RADIO SCIENCE Journal of Research NBS/USNC- URSI Vol. 68D, No.1 , January 1964

Comparison of Observed VLF Attenuation Rates and Excitation Factors With Theory

A. D. Watt and R. D. Croghan

Contribution From DECO Electronics, Inc., Boulder Division, Boulder, Colo.

The properties of VLF propagating modes are briefly reviewed and simplified eq uations are presented which can be employed in calculating t he fields p roduced. Experimentally deter­min ed exc itation factors are co mpared with t heoretical curves obtained by Wait an d fo und to agree rathcr closely. At tenu ation rates are shown as a function of frequenc y and are fou nd t o agree ra t her closely wit h calculated valu es us ing a proposed simplified per turbation solu ­t ion for attenuat ion ra tes based on r eflec t ion coeffic ients at t he ground an d ionosphere. When employing values of ionospheric reflection coeffi cients recent ly presented by vVa it and vValters, the nonreciprocal effects in attenuat ion ra te are fo und both t heore t ically and exper imen ta lly to be much grea ter in t he 10 kc/s region t han in t he 20 t o 30 kc/s r egion. Fin all y, expcr imcn Lal field strengt h versus d istance data are compa red wit h mode calcula­t ions and fo un ei to compare well all t he way from 1 mega meter ou t t o and includ ing fields at t he ant ipode (20 megameter s) .

1. Introduction

The majorit:v of VLF Lmnsmitting insta1lations em ploy Jrequencies lyin g within the 10 to 30 k c/s region . Within this frequency region , and par ticll­larly ftt great dis tances, most of the energy can be considered as being propagated as a guided wave in the space between the ear th and a conducLin g iono­sphere. Obser ved electromagnetic fields within t he ear th-ionosphere caviLy indicate t hat the act ual physical case can be well approximated with a model such as shown in fig m e 1 where the ear th is considered as highly conducting wi th a reflection coefficient of + 1 and the ionosphere is highly reflective with a reflection coefficient of approximately - l. For these idealized assumptions, the first order tr ansverse mao'netic (TM1) wave will have electrieal field lines similar to those shown on the left h a nd side of t he fio- ure . The m:mner in which the magnit ude of the v~rtical electrie field, E z, and the horizontal electric field, E y , var y with height, z, is shown on the low~r left ha.nd side of the figme . The scale chosen for thIS figme is representative of what is expected with a fre­quency of 15 kc/s. On the r igh t hand side of the figure are shown th e electric field lines for the TM2 ; i.e., the second order transverse magnetic wftve. The ftl1lplitude-versus-heigh t vari~tions . of the v~rti?al electric ftnd horizon tal electn c fields are agam 111-

dicated at the bot tom of the fig m·e. The electric field lines are only shown within th e cavity and no atte mpt is m ade to indicate the field lines ly ing outs ide the boundaries in the actual physical case where conductivities are not infinite.

For distan ces where neftI' field effects can be neo-lected W ftit [1962 , p. 199] h as shown thft t the ve~tical electric field E z can be represe nted in integral form or as the summation of an infinite number of

modes. In Lhe practical case for distances less t han about 1 M m , the tota l electric field at VLF can be well approximated as the sum of tho groundwave and on e or t wo sky reflec ted n LyS . This field is

m~2 or 3

E z=E z.o+ ~ E z.m m~l

(Ll)

where E z.o is Lhe groundwave contribution and E z .... is the mth h op skywave contribution . .

For distances greater th an 1 M m, the vertlCal elec­tric field can now be r epresen ted as the sum of a rela ti vely small number of waveg uide modcs 1

n~ l to 3

Ez~ ~ E z• n n~ l

(1.2)

The field produced for a given mode can be written in decible terms as

E z.n[db , v/m] = 10 Log PT+K~- 10 Logj- l0 Log h i. t

+ 10 Log A n. 1- 10 Log (a sin d/a)

- 10 Log h i • T+ I0 Log An• T+ 20 Log

(1.3)

where : E z. n[db , v im] is t he ver t ical electric field produced by the nth mode in db relative to 1 vim,

I At VLF tbe n~O mode whieh is actuall y a TEM mode is bighly a ttenna ted and is not expected to contribute to tbe observed fields.

FIGU RE 1. Elech'ical fi eld structure for wave g1tide modes.

P r is the power r rtdiated into the half space above the earth in watts, [{~ is a constant which relates field strengths at the surface to power radiated and is equal to 104.3 for modes of n = 1,2- -, j is the frequency in cycles per second, h i. t rtnd hi. T are the effective ionospheric heights at the transmitter and receiver locations, nominally 7 X 104 m for day and 9 X 104 m at night. A n. t is the mode excitation modi­fication factor which is defined as the ratio of power launched into the concentric spherical shell guide rel­ative to t hat for a fiat guide with perfectly con­ducting earth, a is the earths radius ~6.4 X 10 6 m, el is the path distance, (a sin ella) accounts for energy spreading in the spherical guide structme, An. r is the mode field modification factor for a cmved earth at the ionospheric heights applicable at the receiver, 20 Log Gh . n is the height gain factor in decibles relative to the field at the smface, i.e. , z= O, L d• n is a factor in deci­bels which accounts for losses rtt discontinuities along t he path, such as abrupt changes in smfrtce conductivity, or in guide height such as can occm for a sunrise-sunset boundary, and a is the effective attenuation rate in db /Mm 'which is normally different for each mode number.

As we will see later, this idealized modd and

2

associated equations is able to account rather closely for the observed variations in field strength for transmitters and receivers situated within the earth ionsophere cavity.2 The important problems faced in obtaining numerical values for the factors in (1.3) consist primarily in determining: (1) the efficiency of a given transmitting installation in lalmching radiofrequency energy into the half space above the earth, (2) the efficiency with which this energy couples into the propagating mode, (3) the manner in which the energy spreads throughout the concentric spherical shell cavity, (4) the height gain characteristic, (5) the discontinuity loss factor , and (6) the attenuation mte in the last term which accollllts for losses along the path .

The effective r adiated power P, can be determined from near field measmements applied to well-knovVIl relations. The freq uency, of comse, is known and the other geometrical factors involving distance, height to the ionosphere, rtnd the spreading terms can be rather precisely determined. The principal re-

2 Normall y in the 1 to 10 Mm distance region the fields are considered as being produced primarily. b y the TM, and TM, modes. The possibility of TE modes co ntribuilng must not be neglected part icularly at short or very lon g distances

mll,inin g unknowns relate to the excita tion effi ciency flnd ittten tuation r ates.

In order to determine attenuation ra tes, Wait [1958] employed a technique in which he plo t ted the sum of the ver tical electrical field in decibels relative to 1 v per meter and the spreading term 10 Log (a sin el /a ) , as a fun ction of the distance. This technique has been employed by the authors for a large number of observed field strength versus di titnce contoms to obtain both excitation factors and at tenuation r ates . A typical E z (a sin d/a) versus cl cmve is shown in figm'e 2 for the tritns­mitting station of LCM of Stavangel' , Norway operating at a frequen cy of 24.4 kc/s . The data WitS taken by ROLmd et al. [1925]. For a dis tan ce of 1 km , t he energy spreading term (a sin ella) becomes equal to zero and if the radiated power , frequell c~T , and ionospheric heigh t are known, it is possible to arrive at it 1 km intercept point which for all prn,cLical purposes cn,n be plo tted ror d= O Mm (megameters) on the eurve in figure 2. For t his particular sta tion , the cnJculn,Led d = O intercept value is 89.5 decibels while the actual in tercep t is seen to be some 9 db below Lhe flat ear th calculHtion. Since the attenuH,tion is negligible for the 1 km distance, the res ul tin g field strength difference is actually equal to 20 Log A which is the to tal modifi­ca t ion required for the sphericrl,l ear th case ; i .e ., 20 Log A = 10 Log At+ 10 Log AT if the ionosphere height is the sarne at Lransmitter itnd receiver. The slope of the CllTve , sin ce the distance spreading term has been itdded to the observed fields, is see n to be constan t and for t his particular case is equal to itbout 2.3 db /Mm . The a t tenun tion r atl" Ct,

is determined by losses at the ear th and ionosphere bowldaries and will be shown later to be dependen t upon many factors including: frequency, diurnal effec ts, se ltsonal effects, latitude effec ts, solar nctiv-

100

ity , meteoric activity, direction of propagation rela tive to the earth 's magnetic field , and earth's sLlrface conductivity.

2. Excitation Factors and Height Gain

The power radiated into the half space above the ground surrounding the antenna is ' given by the well-known relation

(2.1)

where I is the rms antenna cmren t, he is th e effec­tive antenna height in meters, and A is the Wlw e­length in meters . vVhen the antenn a is considered as being located between two p arnllel plates, the fields at a large dis tance from t he source cn n be considered as though they were produced by a set of images producing an equivalent line current as shown by Wait [1960]. Employing th e field pro­duced by this equivalen t line source, it ca ll be hown that the power laun ched in Lo a gi ven spherical earth mode relat ive to the to tal half' spa ce mclia ted power is

P T , n = (0. 1.2 . .. )

P r, hal r space

7JoAA 1.12X 108 A 3207["71,'""-' j h (2.2)

where 7Jo is th e impedance in free spitce, j is L1 lC fre­quency iu cycles per second, 71, is the ionospheric heigh t in meters, and A is the mode exc ita t ion mod­ification fa ctor. For a spherical earth , the varill tion in elec tromagnetic field strength with heigh t chnnges from that of t he fiat ear th case. This change in field s trength wilh height modifws, by a racLor A, the amount of energy which is coupled ill to th e spherical citvity or concen tric spherical cn.viLy. In addition , t he field strength observed at the surface by the receiver is reduced by a factor A~ for a fixed

I Sfovanger, L CM

f = 24.4 kcfs

90

.D "0

--' 60 ~ "0 c .;;;

2

'" 70 2 Q

+ w

60

!'" .. , .. m. 20 log A:-9db .. --I-----~ r------r-. . .-I---

Va: 2.3 dbfMm . . . ~ f------.-r--.

r=====---From Round, 1922

50

40 o 2 3 4 5 6 7 8 9 10

DISTANCE, d, Mm

FIGU RE 2 . T ypical E (a sin d(a) versus d curve.

3

energy flo" T in the guide . The result, assuming hi is constn,nt, is that t he vertical electric field calcu­lated for a flat ear th must be modified by A to the first power . Wait [1962] has derived values for the modification factor A which are shown in figUTe 3 for a typic,Ll day time ionospheric height of 70 km. The CUTves are for the first and second order modes where the earth and ionosphere boundaries are considered as perfectly reflecting.

In order to determine A experimentally, a large number of field strength versus distance CUTves were plotted (in a manner similar to that shown in fig. 2) and the resulting experimental data points shown in figure 3 appear to group around t he n = 1 curve over quite a large frequency region. The few data points shown at the upper right hand side of the figure near the n = 2 CUTve , were obtained from line inter­cepts which appeared to be representative of second order mode propagation. These line intercepts cor­rtlspond to a rather high attenuation rate portion of the field strength versus distance CUTve that in general is only applicable out to several mega­meters from the SOUTce. As might be anticipated, these effects are seen essentially only at the higher frequencies; i.e., about 20 kc/s and up.

It is interesting to observe that on several occa­sions the excitation factors appear to lie appreciably below the theoretical CUTve. For example, at 21 kc/s on one occasion the excitation factor was near the CUTve while for the other example shown, the excitation modification apparently produced was about 5 db below the theoretical value. The par­ticular field strength versus distance Clll"ve associated with this low excitation factor had a rather low attenuation rate, and it is likely that the propaga­tion conditions were approaching the earth detached case as described by Wait [1962] where most of the energy is concentrated near the ionosphere and any

z o § U ~ - I

-2

0-

0

I--

5

0

5

0 10

I "1""""--' ~ 1 ~ It· I From wo~~on1 h~7Ckm +-

t-.l, J J [ . l I "

I t--- 'T'-II 't ~ I From WOI I,

I ~iJ. (l '" I and h = 70km

I I-

I I

[\ I I

I

- I-1\

1\

15 20 25 30 FREaUENCY, f ,kc/s

FIGU RE 3. E xcitation factors (theoretical and experim ental).

4

coupling to antennas at the earth's sUTface is very small. Obviously, in this cn,se the vertical electric field versus height will not be a maximum at the earth's surface.

In the experimental data shown, an attempt was made to group the examples into propagation in both the north-south direction as compared to that in the east and the west directions. In addition, those paths which were launched over sea water and others over land were also examined . It was impossible from the rn,ther limi ted data available to determine for certain any trend such as an increased excitation loss A for launching over land or in any specific direction. Since, as we will see in the following section on attenuation rates that the ionospheric reflection coefficients are different for various directions of propagation, it is anticipated that a close examination of excitation factor may indicate some sensitivity in A to direction of propaga­tion relative to the earth's magnetic field, but at present it must be concluded that we have not demonstrated this point. It is interesting to observe here that Wait and Spies [1963] in their rec~nt descriptions of height gain for finitely conductmg surfaces show that the excitation factor shows a somewh~t lower reduction, i.e., more efficient excita­tion, for poorly conducting earth t.han for perf~c.tly conductino' earth . This of COUl'se IS for a condItIOn where the\vhole earth's smface is uniformly poorly conducting. For the case where the guide pa,rameters are primarily determined by a sea-ionosphere set or boundaries and the transmitter is located some­what inland, there may be a cutback modification required which is expected to show a ~ecr~ase 111

excitation efficiency when the antenna IS sItuated over n, finite amount of poorly conducting terrain. For normal conducting grounds at VLF this modifica­tion is expected to be rather slight; however, as frequency increases, particularly up into the LF b!1lld, t Ilis type of modification can be very pro­nounced as showl) for arctic pn,ths by Watt, Maxwell, and Whelan [1959] .

3. Attenuation Rates

The effective attenuation rate used in the wave­guide modal equation represents an aver:age loss per unit distance for a discrete p~'opagatlOn p.ath and time' therefore, any change 111 the electncal properties' of the ionosphere with time and any change in the electrical properties of the earth and ionosphere over various paths will give a cor­responding change in the effective attenuation rate. It is well ]\:110Wn from work by Budden [1952], Barber and Crombie [1959], and Wait [1961] that the attenuation rate is also affected by the earth's magnetic field. This effect, which is produced by the modified electron motion in the presence of a magnetic field, may be treated as an earth's magn~tic field factor M(c/>a) 3 which modifies the attenuatIOn

3 Wait uses the symbol P for this factor.

rate flS follows

M( )= AtLenuation with Magnetic Field ¢a Attel1llation without Magnetie Field

(3.1)

where

¢a= azimuthfll direetion of propagation with respect to the horizontal component of the earth's magnetic field.

The value of M is fllso dependent upon the geomagnetic latitude which determines the magnitude of t he horizontal components of the ear th's field. Since M is the influence of the earth's magnetic field on VLF propagation by virtue of modification 01' the reflection coefficients at the ionosphere, any additional loss in the waveguide produced at the lower , i.e ., earth 's surface, boundary is not dependent upon M.

To a first approximation , the effective loss over a given propagation path el' megfllneters long 'with vII,rious e ffective ionosphere and ground conductivities along Lhe path can be considered liS the sum of all the incrementfll losses along the guide su.rfaces. The efl'ecLive loss can be written as

Ni -'- J\Tr

ad/ 106= acl' = ~1\/[k(¢a) at,k Llel~ + ~ Llaq, jM; (3.2) k= 1 j= 1

where: N j and N u are the number of ionospheric and ground path in crements co nsider.3d , M k (¢a)a l. kLlcl~ is the loss co ntributed by the ionosphere over Lhe incremental distance Llcl~ , and Llan, jLlcl; is Lhe loss contributed by the earth over t he incre­mental distance Llel/. For paths wbere the boundary surFaces ean b e considered as uniform, tbe attenua­t ion rate becomes

a = 1l![ (¢a) at + Llan• (3.3)

The contribution due to ground loss can be shown to be related to ground conductivity by the ex­pression obtainable from W ait [1957]

Llag[ dbjMm]~46f /2CT - l /2h -1; (3.4)

where: f is the frequency in cycles/seeond , CT is the ground conductivity in mhos /meter, and h is the effective ionospheric height in meters. This ex­pression is valid only when f is low enough that the mode is not becoming earth detached ; i.e., about 15 kc/s or less for n = 1. The conductivity value must also not be too low for this relation to apply. The earth detach ed mode may be seen by the more rigorous computations of Llan by Spies and V'ol ait [1961] in which a maximum value of Llag is reached with an increase of frequency, and a fmther increase will decrease Llaq.

A great deal oJ work has been conducted in cal­eulat ing the attenuation rates of the ionosphere flnd earth of different conductivities by a number of authors. The .resul ts are presented either in the

5

form of attenuation rate or in the form of reflection coefficients at the earth find ionosphere.

The at tenuation rate can be obtflined from the reflection coefficients flS a pertmbation solution which assumes thflt

where: H g and Hi flre the reflection coeffi cients of the ground and ionosphere respectively, and 2cl; is the average distflnce in megameters con taining one ground an d one ionosphere reflection at mode res­onance . An approximate solution for el j tbat is valid over fln appreciable range of frequencies yields

a[db/Mm]~1.2X 1013(R q[db ]

+ R;[db]) (27r7b - ¢g- ¢ t)/fh 2 (3.6)

where ¢ u and ¢i are the phase lag upon l'e nection at the ground and ionosphere , respectively.

Values of Hi from W ait and W fll tel's [J 963] are shown in figll1'e 4 as a fun ction of frequency an d pIIl'lImetric in the term l which is the conductivity gradient of the iono phere.4 Typical conductivity gradients are shown in figure 5 for both dllY and night. The conductivity grad ient term , l , may be cl-tlculn,ted from these cur ves by the followin g rela tionship :

Z-Zo (3.7)

where Zo flnd Z arc the io nosphere heights COlTcspond­ing to the conductivities CTO a nd CT, respectively.

The ionospheric conducliviL.v neglccting Lhe earth 's magnetic field is given by Jordan [1950] as

N e2v (J

m (v 2+w2)

~2.78X lO-8N/v (3 .8)

where: e and m are the elecLron charge lind mass, AT is the number of electrons pCI' cubic meter, flnd v is the effective collisional Ireq uency in collisions pel' second . Typicfll daytime and nighttime values of the conductivity gradicn t fl re lday~2 . 6 km flnd In Ight'" 1. 5 kn1.

Anticipated sea water path attenuation rates can be calculated with the aid of' (3.6) assuming that f = 20 kc/s, Rg"""O db , ¢g= O, hday= 70 km, and hn lght= 90 km. From figm'e 4 , R i day"'4.5 db and R t nlght= 3.5 db , and from Wait flnd 'IVn.lters [1963], ¢ i day= 2.4 and ¢ i nlght= 2.7. The resulting calculated attenuation rates are

D'day = 2.2 db/Mm

anlgh\= 0.9 db/~/Im .

'Note that Wait uses the para meter fJ which equals 1/1. One of the most Significan t recent contri butions to VLF propagation theory is con tained in the papcTt-." Reflcction of electromagnetic wa ves from a lossy mag~l cto .plasma/' by J . l~. Wa it a nd L . O. Walter s [1963aJ. The model employed III th lS pa per IS a close representation of what we I: resently ex pect for t he ionosphere. The re­sultant values of R, now re ffect the influence of the earth 's magnetic field as well as finite conductiv ity gradients.

-6.0

DoJ From 1it [196JJ / "I " .. ..1. 0., ../ )--- Grazing Incidence, cost/>: 0 .1 6 -5. 5

V ,g L 1= 3.3 km / --=- - 5.0 ",-

...: z w -4.5 u ;;:: LL W 0 u - 4 .0 z Q f--U W -" LL

k

/ /

V V

t::-:-:-:--, L~

/ ~km ,

V V

./

-----~

~ l,~I.4km

----~ A .... erage Normal Night

~ -~ ~ ~ - 1---- .£, ~ 0. 5 k m

-3. 5 w

'" - 30

-2.5

10 12 14 16 18 20 22 24 26 28 30

FREQUENCY, f, kc/s

FIGURE 4. R eflection coefficients versus frequency f or nonsharply bounded ionosphel'e .

100

III II I I I IIIIII Night, based on Belrose and Wright data

90 rodient sca le, 11 ~ 1.5 km -I--e--I-

80 ~- 1--1---I---"'

E ~

!-----'

f---70 I

to W I

60

50

40

V I--~

~ r-- I---

f-I---"'f- Day, based on 8elrose 1962

gradient scale,)'" 2.6 km

)~~ , II

2.3 log ("'1"'0)

III' Tr im 11111 1 1

CONDUCTIVITY, <r, mhos/m

FIGU RE 5. Typical ionosphere conductivity gradients.

Curves of experimentally determined daytime values of attenuation rates are shown in figure 6 as a function of frequency and parametric in direc­tion of propagation. Much of the data for this figure came from curves similar to figure 2. The curves were drawn through the average of all the points within a plus or minus 45° sector of the given direction,

For frequencies above 25 kc/s, existing data is contaminated by higher order mode contributions. Because of this, the dashed portions of the curves

6

are based primarily on theoretical values by Wait and Walters [1963a].

Wait [1964] has calculated the change in attenua­tion rate produced by an exponential ionosphere relative to that previously calculated using a sharply bounded ionosphere [Spies and Wait, 1961]. The resulting exact solutions of a for an exponential ionosphere (h= 70 km day and 90 km night) may be seen in figures 7 and 8 for the first and second order mode respectively. The curves were obtained by using typical values of the conductivity gradient

I

I

r

-----

2 WEST TO (AST

FREQUENCY f. kc/s

FIGURB 6. Attenuation Tates JOT pTedominately sea water paths veTSUS j?-equency JOT modeTate and low sunspot numbeTs (expeTimental) .

01 0=----.......,:,s,------='20::----=2!,-s --3="0,---~3f=.5-4"=0-.f=.S----fs-=-0 """'S!,-5 --0'6'0

FREQUENCY, kc / s

FIG U RB 7. Attenuation rates over pTedominately sea wateT paths jor n = 1 (ex perimental and the01'et'ical),

expected for day and night. Indicated on the curves are experimentally determined values of atte nuation rate , It can be seen that the theoretical values are in good agreement with those ob tained by experilTlentally collected data for the first order mode, For the second order mode , the experi­mental values obtained are much more uncertain which ma,y account for the only fair agreement during the night. This un certainty may be due to the randomness of nighttime propagation condi­tions; i,e" variable land h, In addition, the distance involved in which the second order mode is pre­dominate is usually very short for accurate a deter­minations.

4, Field Strength Versus Distance

Figure 9 shows the observed vertical electrical field strength as a function of frequency for a typical

7

12

td' NL,., n=2

10

1\ \

\ \

'" \ "'-."-..... ~~

EXPE1RIMEN1TAL lAY

.L = 2 5 doy

,~ / I I I ---~~ i----- EXPERI MrTAL INIGHT

.......... r-- -' -I'·' "r'

IS 20 25 30 35 40 45 50 55 60

FREQ UENCY, k C/S

FIGU RB 8, A ttenuation rates ove1' p1'edominately sea water paths fOT n = 2 (eXIJCTimental and theoretical),

west to east propagation path, Also shown on the figure are the calculated groundwave and modal fields using values of the excitation factor A as shown in figme 3 and expected values of attenuation as shown for n = 1 in flgure 6 and n = 2 in figure 8, At distances less than 300 km , the groundwave is pre­dominate a,nd is practically independent of frequency over the VLF range, This may be seen from the matchin g of data points at 20 and 16 kc/s, At ap­proximately 100 km , an interferen ce pattern begins to appear which is likely due to interJerence between the groundwave and the first hop skywave, Near GOO km, the groundwave and skywave a.re approx­imately 01' eq u al ampli tude, Since their phase versus distan ce rates a.re different, a strong cancellation , or null, is expected in this region,

Beyond 1 Mm where we are now considering mode theory, the fu'st order mode is apparently predomi­nate and has an atten uation rate of approximately 2 db/Mm, Beyond about 16 :Mm , it can be seen that th e convergin g energy due to antipode focu ing actu­ally increases the fields at a greater rate than the loss due to attenu ation, This buildup in field stren gth con tin ues un til the an tipode is reached, It can be seen that the observed antipode value [Garner, H)62] is very close to the calculated value, Included on the figure are the un attenuated mode fields for the first an d the second order modes,

If the transmitted frequency is increased, the attenuation of the second order mode will decrease rapidly and at the same time the excitat.ion of the first order mode will decrease, It then is apparen t that as the frequency increases the second order mode will predominate to greater ranges. Figure 10 is a CUl've of vertical field strength as a fUllction of fre­quency for east to west propagation ['or data in the 21 to 25 kc/s r egion, The excitation factors were ob­tained from figUl'e 3 and the attenuation rates were chosen to best fit the data, The first large null ill

" -'<:

II o..~

{ "-2 Q) >

.~

~ .D -0

N W

" -'<:

II o..~

E-

~ "-

2 Q)

. ~ 0 ~ Ll -0

I-I-e.!) Z W n:: I-(f)

0 -.J W I.J...

9 0 ,

80

70

60

50

40

30

20

10 10

80

70

GO

5 0

4 0

3 0

~ ~~

I' ~~ ~ I

~ I

\~ ~ . I c;:? ~na~sorble~ Mode Flel1s

\/ ,, ~

\t n=~, t ~ , 1 5 1 I ' ~~ I I I I

'\ /1:,,1>.=-3 /

~'v \ 1----t, /! Antipode ./ Volues I

\ \ ~colcluloted fJ\' /n=I,I>.=-3

' Observed \ \i ()(= 2

\ \ \. •

\ 1\

~ '\ 1

x 20 kc!s WWVB Plush, Aug. 2, 1961 GROUND \ n=2

• 16 .6 kc!s N PM Bickel, Dec. 8, 1955 WAVE, A= 1.5

• SEA WATER ()(=8 "\ • 170 kc!s WQL Round, July, 1923 \i ~ i47 rilrli llorner, r2

1 I • j

10'

DISTANCE FROM TRANSMITTER, d, km

F I GURE g, Field strength versus distance at 16 kc/s faT pTopagation to the east,

~, GROUND WAVE.

SEA}'ATER

'J

"" , '---- '-.. ~ X\

~ n= 2, 1>.= 0, 0l=0 \"\ ......... --<:

\ ~

'. 1'-1" V Uno bsorbed

~.:..j Made, Fields

\~'" -\ "

H~ i--'n=l , 1>.=-10, (;(=0

\ '\ __ 22. 3 kc!s N SS, Plush, Aug., 1961 \ -- 25 kc !s LCM, Round, 1922 [\ n=1 1>. =-10 Cl=2 .5

20 ~ ~~ r- -6-- 21 kc! s FT, Holl ing sworth, 1925

. I" 1"1 rmlr"" r II I ~

10 10

n = 2, A =O, CX=5.5./

I IIII ~I ..--r--~

10 4

DI STANCE FROM TR ANSMITTER, d, km

FIGU RE 10. Field stTength versus distance at 25 kc/s fOT propagation to the west.

8

10'

10'

field strength is now seen to occur at 700 km and is again likely caused by cancellation between the groundwave and the fU'st hop sky wave.

Con idering mode theory for distances greater than 1 Mm, the secon d order mode appears t o be the predominatc mode out to about 3 Mm where inter­ference now occurs between the first and second order modes. B eyond 4 Mm the fU'st order mode appears to be predominate. On some occasions, the second order mode has been observed to be predomi­nate a t nighttime for distances up to 6 Mm or more for frequencies above 18 kc/s.

The authors gTatef' ully acknowledge information obtained during helpful discussions with J. R. Wait, R. W. Plush , W . E. Gustafson , J. A. Pier ce, M. L . Tibbals, W. E. Garner, and F. J. Rhoads. The assistance of Mrs. W. Mau in prepar ation of t he manuscript fLncl C. W. Vogt and E . F. Obrrteufi'er in preparing the illustrations is also ach::n owledged.

5 . References Barbel', N. F., a nd D . D . Crombie (1959), VLF R eflections

from t he ionosphere in t he prcsence of a t ransverse m ag­netic fic ld , J. Atmos . T errest. Phys. 16 , 37.

Budden, K. G. (1952), The propagat ion of a radio-atm.ospheric, Phil. Mag. 43, 1179- 1952.

Ga rn er, IV. K, Jr. J . Rhoad s, J . E. Bickel, a nd R . IV. Plush (1962), Measureo ampli t ude and phase of the antipodal fie lds of a VLF t ran smitter, paper presented at Fall URSI M eeti ng, OttalVa, Ca rmela, 15- 17 Oct.

J ord a n, E. C. (1950), E lectromagnetic Wa ves in Radia ti ng Systems (Prentice-H a ll, E nglewood Cliffs, N.J .).

9

R ound , H . J ., T. L. Eckersley, K. Tremellen, and F. C. Lutmon (Oct. 1925), R eport on measurements made on signal strength at g reat dis t.ances during 1922 a nd 1923 by an expeeli tion sent to Australia, l EE J . 63, No. 346.

Spies, Ie. .P., and James R. Wai t (July 17, 1961), Mode cale ulatt~)t) s for V~F p ropagation in t he earth-ionosphere

.. wave gutd e, NBS l ech. Note No. 114. Wai t, J . R. (June 1957), The mode t heo ry of VLF ionospheric

propagation for fini te g round conductivi ty, Proc. IRE 45, No.6, 760--767.

Wai t, J. R. (1958jlII), A study of VLF fi eld stren gth data­bo th old and new, Geofisica Pura e Applicata- Milano 41, 73-85. '

Wait, J . R. (Mat'.-Apr. 1960), T errestrial propagation of very-low-frequency radio waves, a t heo retical investigation J . R es. N BS 64D (Radio Prop.), No. 2, 153-204. '

Wait, J . R. (Jan .-Feb. 1961), A new approach to the mod e theory of VLF propagatio n, J . R es. NBS 65D (Radio Prop.), No.1 , 37-46.

Wait, J. R. (1962), E lectromagnetic Waves in a Stratified Media (P ergamon Press, Oxford ).

Wai t, J. R . (July-A ug. 1963), lnftuence of the lower iono­sphere on propagation of VLF waves at great distances J . R es, N BS 67D (Radio Prop. ) , No.4, 375- 381. '

Wa it, J . H. ., a nd L. C. Wal ters (May- June 1963), R e flection of VLF radio waves from an inhomogeneo us ionosphere. Pad 1. Expo nentia lly va ryi ng isotropic moclel , J . R es.

p N BS 67D (Radio Prop.), No. 3, 3G 1- 367. Wa it, J . R , ancl L. C. W a lLe rs (Jan.-Feb. 1964), R efl ection of

electromagnetic waves from a lossy magnetoplasma, J. R es. N B S 68D (Radio Prop .), No. 1, 97.

Wa it, J . R , an~1 K. P . Sp ies (iHa r.- Apr. 1.9G3), II?ight gain for VLF radlO waves, J . Res. NBS 67 0 (Radto Prop .) , No . 2, 183-1 7.

Watt, A. D. , E. L. Maxwell , a nd E . n . Whela n (July-Aug. 1950), LolV f req uency propagation paths in arctic areas . J. R es. N BS 63D (Rad io P rop. ), No. 1, 09- 112.

(Paper 68Dl-307)