 mho/m and Cr = 15 ......................................... 23

17. Conductivity versus frequency for various volume percentages ofwater .25

18. Dielectric constant versus frequency for various volumepercentages of water ............. .................................. 26

19. Magnitude of transfer function A(w), measured sensor voltageVo(c), and "unfolded" sensor voltage V(W) at TP4, usingLongmire's soil data (10-percent moisture content) .................. 26

20. Phase shift function O(w) response of sensor at TP4, usingLongaire's soil data (10-percent moisture content) .................. 27

21. Comparison between calculated and measured transmitted electricfields at TP4, using Longmire's soil data (10-percent moisturecontent) ............................................................ 27

22. Comparison between calculated and measured transmitted electricfields at TP4, using Longmire's soil data (25-percent moisturecontent) ............................................................ 28

66 S,.06,

t.~.p O u %....%.~~ 4 4

Page 9: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

, I RT2J 77 77j.- 7 jO .rV

FIGURES (Cont'd)

23. Comparison between calculated and measured transmitted electric

fields at TP1, using Longaire's soil data (10-percent moisture

24. Comparison between calculated and measured transmitted electric

fields at TP1, using Longmire's soil data (25-percent moisture

contnt)..**.. ......... **o.* .... *o .... ..... o 2

Table 1. Coefficient an for Universal Soil .... ................ 24

ee.4Y,%oJ V e So

owd oIs 1 o s %% % 6N %.

Page 10: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

1. INTRODUCTION IAnalytical techniques exist for determining the electromagnetic (EI4P)

fields that are transmitted into the ground for given parameters of the ground

* and the incident field. The main objective of this paper is to indirectlymeasure the conductivity a, dielectric constant cr, and electric (E) fieldro"'*below ground due to an incident EXP field as produced by the repetitive EMPsimulator (REPS). REPS is a horizontal dipole radiator driven by a 1-MVrepetitive pulse generator. The measurements were taken at the Harry DiamondLaboratories (HDL), Woodbridge Research Facility (WRF), Woodbridge, VA.

There are two methods to accomplish this objective:

(1) The determination of the "calculated" transmitted E field, Et, fromthe measured magnetic field, Hx , at 1 m above ground, and the associated -m

Maxwell equations and Fresnel coefficients in a continuous air/ground inter-face. The ground can be treated as a good conductor whose most importantelectrical parameters are conductivity and dielectric permittivity, C. *

(2) The determination of the "measured" transmitted E field from theinduced voltage, V, across a buried capacitive parallel-plate E-field sensorwith a plate separation X. This V is "unfolded" from the measured voltage,Vo, at the sensor load through the use of the time-domain and frequency-domainsolution techniques. The time-domain solution is derived from an equivalentcircuit model of the E-field sensor. From this solution, the sensor can be

characterized as an E-field sensor and an E (first derivative of E) field *

sensor. The frequency-domain solution technique depicts the behavior of the Efield below ground through parametric variations of frequency-independent(constant) ground parameters. The frequency-domain solution of the sameequivalent circuit model of the E-field sensor uses ground parameters that areeither frequency independent (constant) or frequency dependent to describe thetransfer function, A, or sensor calibration of the sensor.

These two methods independently arrive at the solution of the transmittedE field below ground but both depend on a and £r" The parameters a and Crwere the only ones adjusted to provide agreement between the calculated and

* measured E fields transmitted below ground. When the calculated and measuredE fields are in good agreement for given a and Cr , a conclusion can be drawnfrom the results. %

A flow chart of an indirect measure of below-ground E field, conductivity,and dielectric constant is shown in figure 1.

This report presents comparisons between calculated and measured trans-mitted E fields using both constant and frequency-dependent ground parameters.

P"11VIOJS PAGEI$ ILANK --9 ,1

%' - .:

Page 11: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

ANALYTICAL MEASUREMENTMETHOD METHOD

MEASURED ABOVE IROUND USING MEASURED BELOW ROUND USING PARALLEL

SIR SENSOR PLATE E-FIELO RNSOR

MAXWELL EQUATIONS AND FRESNEL VLau) =ANiaxV@

COEFFICIENTS TO CALCULATE

2 N FOURIER TRANSFORM +TRNMTE ff V'"I-9-1- IVERSE FOURND TRANSFORMt 1. C2. C3, C4 - CONSTANTS, DEPENDENT Oil

WEUIT PARAMETERS

Figure 1. Flow chart of an indirect measure of below-groundE field, conductivity, and dielectric constant.

2.- ANALYTICAL CALCULATION OF TRANSMITTED E FIELD

When an E4P is incident at the plane boundary of a linear, homogeneous,isotropic, and conducting medium, some of it is reflected and some is trans-mitted into the medium. The transmitted E field can be found with the use ofFresnel reflection and transmission coefficients. 1- 3 The Fresnel coefficientsare a function of the electrical properties of the ground and the incidentangle of the electromagnetic wave. It is assumed in this study that theincident wave is a linearly polarized plane wave (of constant amplitude andphase) and the air/ground boundary is a semi-infinite plane.

The pertinent equations involve plane monochromatic waves (i.e., withsingle frequency) as directly derived from Maxwell's equations. Detailedderivations governing these equations can be found in works cited in theSelected Bibliography. Figure 2(a) diagrams the wave vectors of the incident,reflected, and transmitted waves used in this study. Figure 2(b) shows theconventional directions of electric and magnetic fields for horizontal polar-ization.

1E. C. Jordan and K. G. Balmain, Electromagnetic Waves and RadiatingSystems, Prentice-Hall, Inc., Englewood Cliffs, NJ (1968), 2nd ed.; ch 5, p144 ff.

2J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, Inc., New .York (1962), ch 7, p 216 ff.

3,. Born and E. Wolf, Principles of Optics, Pergamon Press, Oxford (1970),fourth ed.1 ch 1, p 40; ch 13, p 615 ff.

10

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IIf

S• ,% % %. % %. % ,% % • % ."_ .', ,. -Z,", .- ' , ,'m-, ' - - ' • ,,. _, , . .L

! I -". .'.',,".'.'.".'-"."-" .,.,. '. .. " ", " %' % , """Z ; ' - .. .

Page 12: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

.161.,

(a, (b)

6 F*FIELD MEASUREMENT POINT

GROUND x

kk

Figure 2. Waves and fields: (a) wave vectors of incident reflected andtransmitted waves and (b) conventional directions of electric and magneticfields for horizontal polarization.

The solution for the incident electric field above ground treated by Marx4

is

Eo(w) {ZoHx(w)/[sin i, (i - Rh(w)e-jtd)l]} Isin(wtd)/(wtd)12 • (1)

Eo (w) is a function of the free-space wave impedance ZO , the magnetic fieldH (w), incident angle *, Fourier transform variable w (W = 2wf), the Fresnelcoefficient for horizontal polarization Rh(w), and time delay td. The timedelay describes the difference of arrival time between the incident and re-flected pulses at the field measurement point above ground as shown in figure2(a). The last term of equation (1) is a filter function that removes thesingularities at

wtd = kw , k = 1, 3, 5,

Rh(w) is found to be

sin, - [Cr - jc/eow) - cos2I]'/2ROO( = -(2)h()=sin * + [ r - j(o/COW - cos2 *11/ 2 '

where co is the dielectric permittivity of free space. The time delay is

td - 2h sin 1 (3)c

where h is the height of the H-field sensor above ground (1 m) and c is thespeed of light.

4Egon Marx, Simulator Fields and Ground Constants, Harry Diamond Labora-tories, HDL-TR-1785 (February 1977).

.%

'e r11%4%% ,V

66N

Page 13: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

The transmitted electric field Et(,) is

Et(w) = Th("eydE0 (w) , (4)

where d is the distance from the interface in the soil and y is the propaga-tion constant, defined as

y = (_w 2 IIe + jwpaJ/ 1 2 • (5)

The transmission coefficient 5 Th(w) is

Th(w) = 2 i ,.(6){sin * + [er - j(o C o) - cos2 *,]"/2}

The time-domain electric field Et(t) is numerically computed through an in-verse Fourier transform6 of equation (4). Finally, Et(t) is averaged over a12-in. depth from 1 to 13 in. below the surface; the result is taken as the Efield at 7 in. below the ground.

3. EXPERIMENTALLY MEASURED FIELDS

Field measurements were made at the REPS facility at the following loca-tions (see fig. 3):

(a) test point 4 (TP4), close to the centerline at x = 800 ft and y = 82.5ft south of the centerline, and

..

. .(b) test point 1 (TP1), off the centerline at x = 800 ft and y = 609 ftnorth of the centerline.

At each test point, two field measurements were taken: (1) the totalmagnetic field, H,(t), at 1 m above ground and (2) the transmitted componentof the tangential E field averaged over a 12-in. depth from 1 to 13 in. belowthe surface.

The H x(t) was measured with a conventional Stanford Research Institute(SRI) cubical sensor box.7 Figure 4 shows the measured Hx(t) at TP1 and TP4.

5Egon arx, Reflected and Transmitted Fields for a Plane-Wave Pulse inci-dent on Conducting Ground, Harry Diamond Laboratories, HDL-TR-1740 (April1976).6Alfred G. Brandstein and Egon arx, Numerical Fourier Transform, HarryDiamond aboratories, HDL-TR-1748 (September 1976).

7B. C. Tupper, R. H. Stehle, and R. T. Wolfram, EMP Instrumentation Devel-opment, Stanford Research Institute, report 7990, under contract to Harry

*. Diamond Laboratories, Contract DAAK-02-69-C-0674.

12

4 . .• % . ,% ,.? . .% . , . . .. .% . ,, .- % . . -

Page 14: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

SOUTH

.REPS

x '.'- .FIELD SENSOR

R6214 CAKE ROME OPTIC TRANSMTTER0FIE OPTIC CABLE

NZ INSTRUMENTATION

Figure 3. Isometric view of buried E-field sensor(dashed lines), measuring instruments, and REPS.

The transmitted E field was measured by the use of two buried parallelaluminum plates. These plates are 12 in. long x 12 in. wide x 1/4 in. thick.They were separated a distance I of 1.75 in. at TP4 and 2.5 in. at TPI. In

O- both cases the plates were inserted to achieve intimate ground contact. Thevoltage V0 (t) generated across the plates by the field was measured by the useof a fiber-optic transmitter attached to the plate by an RG214, 50-11 coaxialdouble-shielded cable. This cable was 1.75 ft long at TP4 and 3 ft long atTP1. The 50-0 fiber-optic transmitter was connected to the instrumentationvan remote-reading equipment by a fiber-optic cable and a 50-l fiber-opticreceiver. The fiber-optic transmitter and receiver data link were designedand built by Jim Blackburn of HDL. Figure 5 shows the measured sensor voltageV0 (t) at TP1 and TP4. -

13e4%.9

* e*~ . * J ~ ~'.qiq V~ ..%C ~ ~ ~ W Ir.'0 IL%

Page 15: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

ma .....

50

40-,- -,

S20

, 3o~-i it

, I'

-10

N 20

-00 o-

* -4 o -/ -.--

-0 '''il0

, 0 /-20, I ,; I'l 1 I/\'-A",I/v

0 60 120 160 240 300 360 420 460 540 60

TIME (S) (xlO "8) •*Figure 4. Measured HxlCt) fields at 'TPI (dashed line) and TP4 (solid line).

200

680

fit

40I I-I

.- i t A %

o. L v\ V -, i ,, ; "

A -40-soI I I I lI I i I , -

0 12 24 36 46 60 72 84 g6 106 120

TIE (s) (xl1)Figure 5. Measured sensor voltage Vo(t) at TP1 (dashed line) and TP4 (solidline).

14

r..- - - . , ,... . If d ,. .,. -... - ,

. ' " - -,- - " " ",,." " " % % %" .P 4 -'.,d- qp- 6, 46 ., ..... . . .,*., , . . . .,,t-, . , .. , ,,

Page 16: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

4. EFFECTS OF CONSTANT GROUND PARAMETERS--SENSOR CHARACTERIZATION

The E-field data are obtained from the measured voltage by the use of theequivalent circuit model as shown in figure 6. This model is described byBaum8 as a short dipole antenna model. When time variations are slow enoughthat the short antenna approximation is valid, and assuming that the edgeeffects of the plates are not a significant factor, the equivalent circuit isused to represent the following relationship between the voltage through the

load, Vo (t), and the magnitude of the electric field, Et(t):

--sI + / -- + Cc dt , for t > o (7)-C dt

Here V(t) = Et(t)£, G = 1/Rs = Csa/c, RL is the load resistance, Cs = area,c/1 is the sensor capacitance, and Cc is the cable capacitance. This is thesame model for the E-field sensors used in Aurora with time-varying air con-

="-%:.ductivity. 9

V = I

S- O + +V0

Figure 6. Equivalent circuit of E-

1 C~o field sensor.'":C S G cc- RL LT C© C"

The solution of differential equation (7) is composed of a complementaryand a particular integral. In network terminology, these are also referred to

as the natural, source-free, or transient response and the forced or steady-

state response, respectively. Examination of equation (7) reveals that when* RL is large and Cc is zero, the source terms are zero and the solution is only

complementary. Solving equation (7) by the method of variation of parameters,the solution for Et(t) is

8C. E. Baum, Electromagnetic Pulse Sensor and Simulation Notes, Vol. 1, AirForce Weapons Laboratory, Note 13 (June 1970).

9Rolando P. Nanriquez, George Merkel, William D. Scharf, and Daniel Spohn,

Electrically-short Monopole Antenna Response in an Ionized Air Environment,Determination of Ionized Air Conductivity, IEEE Trans. Nucl. Scli. NS-26, 6(December 1979), 5012-5018.

15

,0t" -"% ',-

% * % . %

• .. % • N J. .4. -**" .* %.• . . -.. .... . ---% ". "..- • - -o . . . .- " . " . . .. .. * - - ' _,, ,- , • , % ' P ." , ," . ", . F -,". ... / , ... • . -.,v*,', , - . ", ", . •* ,..'.•. *

•S'"- 4

*

,

,:.,, .o., ..,.:,:,.-..-o ,.....,.*. ..- b.--

Page 17: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

Cs + CC Cs - GRLCc -t/RsCs

sEt(t) Vo(t)2

x f eV 0 t ') dt' , for t > 0 . (8)0

Several important observations may be made from equation (8). When RL islarge and Cc is zero, and the transit time (9/c) of the antenna model is longcompared to the rise time T of the incident pulse (i.e., RLCs >> T), the firstterm on the right-hand side of equation (8) dominates. In this case, thesensor can be regarded as an E-field sensor. On the other hand, when RLC s <T, the second term of equation (8) dominates and the sensor can be regarded asan E-field sensor. Otherwise, the sensor can be described as a combination ofan E- and E-field sensor. The transmitted electric field Et(t) can be numeri-cally computed from equation (8) or, alternatively, the voltage V(t) - LEt(t)can be obtained by solving the differential equation (7) by a Runge-Kutta orGear method. The solutions of the first and second terms of equation (8) areshown in figure 7 at TP1 and figure 8 at TP4, respectively, with a constant o= 0.007 mho/m and er = 15.

250

200

150

* "100

:5,0

0

-50

d~.0 120 240 360 480 600 720 640 960 1060 120TIME (s) (0-)

Figure 7. Results of first term (solid line) and second term(dashed line) of equation (8) at TP1 with a -0.007 inhale and

-15.

Cre

16

%~';;.

Page 18: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

360-

300 -

. , 2 4 0 -

~180

120

-60I:* 0 ' " I I \I i

* 100 200 300 400 500 600 700 800 900 1000 1100TIME (s) (x10 9 )

Figure 8. Results of first term (solid line) and second term(dashed line) of equation (8) at TP4 with a = 0.007 mho/m ander = 15."-

r

Actual measurements of a and Cr were not available for the time this testwas performed. However, previous data collected by the National Bureau ofStandards (NBS) show that the ground conductivity is approximately 0.007 mho/mand the Cr is 15 at I MHz. These data are discussed elsewhere1 0 and measuredfor a limited frequency range. The results from equation (8) and the time-domain Fourier transform of equation (4) are shown in figures 9 to 13, at TP4,for a varied with 0.001, 0.007, and 0.02 mho/m at er = 15, and Cr varied with1, 15, and 80 at o - 0.007 mho/m. Figure 14 shows the comparison between theresults of equation (8) and the time-domain Fourier transform of equation (4),at TPI, for a - 0.007 mho/m and Cr = 15. The significance of the parametricvariational effects to the expected values at the extreme is apparent. As aand Cr increase, the amplitude of the electric field decreases. Thewaveshapes at late times and low frequencies are somewhat altered at higherconductivities. The peak amplitude is particularly sensitive to the changes ofthe dielectric constant at higher frequencies.

"'Norman V. Hill, Effect of Frequency-Dependent Soil Parameters on Reflec--4 tion Coefficients, Harry Diamond Laboratories, HDL-TR-2004 (December 1982).

17

.6P

.V556_%. % L.

Page 19: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

7''

40

20 j

10 -"

0 -V v f

-10

-201 1 10 10 20 30 40 50 60 70 so 90 100

TOHE (s) (M-O81

Figure 9. Comparison between calculated (dashed line) and measured (solid

ine) transmitted electric fields at TP4, with a 0.001 mho/m and er = 150

400 -

6 400 -

ZI 200O

100 -

' 0 A-.-

.%

0 10 20 30 40 50 U 70 go I 100TIE (S) (x 8)-

F-. Figure 10. Comparison between calculated (dashed line) and measured (solid

line) transmitted electric fields at TP4, with a - 0.007 .ho/m and Cr - 15.

S.

I! I-

% % %%II ."pN%%

Page 20: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

460

• " 480 -e

400

320

S240

~.160

-80-

9 I I I I I I I I

* 0 10 20 30 40 50 60 70 60 90 100TIME (s) (xl0 " )

Figure 11. Comparison between calculated (dashed line) and measured (solidline) transmitted electric fields at TP4, with a - 0.02 mho/m and Cr = 15.

75-

s 0

". 45E

30

15

0

• -15 10 0 10 20 30 40 50 60 70 S0 90 100

TIME (s) (0O- 1).p.'

Figure 12. Comparison between calculated (dashed line) and measured (solid,.m+ line) transmitted electric fields at TP4, with a - 0.007 mho/m and Cr -

-. 19

*' 4. % % %/C L v b.~ I

+o++ ,+++ + o +.,o ° +,.. ++ ,. +,, . .,,. .,,.,..,.+ , . ..: - s,%

Page 21: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

400

320

S240

160

80

0 10 20 30 40 50 60 70 8o go 100TRME (s) (x10 3)

Figure 13. Comparison between calculated (dashed line) and measured (solid*line) transmitted electric fields at TP4, with a 0.007 mho/m and er =80.

500

400 r

300 j

6 200

00S

-100

0 10 20 30 40 so s0 70 s0 g0 100TIME (s) (xz10')

*Figure 14. Comparison between calculated (dashed line) and measured (solid*line) transmitted electric fields at TPI, with a 0.007 mho/m and er 15.

20

5%,%

WS% N~ % ~% ~sS % 9S.%OP~ %%~.* A ,*

Page 22: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

One of the unique features of the measuring system, depicted in figure 3," is the fiber-optic system. The advantage of implementing this system is to

electrically isolate the E-field sensor from the instrumentation van, therebyeliminating the need for a long cable between the sensor and the van.

*, 5. EFFECTS OF FREQUENCY-DEPENDENT GROUND PARAMETERS--SENSOR CALIBRATION

The use of constant (frequency-independent) values for a and er results ina sensor calibration (or transfer function) A that is a constant. This A canbe used to determine the transmitted E field across the parallel-plate sensor -

as .

Et(w) = - A . (9)

However, in reality, a and er are frequency dependent, and for larger varia-,0%tions of frequency, a more accurate calibration of the buried E-field sensormust include a frequency-dependent transfer function.

*Let A(w) be the transfer function of the buried E-field sensor as deter-mined by taking the Laplace transform of equation (7) in the s-domain (s =jw). In general, the transfer function is a complex quantity and can bewritten as

A(w) = V(w)/Vo()o (10)

A(W) is also stated in terms of magnitude and phase as

A(w) = IA(W)Ieiw), (11)

where IA(w)I is the amplitude-response function and f(w) is the phase-shiftfunction of the sensor. The transfer function depends on the circuit parame-ters as

A() - M + sB (12)

G + sCs0where M W 11 + RLG)/RL and B - C5 + Cc . The amplitude-response functionJA(w)I is

I^(-)1 " [1/( G 2 + w2Ci)][(MG + W2BCs)2 + W2(BG - M2]1/2, (13)

and the phase-shift function O(w) is .

)(BG - CsK) " ,'MG + w2BCs

21

ve%0% e. 'Va

%, % N

%a 4 1 % I % %, . ~* ~ * . # w * * .~ p ~ ~ 4 %* SI' * a % .' '1

Page 23: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

The results for IVo(w)l, IV(w)I, IA(w)I, and O(w) as a function of fre-quency are shown in figures 15 and 16 at TP4, respectively, for a constant a - .'.

5 0.007 mho/m and er = 15. Ideally, this sensor should produce an amplitudefrequency response that looks "flat" in the frequency band of interest and aphase shift that is a linear function of frequency. In other words, thespectrum of the measured input voltage V(w) is identical to the spectrum ofthe output voltage Vo(w) as expressed in equation (10). This means that theinput voltage is passed undistorted by the measuring system. But for somecases, when the amplitude and phase frequency response are functions of a and J,£ r that vary with frequency and moisture content, the output voltage may besubstantially different from the input. From these viewpoints, depending onthe ground parameters, the sensor's transfer function could appreciably alteror distort the output voltage.

Finally, the "unfolded" measured transmitted electric field is

Et = A(w)Vo(w)/z . (15)

10-1

10"1

10"4

10"7-1"

10-6 -___ ,' ,

10-7

10-- -

1011"

10.12 1 1 1

101 102 103 10 10 107 108 1 9 '

FREUJENY (Hz)

Figure 15. Magnitude of transfer function A(M) (solid line),measured sensor voltage Vo(M) (dashed line), and "unfolded"sensor voltage V(w) (dash-dot line) at TP4, with a = 0.007mho/m and er 15.

22

%0.~ ~~~ ~~~~ %. , ;. .. - , ., .. , ,....,.

Page 24: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

I 7 K

-30

-60

_-90

% toLU -120%

-150

-160--

4- 21 0 , I I I ,I I

101 102 101 4 18 106 107 lo 109

FREOUBNCY (Hz)

Figure 16. Phase shift function (a) response of sensor at TP4,

with a = 0.007 mho/m and er = is.

Several studies have been conducted concerning the measurements and theo-

retical formulations of the electrical properties of the soil, namely, a ander as functions of frequency and moisture content. Longaire and Smith1Ideveloped a universal formula for a and cr over the frequency range of 5 Hz to3 x 1012 Hz, based on Scott's data12 for soils and Wilkenfeld's data for someconcrete and grout samples (Wilkenfeld's data can be found in Longmire and

Smith I1 ).

I IC. L. Longairs and K. S. Smith, A Universal Zapodancs for Soils, MissionResearch Corp., Santa Barbara, CA, Contract Moo DRAO01-7 5-C-O094 (October1975).•

12j. m. Scott, EWectrical and Magnetic Properties of Rock arW Soils, Notse;le, Electromagnetic pulse Theoretical motes, Air Force Weapons LaboratoryoBW/2-1 (April 1971); also U.S. Geological Survey Technical Letter, Special Proj-act 16 (26 may 1966).

23 '

%,,

ap F..JI..

%'

• 4..,4,: . .. . , . , . , . , ,.*4. . • , , , . , . , . , , .

Page 25: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

The a and er derived from Longmire and Smith's "universal RC networkmodel" are

N a

Cr = c + (relative) (16)

n: (f fnn)2

Na- 0 o + 2w% anf n (mho/m) (17)

n=1 n + (f/fn)2

where

N 13,

=c 5,

f = frequency (Hz),

an = the constant coefficients (see table 1),

fn F(P)fn(10%)'

* f (10%) = o1 n-1 Hz,

',.'. F(P) = (P/10)1 .2 8 ,

P - water content (percent), and

1S0 = 8.0 x 10 .3 (P/10)1' 5 4 (mho/m).

Figure 17 shows the ground conductivity a versus frequency for various volumepercentages of water. Figure 18 shows the dielectric constant Cr versusfrequency for various volume percentages of water.

TABLE 1. COEFFICIENT an FOR UNIVERSAL SOIL

(see eq (16) and (17))

n a n an n an

1 3.4 x 106 6 1.33 x 102 11 9.80 x 10- 1

2 2.75 x 105 7 2.72 x 101 12 3.92 x 10- 1

3 2.58 x 104 8 1.25 x 101 13 1.73 x 10- 1

4 3.38 x 103 9 4.805 5.26 x 102 10 2.17

O.:

go

24

yw

,"-

Page 26: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

o.

Because of the unavailability of Woodbridge's soil data over a wide rangeof frequency, it was necessary to implement Longmire and Smith's universalformula for a and E r in the program. However, some old data taken by NBS forWoodbridge's soil show relatively low a and er; Hill10 discusses these data.In the analysis, 10-percent soil moisture content, a = 0.007 mho/m, and Er

V. 15 provided close agreement between calculated and measured transmitted Efields below ground. The results for IV MI. IV( )I, A(W)I, and OM with10-percent moisture content at TP4 are shown in figures 19 and 20. The com-parison between the inverse Fourier transform of the calculated transmittedelectric field (eq (4)) and the "unfolded* measured transmitted electric field(eq (15)) using a and Er dependent with frequency at 10- and 25-percent mois-- ture content are shown in figures 21 and 22 at TP4, and figures 23 and 24 at

TPI. Indeed, the transfer function of the sensor is highly sensitive to theelectrical parameters of the soil.

J~. A.

A-5%, B-10%, C-15%, D-20%, E-25%.,.-.

AA

10-" 34.

00e08

j 25

40 0wi~l

14

15

11 0 0 0

fI. ,EESU CY (Hz)

2'. Figure 17. Conductivity versus frequency for various volume,-/"percentages of water.

% ..- _ _0

... ,'-.".,, 10 Norman V. Mill, Effect of Drequencv-Dependent Soil Parameters on Ref ec- "'.'" tion Coefficie.. , ilarr i Dlaaonl Leboratrfle, NDL-TR-2004 (December 1952).•

2

[->_" 251:

Page 27: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

is -

"106 1 11 "1, 1

A-5%, B-10%, C-15%, 0-20%, E-25%

SS10_

"" 104101 -_,

LU C

C 102

'S 10'I I I I I , I ,

101 102 103 104 105 106 108 log

FREOUENCY (Hz) .Figure 18. Dielectric constant versus frequency for various volume .5

percentages of water.

1001 T 1 .* 10"1 ,

-

-. 10-2

", I -10-110-1

S ---------------

.5. 1.-1

0 10-11

- ~10-12 I . I

101 102 lO3 10 10 1 Si 100lo lp"t

FEOUMCY (Nz)Figure 19. Magnitude of transfer function A(M) (solid line), measured sensorvoltage Vo(M) (dashed line), and "unfolded" sensor voltage V(w) (dash-dotline) at TP4, using Longmire's soil data (10-percent moisture content).

26 -6..... .. - . . . "'I ...- , '"." ". " . % %

Pe... ,* . ; ,+ . .U:' " • . • ".' * "p 5%* ' ' " " " - . 5 : '' :o .. .,, , ... o,.,. ..- , . , .. '. ... ,..

Page 28: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

-A 7• . . . . ,>S

401

20-40

-20

-., -20

l -40

-60

-80

9 -100101 102 103 1e 105 106 10t 10 log

FREQUENCY (Hz)Figure 20. Phase shift function O(w) response of sensor at TP4, usingLongmire's soil data (10-percent moisture content).

480 -[

' 400 -

320

6 240

A

-0

1. III 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ ",.

0 10 20 30 40 50 60 70 80 90 10

NM (S) (xl " )Figure 21. Comparison between calculated (dashed line) and measured (solid

- line) transmitted electric fields at TP4, using Longmire's soil data (10-percent moisture content).

27

111111:i.

swimW

Page 29: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

-.

S. 360

300

240

IgoS180

MP~ 120

60

\* *. -V-60

0 10 20 30 40 50 60 70 80 90 100

TIME (s) (x0 8)

Figure 22. Comparison between calculated (dashed line) and measured (solidline) transmitted electric fields at TP4, using Longmire's soil data (25-percent moisture content).

400

2 320

240

160

>:--. ~ ~ . o .',/.,,"""" -",-,,.,-

-60 V

--. , ,

10 20 30 40 50 60 70 s0 90 100

TIE (s) (zo "I)

* Figure 23. Comparison between calculated (dashed line) and measured (solidline) transmitted electric fields at TPI, using Longmire's soil data (10-percent moisture content).

28

. % . .. , ... .. . . .. , . .a. O .. 5,%. . " .

NU% % %

Page 30: IlU CONDUCTIVITY fIlflIIIIIIIlf AND DIELECTRIC …reflected, and transmitted waves used in this study. Figure 2(b) shows the conventional directions of electric and magnetic fields

300

I

240

p 1 60*, ,-.-

-120

-6-

4e -12Sn ,J l I I J ,

0 10 20 30 40 50 60 70 s0 90 100

TIME (S) (xlo )

Figure 24. Comparison between calculated (dashed line) andmeasured (solid line) transmitted electric fields at TP1, usingLongmire's soil data (25-percent moisture content).

6. CONCLUSION AND RECOMMENDATIONS V

This paper documents an attempt to experimentally measure the E-fieldcomponent of an EMP below ground and to compare the results to an analyticalcalculation. The results of equations (4) and (15) showed good agreement for10-percent moisture content, constant a = 0.007 uho/m, and Cr = 15.

The measurements can be improved by the use of a differential-mode voltageprobe to measure the transmitted E field. The RG214 cable can be removed andthe sensor directly connected to the fiber-optic transmitter. Another im-provement would be to accurately determine a and Cr over a wide range of

* frequency and depth at the same location where the fields were measured, andat about the same time. The availability of more soil data would reduce theuncertainty in the sensor calibration.

The assumption that the E3P was a plane wave over a homogeneous planesemi-infinite ground in the far-field radiation zone may be justified by the,-'quality of the results. The transmitted E field vanishes at late times (>1ms) but the transmitted H fields may not. Also not taken into account werethe multiple reflection of the fields and the effects of dispersion due to theexistence of different layers of strata below ground. These uncertainties canbe resolved by measurement of the N and H fields at different depths below theair/ground interface.

NN%, 29

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Analysis has shown that it may be possible to indirectly measure a and cras a function of moisture content and frequency with the parallel-plate E-field sensor. The sensitivity of the sensor is demonstrated through thesensitivity (S) analysis of the equivalent circuit model of the sensor'sresponse to varying moisture content (P), i.e., S = 3V/3P (see fig. 21 to 24).

Perhaps the most significant aspect of this effort is that, through anadequate calibration of the buried E-field sensor, a method now exists for theimmediate and relatively easy indirect determination of ground conductivityand dielectric constant. This method, through the Fourier transform, couldthen be made available as frequency-domain data and applied as derived to allEMP coupling programs.

The curve-fitting equations (eq (16) and (17)) used by Longmire andSmith"1 that determined the er and a based on Scott and Wilkinfeld's data canbe further modified by adjusting the necessary coefficients in the equations

0 to obtain a closer correlation between the calculated and measured transmittedelectric fields. A computer-aided optimization procedure1 3 is needed toaccomplish this task. This curve-fitting method can analytically improve thedetermination of the a and er for Woodbridge's soil. Ni

The use of calibrated, shallow, buried parallel plates should be made partof all field-test system programs because it is a simple, inexpensive methodof determining the soil conductivity at the same time that the experimentalcoupling data are collected on the system. Thus, a conductivity measurementmade at the beginning of each test day can be used to predict the signallevels expected. And, in addition, an accurate evaluation of experimentallycollected data can then be used by the analyst to predict the levels of in-duced signals for any conditions of soil.

Future efforts will be to explore ways of improving the measurement methodby (1) the determination of the effects of RG214 cable on the measurement,

" (2) an independent direct measurement of a, erg and P by whatever means,(3) the use of a different buried sensor (dipole, magnetic loop, two parallelcylinders, two parallel spheres, etc), and (4) the measurement of conductioncurrent density (aEt) below the ground using the parallel-plate sensor. Thislast measurement can be performed by connecting a large resistor between thesensor and a short RG214 cable. In series with the cable will be animpedance-matching device. This device will match the high-impedance sensor

* system (sensor and resistor) to the low-impedance data-link system (cable andfiber-optic system). The use of an impedance -matching device makes it possi-ble to directly measure the induced sensor voltage. The signal propagatedbelow the ground will be produced by the REPS.

11C. L. Longmire and K. S. Smith, A Universal Impedance for Soils, MissionResearch Corp., Santa Barbara, CA, Contract No. DNA001-75-C-0094 (October1975).

13R. Fletcher and N. J. D. Powell, A Rapidly Convergent Descent Method forMinimization, Computer J. 6 (1963), 163.

Op

30 V.r.'

I%

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.00

A fifth way to improve the method is by the measurement of displacementcurrent density--e(dEt/dt)--below the ground. This measurement can be per-formed by covering one of the plates with a thin insulator (e.g., plastic) andburying these plates below the ground. The results of all these measurementswill further validate the results obtained from the existing analytical tech-niques employed in this report.

A conclusion reached as a result of this study is that the equivalentcircuit model of the sensor is an adequate model for REPS field rise times andtypical ground parameters. The modeled sensor system performed well andprovided physical insight to the problem. The transfer functions were eval-uated directly from the circuit model and showed the characteristic responseof the sensor. V

The determination of the E field below ground due to an incident EMP field

is summarized as follows:

(1) The H field above ground was measured and used to calculate the trans-mitted E field with the aid of Maxwell's equations and the Fresnel coeffi-cients.

(2) The induced voltage across the parallel-plate sensor was measured and"unfoldedu in two ways:

(a) time-domain formulation of the equivalent circuit model of the E--field sensor using constant ground parameters, and

(b) frequency-domain formulation of the same equivalent circuit modelusing ground parameters dependent on frequency and moisture content.

Finally, the applied conceptual and measurement scheme showed satisfactory Presults and provided vital information about EMP field sensors and the elec-trical properties of the conducting ground. A.

% .ON . A.. . .L

" ,:'

A... A

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LITERATURE CITED

(1) E. C. Jordan and K. G. Balmain, Electromagnetic Waves and RadiatingSystems, Prentice-Hall, Inc., Englewood Cliffs, NJ (1968), 2nd ed.; ch5, p 144 ff.

(2) J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, Inc., NewYork (1962), ch 7, p 216 ff.

(3) M. Born and E. Wolf, Principles of Optics, Pergamon Press, Oxford(1970), fourth ed.; ch 1, p 40; ch 13, p 615 ff.

(4) Egon Marx, Simulator Fields and Ground Constants, Harry Diamond Labora-tories, HDL-TR-1785 (February 1977).

(5) Egon Marx, Reflected and Transmitted Fields for a Plane-Wave Pulse Inci-dent on Conducting Ground, Harry Diamond Laboratories, HDL-TR-1740(April 1976).

(6) Alfred G. Brandstein and Egon Marx, Numerical Fourier Transform, HarryDiamond Laboratories, HDL-TR-1748 (September 1976).

(7) B. C. Tupper, R. H. Stehle, and R. T. Wolfram, EMP InstrumentationDevelopment, Stanford Research Institute, report 7990, under contract to

Harry Diamond Laboratories, Contract DAAK-02-69-C-0674.

(8) C. E. Baum, Electromagnetic Pulse Sensor and Simulation Notes, Vol. 1,Air Force Weapons Laboratory, Note 13 (June 1970).

(9) Rolando P. Manriquez, George Merkel, William D. Scharf, and DanielSpohn, Electrically-short Monopole Antenna Response in an Ionized AirEnvironment, Determination of Ionized Air Conductivity, IEEE Trans.Nucl. Sci. NS-26, 6 (December 1979), 5012-5018.

(10) Norman V. Hill, Effect of Frequency-Dependent Soil Parameters on Reflec-A. tion Coefficients, Harry Diamond Laboratories, HDL-TR-2004 (December

1982).

(11) C. L. Longuire and K. S. Smith, A Universal Impedance for Soils, MissionResearch Corp., Santa Barbara, CA, Contract No. DNA001-75-C-0094 (Octo-bar 1975).

(12) J. H. Scott, Electrical and Magnetic Properties of Rock and Soils, Note18, Electromagnetic Pulse Theoretical Notes, Air Force Weapons Labora-tory, EiP 2-1 (April 1971); also U.S. Geological Survey TechnicalLetter, Special Project 16 (26 May 1966).

(13) R. Fletcher and M. J. D. Powell, A Rapidly Convergent Descent Method for

Minimization, Computer J. 6 (1963), 163.

32

. . . . - -.. .. , .---. -

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V.

SELECTED BIBLIOGRAPHY 46,..".

Baum, C. E., The Reflection of Pulsed Waves from the Surface of a ConductingDielectric, Air Force Weapons Laboratory, EP Theoretical Note 25 (1967).

King, R. W. P., and C. W. Harrison, Jr., J. Appl. Phys. 39 (1968), 4444.

Klebers, Janis, Time Domain Analysis of the Electromagnetic Field in the Pres-ence of a Finitely Conducting Surface, Proceedings: Department of the ArmySecurity Agency DIP Technical Conference (1969), p 4-1.

Kraichman, M. B., Handbook of Electromagnetic Propagation in Conducting Media," Headquarters Naval Material Command, NAVMATP-2302 (1970).

Marx, Egon, Simulator Fields and Ground Constants, Harry Diamond Laboratories, ;.-.#HDL-TR-1785 (February 1977).

Marx, Egon, Reflected and Transmitted Fields for a Plane-Wave Pulse Incidenton Conducting Ground, Harry Diamond Laboratories, HDL-TR-1740 (April 1976).

Messier, M. A., The Effect of Ground Reflection on Observed DIP Waveforms, .

Topical Report, Mission Research Corp., Santa Barbara, CA (1974).

Monroe, Richard L., J. Appl. Phys. 40 (1969), 3526; 41 (1970), 4820.

Vance, E. F., Coupling to Shielded Cables, John Wiley & Sons, Inc. (1978).

Wait, J. R., and C. Froese, J. Geophys. Res. 60 (1955), 97.

%'.I

0 33

II r It. "

? . .V 4IV . . ""' . . : , " .-" a, .. ,'T,, .. . .

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- -. -~ ---. -.-. : -.

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COMMANDER CAMP H. N. SMITH, HI 96861US ARMY NUCLEAR & CHEIICAL AGENCY

ATTN MONA-WE COMMANDING OFFICER7500 BACKLICK RD NAVAL RESEARCH LABORATORYSPRINGFIELD, VA 22150 ATTN CODE 4720, J. DAVIS

WASHINGTON, DC 20375DEP CH OF STAFF FOR RSCH DEV a ACQDEPARTMENT OF THE ARMY COMMANDERATTN DAA-CSS-N NAVAL SURFACE WEAPONS CENTERWASHINGTON, DC 20310 ATTN CODE F-56

DAHLGREN, VA 22448* 'COMMANDER

us ARMY RSCK & STD OP (RUll) COMMANDERATTN CHIEF, PHYSICS a M4ATH BRANCH NAVAL SURFACE WEAPONS CENTERFPO NEW YORK 09510 ATTN CODE F32, E. RATHBURN

ATTN CODE P30CHIEF WHITE OAK LABORATORYUS ARMY SATELLITE COMMUNICATIONS SILVER SPRING, Nd 20910

AGENCYAT"M DRCPN-SC DEPARTMENT OF THE NAVYFT NOMiOGUT, NJ 07703 DIRECTOR, NAVAL TELECOMMUNICATIONS

DIVISIONOFFICE OF THE CHIEF OF NAVAL OPERATIOUS

'4 ATTN OP941, NAISLMAIER

36

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DISTRIBUTION (Cont 'd)

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i DEPARTMENT OF THE NAVY (Cont'd) LAWRENCE LIVERMORE NATIONAL LAS

ATTN 0P943 ATTN TECHNICAL INFO DEPT LIBRARY

WASHINGTON, DC 20350 ATTH L-156, H. CABAYAN, L. MARTINPo BOX 808 S"

HQ, USAF/SAMI LIVERMORE, CA 94550WASHINGTON, DC 20330 IRTDIRECTOR .

AIR FORCE COMMUNICATIONS COMMAND NATIONAL SECURITY AGENCY

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SCOTT AFB, IL 62225 9800 SAVAGE ROADPT MEADE, MD 20755

COMMANDER US AIR FORCE SPACE COMMANDATTN K1O AMERICAN TELEPHONE a TELEGRAPH CO ."

ATTN KRQ ATTN SEC OEC FOR W. EDWARDS

ATTN XPOW 1120 20TH STREET, NW.PETERSON APB, CO 80912 WASHINGTON, DC 20036

1842 EEG AT&T BELL LABORATORIES

ATTN EEISG ATTN R. STEVENSONSCOTT AIB, IL 62225 ATTN J. MAY (3 COPIES)

1600 OSGOOD STHEADQUARTERS N. ANDOVER, MA 01845ELECTRONIC SYSTE4S DIVISION/YS

ATTN YSEA AT&T BELL LABORATORIES

HANSCOM AFB, NA 01730 ATTN J. SCHOLL (5 COPIES)ATTN J. SERRI

HEADQUARTERS CRAWFORDS CORNER ROADUSAFE HOLMDEL, NJ 07733ATTN DCKIRAMSTEIN AIB, GERMANY DON CORP

ATTN CORPORATE LIBRARY

SYSTEM INTEGRATION OFFICE 7915 JONES BRANCH DRIVE

ATTN SYE MCLEAN, VA 22102PETERSON APB, CO 80912

, OOEING CO ,

AIR FORCE WEAPONS LABORATORY/DYC ATTN R. SHEPPEATTN NTC4, TESD, IESM PO BOX 3707

IFIRTLAND AFB, NM 87117 SEATTLE, WA 98124

CENTRAL INTELLIGENCE AGENCY COMPUTER SCIENCES CORPORATIONATTN OWSR/NED SYSTEMS DIVISIONATTN OSR/STD/NTB, A. PADGETT ATTN A. SCHIFF

WASHINGTON, DC 20505 1400 SAN MATEO BOULEVARD, SEALBUQUERQUE, NN 87108

DIRECTORFEDERAL EIERGENCY MANAGE4ENT AGENCY ELECTROMAGNETIC APPLICATIONS, INCOFFICE OF RESEARCH/NPP ATTU R. PERALAATTN STATE & LOCAL FROG SUPPORT PO BOX 26263500 C STREET, SW 1978 SOUTH GARRISON STWASHINGTON, DC 20472 DENVER, CO 80226

FEDERAL PREPAREDNESS AGENCY ENGINEERING SOCIETIES LIBRARYGENERAL SERVICES ADMINISTRATION ATTN ACQUISITIONS DEPTATT ESTE-M MURTHA 345 EAST 47TH1 STREET18TH & F STREETS, MW ME YORK, NY 10017WASHINGTON, DC 20405

GINORGIA INSTITUTE OF T ENOLGOFFICE OF CONTRACT ADMINISTRATIONATTN RES & SW COORD FOR H. DvNYATLANTA, GA 30332

37

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* DISTRIBUTION (Cont'd)

lIT RESEARCH INSTITUTE SCIENCE EGINEERING ASSOC (Cont'd)ATTN J. BRIDGES 1900 N. NORTHLAICE WAY

ATTN I. MINDEL PO BOX 3181910 W. 35TH STREET SEATTLE, WA 98103CHICAGO, ILL 60616

SRI INTERNATIONALINTERNATIONAL TEL a TELEGRAPH CORP ATTN A. WHITSONATTN A. RICHARDSON ATTN E. VhNCEATTN TECHNICAL LIBRARY 333 RAVENSWOOD AVENUE500 WASHINGTON AVENUE MENLO PARK, CA 94025NUTLEY, NJ 07110

TRW DEFENSE & SPACE SYSTEMS GROUPMISSION RESEARCH CORP ATTN J. PENAPO BOX 7816 ATTN W. GARGAROATTN W. STARK ONE SPACE PARKCOLORADO SPRINGS, CO 80933 REDONDO BEACH, CA 92078

MISSION RESEARCH CORP TRW DEFENSE & SPACE SYSTEMS GROUPEM SYSTEM APPLICATIONS DIVISION ATTN E. P. CHIVINGTONATTN A. CHODOROW 2240 ALAMO, SE1720 RANDOLF ROAD, SE SUITE 200ALBUQUERQUE, NM 87106 ALBUQUERQUE, NI1 87106

PRI, INC TRW, INCATTN W. HAAS COMMAND a CONTROL & COMMUNICATIONS6121 LINCOLNIA RD SYSTEM DIVALEXANDRIA, VA 22312 ATTN N. STAMMER

5203 LEESBURG PIKERICHARD L. MONROE ASSOCIATES SUITE 3101911 R STREET, NW FALLS CHURCH, VA 22041SUITE 203WASHINGTON, DC 20009 US ARMY ELECTRONICS RESEARCH &

DEVELOPMENT COMMANDR&D ASSOCIATES ATTN COMMANDER, DRDEL-CGPO BOX 9695 ATTN TECHNICAL DIRECTOR, DRSL-CTATTN W. GRAHAM ATTH PUBLIC AFFAIRS OFFICE, DRDlL-INMARINA DEL REY, CA 90291

COMMANDERR&D ASSOCIATES HARRY DIAMOND LABORATORIESATTN DIRECTOR, DR. J. THOMPSON ATTN D/TSO/DIVISION DIRECTORS1401 WILSON BLVD ATTN RECORD COPY, 81200SUITE 500 ATTN HL LIBRARY, 81100 (3 COPIES)

* ARLINGTON, VA 22209 ATTN HOL LIBRARY (WOOOBRIDGE)ATTN TECHNICAL REPORTS BRANCH, 81300

ROCKWELL INTERNATIONAL CORP ATTN LEGAL OFFICE, 97000PO BOX 3105 ATTN CHIEF, 21000ATTN D/243-068, 031-CA31 ATTN CHIEF, 21100ATTN G. Z. MORGAN ATTN CHIEF, 21200A NAHIm, CA 92803 ATTN CHIEF, 21300

ATTN CHIEF, 21400SCIENCE APPLICATIONS, INC ATTN CHIE, 21500PO BOX 1303 ATTN CHIEF, 22000ATTN W. CHADSEY ATTN CHIEF, 22100McLEAN, VA 22102 ATTH CHIEF, 22300

ATTN CHIEF, 22800SCIENCE ENGINEERING ASSOC ATTN CHIEF, 22900ATTN P. PLEMMING ATTN CHIEF, 20240ATTN V. JONES ATTN R. MARRIQUEZ, 21300 (50 COPIES)MARINER SQUARE ATTN R. RzYZER, 21300SUITS 127 ATTN J. SWETON, 21300

38

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* Ot *