NATIONAL BUREAU OF STANDARDS - NIST · NATIONAL BUREAU OF STANDARDS The National Bureau of Standards‘ was established by an act of Congress March 3, 1901. The ... and methods of

NATIONAL BUREAU OF STANDARDS

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ton D.C. 20234.

UNITED STATES DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS 0 Lewis M. Branscomb, Director

e TECHNICAL NOTE 610 ISSUED NOVEMBER 1971

Nat. Bur. Stand. (U.S.), Tech. Note 610, 170 pages (Nov. 1971) CODEN: NBTNA

Application of VLF Theory to Time Dissemination

W. F. Hamilton and J. L. Jespersen

Frequency-Time Dissemination Research Section Time and Frequency Division Institute for Basic Standards National Bureau of Standards

Boulder, Colorado 80302

Final Report Prepared for N at iona I Aeronautics and Space Ad m i n i s t ra t ion

under Contract No. 51 740A-G

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:610), Price $1.50

Contents

L i s t of Tables . . . . . . . . . . . . . . . . List of F igu res . . . . . . . . . . . . . . . 1 . Introduction . . . . . . . . . . . . . . . 2 . Time Dissemination Sys tems . . . . . . . 3 . Path Delay . . . . . . . . . . . . . . . 4 . Important P a r a m e t e r s for V L F Calculations

5 . Theory of Calculations . . . . . . . . . . 6 . The Calculations . . . . . . . . . . . . . 7 . Discussion and Conclusions . . . . . . . . 8 . References . . . . . . . . . . . . . . . Appendix: Simplified Mathematics of the Theory

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10

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Lis t of Tables

Page

Table 1. L i s t of Calculations. . . . . . . . . . . . . . . . 2 9

Theoret ical Diurnal Phase . . . . . . . . . . . . 32 Table 2. Comparison of Exper imenta l and

Table 3 . Comparison of Exper imenta l and Theore t ica l Group Delay , . . . . . . . . . . . . 35

Table 4. Predic ted Diurnal and Phase Delay. . . . . . . . . 36

Table 5. Pred ic ted Group Delay . . . . . . . . . . . . . . 38

L i s t of Figures

F igu re 1 . Normal Day Prof i le . . . . . . . . . . . . Figure 2 . Figure 3 .

Normal Night P ro f i l e . . . . . . . . . . . Deeks 1200 Prof i le . . . . . . . . . . . .

Figure 4 . Bain and May Prof i le . . . . . . . . . . . Figure 5 . Diurnal P h a s e . . . . . . . . . . . . . . Figure 6 . Relative Group Delay. Normal Day . . . . . Figure 7 . Normal Night . . . . . . . . . . . . . . Figures 8 . 40: Relative Phase . Normal Day . . . . Figures 41 . 69: Relative Phase. Norma l Night . . . . F i g u r e s 70 . 102: Amplitude. Normal Day . . . . . . F i g u r e s 103 - 128: Amplitude. Normal Night . . . . . Figures 129 - 167: Relative Group Delay. Normal Day . Figures 168 . 204: Relative Group Delay. Norma l Night

F i g u r e s 205 - 233: Diurnal Phase . . . . . . . . . . F i g u r e s 234 . 251: Relative Phase . . . . . . . . . . Figures 252 . 254: Relative Group Delay . . . . . . .

Page

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V

APPLICATION O F VLF THEORY TO TIME DISSEMINATION

W. F. Hamilton and J. L . J e spe r sen

The charac te r i s t ics of t ime dissemination s y s t e m s a r e discussed. Pa r t i cu la r emphasis is placed on the advantages and problems of very low frequency (VLF) timing sys tems. The p a r a m e t e r s affecting VLF propagation along with causes of var ia t ions in these p a r a m e t e r s , a r e discussed. T h r e e methods of computing VLF propagation delays - -mode theory, geometr ic-opt ics , and zonal harmonics - - a r e compared. The method of zonal ha rmon ics , used for the calculations in this pape r , is discussed in m o r e detail. A method of calculating reflection coefficients for a continuously varying ionosphere i s descr ibed. p a r e d with experimental measu remen t s . of the calculations a r e included.

The theoretical values a r e com- Graphical resu l t s

Key Words: Diurnal phase; Omega; t ime; t ime d issemina- tion; VLF propagation; zonal harmonics .

1. Introduction

There a r e a number of existing or proposed t ime dissemination

sys t ems which operate in the V L F region of the radio spectrum.

OMEGA is one of the mos t widely known such sys t ems operating in

the 10 .0 to 14. 0 kHz range.

p r imar i ly fo r worldwide navigation, i t has considerable potential for

t ime dissemination.

report . Briefly, OMEGA i s a t t ract ive for t ime dissemination for the

following reasons :

Although the s y s t e m i s conceived

It is this potential which motivates the present

a . OMEGA could provide the bas i s for a unified worldwide t ime

dissemination s y s t e m which does not present ly exis t .

b. A timing signal would be available reliably and continuously

a t any location on the e a r t h ' s surface.

c. The t ime accuracy available to the use r would be commen-

su ra t e with his equipment investment.

In the following sections we discuss:

a.

b.

Charac ter i s t ics of t ime dissemination sys t ems ,

Details of those charac te r i s t ics which a r e par t icular ly im-

portant for the calculations presented in this r epor t ,

c.

d.

e.

calculations

Descriptions of the theory and method of calculation,

Graphical presentat ion of the r e su l t s of the calculations,

Brief summary of the conclusions which may be drawn f r o m

2. T ime Dissemination Sys tems

T h e r e a r e a number of common elements which charac te r ize m o s t

t ime dissemination systems. Among the m o r e important a r e : accuracy ,

repeatabil i ty, coverage, and ambiguity. The accu racy of a s y s t e m is

usually l imited by ones knowledge of the propagation delay, whereas

repeatabil i ty i s usually re la ted to s h o r t - t e r m variat ions in the cha rac t e r -

i s t i c s of the propagation path.

ing the following s imple t ime dissemination system. Suppose the s y s t e m

consis ts of a sine wave which is a repeti t ive waveform. We can't tel l

by looking at the signal which one of the zero c ross ings i s the one that

is on t ime so the sys t em i s ambiguous.

our knowledge of the t ime we mus t somehow pick out the c o r r e c t cycle

and then m e a s u r e i t s a r r i v a l t ime with respec t to our local clock.

To pick the co r rec t cycle, however, we m u s t a l ready know the t i m e

f r o m some other source to an accu racy equal to the period of our sine

wave (100 microseconds in the case of a 10 kHz s ine wave).

u s e r s won't know the t ime to 100 microseconds and in addition, they

would prefer to use the s a m e sys t em f r o m b e g i r i n g to end. - T o reduce

We can i l lus t ra te ambiguity by consider-

If we want to use it to improve

Many

2

the ambiguity i t is usual to t r ansmi t another coherent frequency say at

10 .1 kHz and then inspect the 100 Hz difference frequency.

out the on- t ime cycle of the 100 Hz difference frequency, we need

only know the t ime to 1 0 mill iseconds (the period of a 100 Hz s ine wave).

We s e e that by adding m o r e signals a t different f requencies , we can

reduce the ambiguity of the sys t em to any des i r ed level. However, a s

we reduce the ambiguity, we mus t at the s a m e t ime inc rease the amount

of frequency spec t rum which the sys t em occupies. For very low f r e -

quency sys t ems , we can’t very well put on modulations which requi re

l a r g e bandwidths.

on a 10 kHz c a r r i e r .

be increased by averaging many measu remen t s .

To pick

That i s , you can’t put a signal which occupies 50 kHz

In many cases , the usefulness of the s y s t e m may

3. P a t h Delay

P a t h delay predictions, and thus, the accu racy of the s y s t e m a r e

l imited by knowledge of the geometry of the t r ansmi t t e r and use r loca-

tions and by the availability of information concerning the propagation

medium. At V L F , a t g rea t distances f r o m the t r ansmi t t e r , the signal

velocity has a near ly constant value, whereas near the t ransmi t te r the

average velocity between the u s e r and the t ransmi t te r changes in a n

i r r egu la r way a s a function of distance.

regular to i r r egu la r occurs a t a distance of about 10, 000 ki lometers

f r o m the t ransmi t te r .

in te res t .

signal-to-noise ra t io i s g rea tes t and r ece ive r s ’ costs , in principle,

should be a t a minimum.

path delay, we mus t introduce the ideas of phase velocity, V and

group velocity, V a s they apply to V L F .

In general , the t ransi t ion f r o m

In this repor t , the i r r egu la r region i s of m o s t

It i s important to consider this near region because h e r e the

To consider i n m o r e detail the p rob lem of

P’

g’

3

Let us consider a s imple two-frequency timing system. Suppose

we have two closely spaced cw signals at f requencies f l and f 2 where

f2 - f l = A f ,

t ime m a r k e r to identify a specific cycle of e i ther c a r r i e r frequency.

This removes ambiguities and a m o r e p rec i se t ime of a r r i v a l m e a s u r e -

ment i s made at the higher c a r r i e r frequency.

quency signal will t r ave l f r o m t r ansmi t t e r to rece iver with a group

velocity which depends upon the phase velocity v e r s u s frequency cha r -

ac t e r i s t i c of the propagation medium, Specifically, the group velocity

is related to phase velocity V

In this sys tem, the beat frequency Af i s used a s a coa r se

The difference f r e -

by the following expression: P

where u) is the angular frequency.

velocity breaks down i f the derivative - ( w / V ) i s not well behaved,

In a d ispers ive medium, such a s we a r e considering a t V L F , Vp is a

function of w so that the group delay, t over a path r is given by the

following expression:

We s e e that the concept o f group d

dw P

d

At very low frequencies the phase velocity ve r sus frequency dependence

cannot be expressed a s a s imple function of the proper t ies of the propa-

gation medium, except perhaps a t g rea t dis tances f r o m the t ransmi t te r .

The m o s t accura te r e su l t s a r e obtained f r o m numer ica l solutions of

Maxwell 's equations, i. e. , full wave solutions, with some rea l i s t i c

model of the ionosphere, the approach taken in this paper .

difference frequency may t ravel with a group velocity that i s different

than the phase velocity of e i ther one of the two c a r r i e r f requencies , the

Since the

4

difference frequency signal may slip in phase with respec t to e i ther one

of the c a r r i e r frequencies a s a function of distance f r o m the t ransmi t te r .

This could lead to incor rec t cycle identification of the c a r r i e r frequency

unless the difference in velocit ies i s known.

can cor rec t ly identify a cycle by using different group and phase

velocit ies. Unfortunately, the concept of group velocity applies only

a t g rea t distances f r o m the t ransmi t te r , where the phase velocity

ve r sus frequency charac te r i s t ics a r e well behaved,

- ( , / V ) i s well behaved. Near the t r ansmi t t e r , a different approach

mus t be used.

we will consider f i r s t how a V L F pulse would propagate in this region.

At grea t distances, one

i. e . ,

d d? P

To help i l lus t ra te what i s happening near the t r ansmi t t e r

T h e r e a r e two distinct effects which one mus t consider. F i r s t ,

the average propagation velocity of the pulse (group velocity) may be

equal to o r l e s s than the velocity of light, Second, the. pulse may be

changing i t s shape a s i t propagates through the medium.

point on the pulse has been tagged a s the t ime re ference point, a t the

t r ansmi t t e r , i t i s necessa ry to de te rmine how this "tag" point is mapped

into i t s new position a s the pulse d is tor t s during i t s propagation away

f r o m the t ransmi t te r . If this i s not known, i t wi l l not be c lear to the

use r which point on the received pulse r ep resen t s the re ference point

a s t ransmit ted, In addition, having cor rec t ly identified the tagged

point, one mus t a lso consider the fact that the average pulse velocity

may be l e s s than the velocity of light, A multifrequency V L F sys t em

is somewhat s imi la r to the propagation of a pulse in the following sense:

A short pulse of length r consis ts of a spec t rum of f requencies , i. e . ,

a number of Four ie r components which occupy a spectral region approx-

imately equal to l / - g In a d ispers ive medium, such a s the ionosphere,

each one of these Four ie r components wi l l t rave l with a different phase

velocity.

If a par t icular

In a sense then, when w e use a VLF tone sys tem, we a r e

5

sending one Four i e r component a t a t ime and the u s e r , i f he des i r ed ,

could by storing the received tones add them together to produce some-

thing looking l ike a pulse.

well defined shape a s i t left the t ransmi t te r .

p roper t ies of the propagation medium this composi te waveform wi l l

change i t s shape a s a function of dis tance f r o m the t r ansmi t t e r until

i t has propagated out to the region where the phase velocity is well

behaved. Beyond this point, the composi te waveform would maintain

essent ia l ly the s a m e shape a s a function of dis tance although i t would

not be the s a m e a s t ransmit ted.

t r a n s f e r r a l , i t is n e c e s s a r y to know in detail the s t ruc tu re of this

composi te waveform as a function of distance f r o m the t ransmi t te r .

This composi te waveform would have some

Because of the d ispers ive

To use the t ime sys t em for accura te

Similar ly , u se of the V L F multitone s y s t e m for accura te t ime t r a n s -

f e r r a l r equ i r e s detailed knowledge of the phase ve r sus frequency and

dis tance charac te r i s t ics of the signals. We wi l l t u rn to the detai ls of

theoret ical calculations of V L F phase velocity in Sections 4 and 5.

4. Important P a r a m e t e r s for V L F Calculations

The phase velocity v e r s u s frequency charac te r i s t ics a t VLF a r e

par t icular ly sensit ive to the propagation medium.

medium is charac te r ized by the conductivity of the ground, the e lec t r ica l

p roper t ies of the ionosphere,the direction of propagation w i t h respec t to

the ea r th ' s magnet ic field,and the s t rength of the magnet ic field,

The propagation

The mos t important e lec t r ica l p roper t ies of the ionosphere for

V L F calculations a r e :

a.

b.

C.

The electron density v s height.

The proton density v s height.

The collision frequency between charged and neutral par t ic les

v s height.

6

The composition of the ionosphere is not static. Many different

types of events, for example solar f l a r e s , can cause sho r t - t e rm

variat ions in the ionization.

do not take these sho r t - t e rm variat ions into account but a r e based on

the average proper t ies of the ionosphere a s i t might appear a t noon and

at midnight of the s u m m e r sols t ice a t midlatitudes.

The theoret ical calculations in this repor t

T h e r e i s considerable experimental evidence that the propagation

delay of a VLF signal f r o m one day to the next a t the s a m e t ime of day

is repeti t ive to a few microseconds,

p roper t ies of the ionosphere should be sufficient for many applications.

This i s an at t ract ive feature of VLF signals for t ime dissemination.

We l i s t he re briefly some physical p rocesses responsible for these

average proper t ies .

s o that consideration of the average

The mos t important fac tors a r e a s follows:

a. Solar X - r a y s (2 10 A ) above 85 k m a t sunspot minimum and

above 70 k m a t sunspot maximum;

b,

range;

c .

The ionization of NO by solar Lyman -a in the 70 to 90 k m

P r i m a r y cosmic r ays below 70 k m with the flux increasing by

a factor of about 4 f r o m sunspot maximum to minimum.

subject is very volatile and recent work indicates that water vapor

and metastable s ta tes of O 2 a r e important.

However, this

d e Various react ions between f r ee electrons, ions and neutral

par t ic les ; and

e Mechanical and electrodynamical forces which redis t r ibute

the ionization.

Although, a s s ta ted previously, the calculations in this repor t a r e

based upon the average proper t ies of the ionosphere, i t is important to

rea l ize that t he re a r e sho r t - t e rm variat ions in the medium.

t e r m phase variations a r e one of the mos t noticeable features of a VLF

The shor t -

7

record.

u tes ) than one would expect f r o m so lar controlled phenomena and a r e

undoubtedly a t t imes related to the motions in the neutral a tmosphere .

These fluctuations a r e much shor te r (of the o r d e r of 30 min -

T h e r e is not much information on the turbulent s t ruc tu re of the

mesosphe re (the region of the neutral a tmosphe re which overlaps the

D Region) because this is a region that i s too high for balloon soundings

and too low for satell i tes.

i r r egu la r s t ruc tu re in this region based upon rocket and me teo r t r a i l

investigations. F o r example, sodium cloud m e a s u r e m e n t s by Blamont

and Jage r

they explained by a combination of turbulent mixing and molecular

diffusion. About 10 y e a r s ago, Greenhow and Neufeld suggested the

p re sence of l a r g e sca le i r r egu la r i t i e s in the 80 -90 k m region based

upon r ada r observations of me teo r t r a i l s . However, t h e r e i s some

controversy about these observations s ince l a t e r measu remen t s by

Manring, et a l . , via rocket sodium cloud measu remen t s suggested

that the turbulence explanation may be spurious and in fact may be due

to the rocket.

and Drazin

propagation of gravity waves into the upper a tmosphere .

However, t he re i s some information on the

1 . indicated the existence of i r r egu la r i t i e s below 100 k m which

2

3

An al ternat ive explanation has been made by Charney

who suggest that the i r r egu la r i t i e s a r e produced by the 4

In any case , phase fluctuations of VLF signals a r e in some fashion

related to the i r r egu la r s t ruc tu re of the mesosphere .

A s discussed e a r l i e r , rea l i s t ic calculations of V L F radio fields a r e

obtained f r o m full wave solutions and for the present these solutions

have only been obtained for plane s t ra t i f ied ionospheric models.

the possibility of using this approach to obtain wavefields for a m o r e

complicated i r r egu la r ionosphere does not s e e m part icular ly pract ical

a t the present t ime and i t appears n e c e s s a r y to r e s o r t to s impler m o r e

approximate methods.

Thus,

8

A s an example of one such possible approach, suppose that one is

s e v e r a l thousand k i lometers f rom a V L F t ransmi t te r .

the phase velocity of the radio signal i s near ly constant ( this cor responds

to the situation in a waveguide where mode 1 i s dominant) and i s given

approximately by

At such a dis tance,

where ) is the radio wavelength, h

l a y e r , and c the velocity of light. To a f i rs t approximation, we might

consider that the effect of a l a r g e i r r egu la r i ty would be to change the

height of the reflecting layer by a n amount 1 h, which would in t u r n

the height of the ionospheric reflecting 0

a l t e r the phase velocity. Thus f rom the equation above, we obtain 2

i;n - -- v 16h h

P 0 0

since < < h . 0

This change in phase velocity would produce a change i n the phase

of tl-e received signal which could be interpreted in a s t ra ight forward

manner for th i s situation. However, the situation becomes m o r e

complicated when the i r r egu la r i t i e s a r e small compared to the path

length o r to the radio wave length.

p roblem theoretically.

developed specifically for V H F forward sca t t e r problems and has

attempted to adapt i t f o r the interpretation of V L F phase measurements .

Although th is work appears to be far f r o m exact, it does give s o m e

interest ing resu l t s , Specifically, Crombie considers the two cases

when V L F phase measu remen t s a r e made on a distant t r ansmi t t e r using

two V L F receiving sites.

receiving s i t e s a r e in l ine with the t r a n s m i t t e r , and in the second case

( t r a n s v e r s e c a s e ) occur s when the l ine joining the two r ece ive r s is

5 Crombie has attempted th i s

6 He has taken the work by Rice which was

In the f i r s t ca se (longitudinal c a s e ) the two

9

perpendicular to the l ine between one of the r e c e i v e r s and the t r ansmi t t e r .

He then takes s o m e experimental data of Harg reaves which apply to the

t r a n s v e r s e c a s e and concludes that the ave rage s i ze of the i r r e g u l a r i t i e s

is about 65 k m and that the horizontal dr i f t velocity i s about 35 m / s e c .

Crombie compares these values with some r e s u l t s f r o m Hines , (which

appear to apply to the region in question) which predic t a horizontal

velocity of about 100 m / s e c . for internal gravi ty waves with horizontal

components o f 6 5 km. Although the predicted value i s higher than that

deduced by Crombie, the values a g r e e within a n o r d e r of magnitude.

7

8

5. Theory of Calculations

T h r e e approaches to theore t ica l V L F calculations have seen wide 9 usage: (1) Wave guide mode theory, (2) geomet r i c opt ics , and ( 3 ) zonal

harmonics .

one mode need normal ly be considered.

t r a n s m i t t e r and r ece ive r d e c r e a s e s , m o r e modes a r e necessa ry . Some

disadvantages a r e that physical in te rpre ta t ion of modes is difficult and

the introduction of varying propagation p a r a m e t e r s along the path

becomes ve ry complicated. It i s possible that significant modes may

be overlooked. In addition, un less a F o u r i e r t r a n s f o r m into the t i m e

domain i s employed, mode theory does not account for the observed

difference in a r r i v a l t i m e between the ground wave and the var ious

sky waves

Mode theory has the advantage that a t l a r g e d is tances only

A s the dis tance between the

Geometr ic op t ics , on the other hand, lends i tself well to c l ea r

physical interpretat ion.

wave.

m i t t e r , jus t the opposite of mode theory,

th i s theory become m o r e valid with increas ing frequency, but a r e in

genera l not valid a t V L F except ve ry nea r the t r ansmi t t e r .

Various "hops" a r r i v e l a t e r than the ground

The accu rac i e s of geometr ic opt ics a r e g rea t e s t n e a r the t r a n s -

The approximations m a d e by

Geometr ic

10

optics i s not a r igorous theory f o r electromagnetic wave propagation in

the V L F region.

The mathematical derivation of the zonal harmonic and geometr ic

s e r i e s representat ions f o r electromagnetic wave propagation i s well

documented by Johler

be pr imar i ly nonmathematical i n an attempt to give physical insight to

this method.

10, 11, 12, 13, 14, 15 The approach used h e r e wil l

The use of zonal harmonics in propagation formulae was introduced 16

ear ly in the 20th century by Debye

L o r d Rayleigh

p rac t i ca l application of this theory could be accomplished.

speed digital computer allows summation of the l a r g e number of t e r m s

that a r e requi red for convergence of the s e r i e s . (Here convergence is

used to mean that additional t e r m s do not significantly effect the resu l t . )

In addition, new theoretical advances have great ly reduced the number

of t e r m s required for convergence.

( for electromagnetic waves) and 17

( for sound). It was not, however, until recently that

The high

Zonal harmonics allow the introduction of r igorous analysis while

maintaining the c l ea r physical interpretat ion of geometr ic optics, The

t e r m in the classical zonal harmonic s e r i e s containing both the ground

and ionospheric reflection coefficients can be represented as a geo-

m e t r i c s e r i e s ,

harmonic s e r i e s before the geometr ic se r ies - -y ie lds a s e r i e s , each

t e r m of which i s analogous to the geometr ic optic s e r i e s .

o r d e r t e r m of the geometr ic s e r i e s is the ground wave and the jth term

rep resen t s a wave which has suffered j reflections f r o m t h e ionosphere.

Inverting the o r d e r of summation--summing the zonal

The zero th -

-

The l a r g e number of t e r m s ordinar i ly required for convergence of

the zonal harmonic s e r i e s i s found to be necessa ry only because the

ground wave i s included i n the calculations.

converge with approximately one-fifteenth the number of t e r m s ,

the ground wave may be computed m o r e effectively by other means ,

the remaining t e r m s of the geometr ic s e r i e s can be rapidly computed,

The higher o r d e r t e r m s

Since 18

11

Very few t e r m s a r e required for convergence of the geometr ic

s e r i e s a t VLF. Under no rma l conditions, 10 t e r m s (i. e . , hops) have

been found sufficient for convergence to distances of 8 , 000 to 10 , 000

ki lometers . Grea ter dis tances may requi re a few m o r e t e r m s .

Each t e r m of the geometr ic s e r i e s may be thought of a s a se t of

‘In-waves” (the n t e r m s of the zonal harmonic s e r i e s ) .

waves i s incident on the ionosphere and the ground a t an angle which i s

an approximate function of n.

of incidence which a r e given exactly by functions of n.

has been noticed between using r e a l and complex angles of incidence since

normal ly the imaginary portion i s quite small . )

determining factor for the number of t e r m s required for convergence.

The s e r i e s converges abruptly a s the angle of incidence approaches

9 0 degrees . The contribution of t e r m s where the angle of incidence

is l e s s than approximately 30 degrees is negligible.

even fewer t e r m s a r e required.

Each of the n-

(The r igorous theory uses complex angles

Li t t le difference

This function of n i s the

Consequently,

Because of l a t e ra l displacement a t both the ionosphere and the

ground, no specific angle of incidence is required for a wave to reach

a par t icular distance. La te ra l displacement a s used h e r e means that

a wave may be t rapped and propagate radially within the ionosphere or

ground for some distance before emerging again to continue no rma l

propagation ( s e e figs. 1 2 through 15, pp. 45-48, Johler and Mellecker ,

1970--Ref. 15). Most of the reflection does, however, take place near

the angle predicted by geometr ic optics.

Each n-wave contains a factor which may be called the effective

reflection coefficient.

reflection coefficients for ordinary and extraordinary reflection f r o m

the ground and ionosphere.

tion of both the t r ansmi t t e r and rece iver antennae, for example, only

In essence this factor i s the sum of a l l possible

F o r the case of ver t ica l e lec t r ic polar iza-

12

ordinary reflection can effect the field fo r the f i r s t hop so the effective

reflection coefficient i s T Both ordinary and extraordinary r eflec-

tion can affect the second hop field and the effective coefficient is eeo

T R T t T R T Higher o rde r coefficients become very e m m m e ee e ee

complicated.

with the f i r s t subscr ipt denoting the incident polarization and the second

the reflected polarization ( e i s ver t ical e lec t r ic and m i s ver t ical mag-

netic). The ground reflection coefficient, R , needs only one subscr ipt

since no abnormal component i s generated during ground reflections.

Here T stands fo r the ionospheric reflection coefficient

Since mos t of the reflection for a given "hop" takes place within

a region, local reflection coefficients may be introduced. Fo r example,

a land sea boundary changes the reflection coefficient of the ground and

may be incorporated. Similar ly , i f par t of the path is in sunlight while

the r e s t is in darkness ( io e . , the " terminator" occur s along the propa-

gation path) this fact may be used in the analysis .

The ionospheric reflection coefficients which a r e mos t readily

These may be used a s an available a r e plane F r e s n e l coefficients.

approximation to the t r u e coefficients.

quite good if the coefficients a r e multiplied by a convergence-divergence

factor . The best method, however, i s to allow complex angles of

incidence.

imaginary t e r m will normally be smal l , but i t may not be mathematically

negligible.

The approximation becomes

It has been s ta ted ea r l i e r that the contribution of the

Since the only distance related portion of each n-wave i s the

Legendre function, the field a t many dis tances can be calculated s imul-

taneously.

min imal i nc rease in computation t ime.

Upwards of 2 0 0 distances may be calculated with only

It i s n e c e s s a r y to compute the reflection coefficients for each n.

This i s no difficulty for the ground reflections since this calculation

13

is relatively s t ra ightforward and does not consume much computer

t ime. The ionospheric reflection coefficients, however, a r e compu-

tationally quite complicated and can consume a s much a s 2 minutes

of computer t ime for each set of coefficients required.

reflection coefficients a r e a smooth function of angle of incidence

(of n ) , i t is pract ical to s e t up a table of reflection coefficients and to

interpolate on this table to obtain the des i r ed coefficient.

should be made in such a way that no extrapolation is necessary .

Because the

The table

The e lec t r ica l quali t ies of the ionosphere may be character ized

by electron and ion density prof i les , and a collision frequency model.

To facil i tate calculation of the reflection coefficients, the ionosphere

is divided into layers .

By increasing the number of l a y e r s , th i s representat ion can be made

a s c lose a s des i red to the continuous distribution.

Each layer i s a s sumed to have uniform densit ies.

Maxwell 's equations and the equation of motion of the electron a r e

solved yielding t ransmi t ted and ref lected portions of the incident wave

f o r each of the layers .

waves and solving for continuity a t the boundaries between each of the

l a y e r s , the ref lect ion coefficients a r e obtained.

By keeping t rack of these upgoing and downgoing

Coupling of the ver t ica l e lec t r ic and ver t ical magnet ic polar iza-

tions within the ionosphere causes the generation of an abnormal com-

ponent and necess i ta tes calculation of two reflection coefficients for

the ver t ica l e lec t r ic incident polarization, Also, since ground ref lec-

t ions do not change the polarization of the incident wave ( io e. , t he re i s

no coupling at the ground) , i t i s n e c e s s a r y to compute reflection

coefficients fo r no rma l and abnormal ionospheric reflection of ver t ica l

magnet ic incident polarization. To s u m m a r i z e , four reflection coeffi - cients mus t be computed fo r each angle of incidence; (1 ) ver t ica l e lec t r ic

polarization of the incident and ref lected wave ( T ) , ( 2 ) ver t ica l e lec t r ic ee

14

polarization of the incident wave with abnormal o r ve r t i ca l magnetic

polarization of the reflected wave ( T ) , ( 3 ) ve r t i ca l magnetic polar iza-

tion of the incident and reflected wave ( T ), and (4 ) ve r t i ca l magnetic

polarization of the incident wave and ve r t i ca l e lec t r ic polarization of the

reflected wave ( T ).

e m

mm

m e NOTE: Vert ical e l ec t r i c polarization is in quadra ture (a t 9 0 degrees )

to ver t ical magnetic polarization and may also be called horizontal mag-

netic polarization, Similar ly , ve r t i ca l magnetic polarization may be

called horizontal e l ec t r i c polarization.

Each reflection coefficient gives the phase and amplitude of the

ref lected wave.

ionosphere.

Interpolation on th i s wildly varying phase can be ve ry inaccurate.

p roblem is solved by re - re ferenc ing the phase to a height where the

phase i s slowly varying with angle of incidence.

t imes r e f e r r e d to as the effective reflection height.

The phase i s normally re ferenced to the bottom of the

This causes the phase to va ry rapidly with angle of incidence.

The

This height i s some-

6. The Calculations

Table 1 lists the calculations that a r e repor ted i n this paper.

Throughout these calculations a magnetic dip of 70 degrees and a mag-

netic f ie ld s t rength of 4 0 ampere - tu rns /me te r have been employed.

These values a r e a good approximation of the magnetic field vector

experienced in the United States,

graphs a r e re la t ive to a medium where the index of refract ion is 1, 0001,

All of the phase and group delay

Two ionospheric prof i les (electron density a s a function of height

above the surface of the e a r t h ) designated normal day (fig. 1 ) and

normal night (fig. 2 ) , have been used f o r the majori ty of the calculations

with s ix other prof i les used to demonstrate the types of fluctuations one

might expect under ce r t a in conditions.

night prof i les were r a i sed and lowered 2. 5 km.

The no rma l day and normal

While this i s admittedly

15

an ar t i f ic ia l a l terat ion of the ionosphere, i t was felt that calculations

made by using such prof i les would indicate the var ia t ions to be expected

during ionospherically active periods. The Deeks 1200 profile (fig. 3 )

and the Bain and May

sunspot minimum conditions a s experienced over Grea t Britain.

19

2 0 prof i le (fig. 4 ) r ep resen t sunspot maximum and

The var iable mos t comprehensively t rea ted herein i s magnet ic

azimuth. The majori ty of the calculations w e r e repeated with a t l ea s t

t h ree changes in azimuth. F o r purposes of interpolation, propagation

towards the magnet ic nor th ( 0 deg rees ) has been a s sumed to be rec ipro-

cal to propagation towards the magnet ic south (180 degrees ) .

The surface reflection coefficients were computed on the bas i s of

a conductivity of . 005 mhos p e r cent imeter and a ground dielectr ic

constant of 1 5 for land, and a conductivity of 5 mhos p e r cent imeter

and dielectr ic of 80 for sea .

the values for land were used for the computations.

Unless the graphs a r e otherwise marked ,

Table 2 gives a compar ison of the theory and experimental data.

These data a r e in the f o r m of diurnal phase shift measu remen t s .

Diurnal phase shift r e f e r s to the phase difference between day and

night, result ing f r o m increased ionization of the upper a tmosphe re

caused by the sun 's rays .

night phase a t a given geodetic distance minus the daytime phase a t

that s a m e distance.

in table 3 .

This phase difference was computed a s the

A few group delay compar isons have been made

Table 4 l i s t s the predicted daytime phase delay and the diurnal

var ia t ion for var ious s i tes .

f o r these s a m e s i tes . The values given for Canberra , Austral ia

r ep resen t a n extrapolation f r o m the graphs.

Table 5 gives the assoc ia ted group delays

1 6

Figure 5 gives a comparison of theoret ical and exper imenta l

diurnal phase shifts measu red by NBS on the 2 0 . 0 kHz t r ansmiss ions

f r o m WWVL.

phase values fo r the same t ransmiss ions .

F igure 6 compares theoret ical and exper imenta l re la t ive

F igu res 8 through 6 9 give a phase cor rec t ion in radians f o r var ious

frequencies and magnet ic az imuths under normal day and no rma l night

conditions.

to the phase delay of a hypothetical wave traveling a t the speed of light

in a medium where the index of re f rac t ion i s 1. 0001.

these f igures a r e labeled "Relative Phase . I '

This phase cor rec t ion is that value which must be added

Consequently,

F igu res 70 through 128 give the amplitude in volts p e r m e t e r ,

re fe renced to unity dipole cur ren t , for the var ious frequencies and

azimuths under normal day and no rma l night conditions.

F igu res 129 through 204 give the group delay cor rec t ion in m i c r o -

seconds for var ious frequencies and azimuths under no rma l night

conditions. Again, because this correct ion i s obtained a s the difference

between the absolute group delay and the delay of a wave traveling a t

the speed of light and an index of refract ion of 1.0001, the f igures a r e

labeled "Relative Group Delay. I '

this group delay has been developed by F e y and LooneyZ1 and is analogous

to the method presented e a r l i e r in the text.

The actual method of calculation of

F igu res 205 through 233, "Diurnal Phase , ' I give the phase shift to

be expected between night and day using the no rma l day and n o r m a l

night prof i les .

F igu res 234 through 2 5 4 a r e special c a s e s of the previous calcula-

tions in that e i ther the profile o r ground conditions a r e changed f r o m

previous f igures for the same frequency and azimuth.

7. Discussion and Conclusions

The ana lys i s of the theoret ical data presented h e r e i s a imed a t

It should be noted during the analysis of these timing implications.

17

graphs that the calculations have a tendency to de te r iora te with distance.

This does not affect many of the graphs , but at the point where the t rend

towards l inear i ty with increasing dis tance breaks down, the graph should

be d is regarded o r , conversely, the l inear i ty may be extrapolated to

obtain the des i r ed resu l t s .

m o r e t e r m s (hops) in the geometr ic s e r i e s summation.

The cause of the degeneracy i s a need for

The fluctuations i n the amplitude of the sum of the var ious hops i s

highly cor re la ted to the points at which the amplitudes of two of the hops

a r e equal ( s e e fig. 78--Ampli tude, 12. 5 kHz, 150°, Normal Day).

These amplitude fluctuations a r e a l so well cor re la ted to fluctuations i n

phase. Unfortunately, it is prec ise ly these points of equal amplitude

that a r e mos t likely to be displaced mos t by smal l changes in the

ionosphere. Therefore , t h e r e a r e cer ta in c r i t i ca l dis tances at which

the phase i s likely to be unstable.

i n both phase and amplitude under nighttime conditions, th i s may account

for the l a r g e phase deviations normally experienced at night,

esting presentation of th i s idea i s given in f igure 7.

amplitude a r e combined on one graph fo r 130 6 kHz, 90”, Normal Night.

( r i s a logari thamic s c a l e giving amplitude in vo l t s /me te r and

t ive phase in degrees . )

Since t h e r e a r e m o r e fluctuations

An i n t e r -

Here phase and

is r e l a -

The points on the curve a r e a t 500 k m increments .

I t is interest ing to note that the g r o s s fea tures of the nighttime phase

and amplitude graphs at the Omega frequencies a r e ve ry similar to the

dayt ime fea tures nea r 2 0 kHz.

field upon the ra t io of wave length to ionospheric height. One implica-

tion of this dependence i s that the Omega frequencies may be near ly as

rel iable for t ime synchronization at night as a r e the W W V L t ransmiss ions

during the day.

with a few exceptions, this may indeed be the case.

the night phase f rom s e v e r a l of the Omega stations monitored a t the

National Bureau of Standards again points towards rel iable t ime t r a n s f e r

This points out the dependence of the

The graphs of the theoret ical group delay indicate that ,

The smoothness of

1 8

during the night a t t hese frequencies. Near 20 kHz, however, i t i s

apparent that synchronization cannot be accomplished with any degree

of reliabil i ty during the night.

During the day, synchronization a t the Omega frequencies should

be very reliable.

a r e diss ipated in near ly all c a s e s by approximately 2 , 000 km.

this point on the group delay becomes near ly l inear and ve ry predictable,

The small fluctuations in the group delay g raphs

From

Onc is able to a r r i v e a t a n es t imate of the maximum timing e r r o r

to be expected using a given pa i r of f requencies , by examining the

group delay plots.

which a r e s imi l a r to damped sine waves.

is then the maximum expected e r r o r .

k i lometers ,

a .

In the majori ty of c a s e s these plots have fluctuations

The amplitude of these waves

Neglecting the first 500 to 1000

the folLowing e s t ima tes of maximum timing e r r o r a r e given:

for the Omega frequencies during the day the expected e r r o r

i s approximately + 2 0 p s e c ;

b. for the frequencies near 2 0 kHz during the day, approximately

f 50 I lsec;

c. for the Omega frequencies a t night, approximate

d. for the frequencies near 2 0 kHz during the night,

* 1 2 0 Usec.

Because of the s imi la r i ty of the relat ive phase grapl

y * 7 0 Usec;

app r oxima t ely

s with changes

in azimuth i t appea r s that l inear interpolation may be used for both

azimuth and dis tance f r o m the t r ansmi t t e r during the day. The night

phase, though,is not near ly so well behaved. In fact , the night phase

a t 2700 i s ve ry d i s s imi l a r to the 90" and the 180° phases (which a r e

r a the r alike).

whether these changes take place l inear ly with azimuth.

A possible a r e a for fur ther study would be to de t e rmine

19

The fluctuations (high frequency Four i e r component) in group delay

Wide frequency a r e very much cor re la ted to the frequency separation.

separat ions have fewer and sma l l e r fluctuations than do na r row f r e -

quency separations.

high resolution and subsequently l a r g e ambiguities of wide separat ions ,

and the low resolution but smal l ambiguity of smal l separations.

At s o m e point then, one mus t choose between the

The Omega navigation sys tem, with i t s proposed worldwide cover - age, has g rea t potential a s a t ime synchronization tool.

of f requencies and frequency separat ion, coupled with the possibil i ty of

24-hour utilization, available a t each of the eight stations in the network

offer medium to high resolution t ime synchronization to a lmos t a l l

l o cal e s .

The var ie ty

I

2 0

8. References

[41

[ 51

C61

[71

Blamont, J. E . , and de J a g e r , C . , "Upper -a tmospheric turbulence determined by means of rockets , I f J. Geophys. R e s . , 67, No. 8, pp. 3113-3119, July 1 9 6 2 .

-

Greenhow, J. S. , and Neufeld, E. L. , "Large sca l e i r r egu la r i t i e s in high al t i tude winds, I ' P r o c . Phys. S O C . , 75, pp. 228-234, 1960. - Manring, E . , Bedinger, J. F., and Knaflich, H. , "Measurements of winds in the upper a tmosphere during Apri l 1961, J. Geophys. R e s . , 67, No. 10, pp. 3923-3925, September 1962. - Charney, J. G., and Drazin, P. G . , "Propagation of planetary- sca le dis turbances f r o m the lower into the upper a tmosphere , I t

J . Geophys. Res., 66, No. 1, pp. 83-109, January 1961. - Crombie, D. D . , "Effects of n o r m a l ionospheric fluctuations on propagation of V L F s ignals to g r e a t dis tances , I t

Instability in Electromagnet ic Wave Propagation (AGARD-EWP Sym. , Ankara, Turkey, October 4-12, 1967), AGARD Conf. P r o c . No. 33, K. Davies (Ed. ), pp. 35-43 (Technivision Serv ices , Slough, England, July 1970).

Phase and Frequency

Rice , S. O . , "Statist ical f luctuations of rad io field strength far beyond the hor izon ," P r o c . IRE, 41, No. 2 , pp. 274-281, F e b r u a r y 1953.

-

Hargreaves , J . K . , "Random fluctuations in VLF s igna ls ref lected obliquely f r o m the ionosphere, 3 . Atmos. T e r r . P h y s . , 20, pp. 155-166, 1961.

-

Hines, C. O., ) ' Internal gravi ty waves a t ionospheric heights, ' I

Can. J. P h y s . , 38, No. 11, pp. 1441-1481, November 1960. - Wait, J . R., and Spies, K . P., "Character is t ics of the e a r t h - ionosphere waveguide fo r VLF rad io waves, Nat. Bur . Stand. (U . s. ) Tech. Note 300, 1964. 1 s t Suppl., F e b r u a r y 1965; 2nd Suppl., March 1965.

Johler , J . R., "On the ana lys i s of LF ionospheric rad io propagation phenomena, J . R e s . , 65D, No. 5, pp. 507-529, September-October 1961.

-

2 1

Johler , J . R . , and Ber ry , L. A . , "Propagation of t e r r e s t r i a l rad io waves of long wavelength- -theory of zonal harmonics with improved summation techniques, IT J. R e s . , 66D, No. 6 , pp. 737 - 773, November-December 1962.

-

Johler , J . R . , "Concerning l imitat ions and fur ther cor rec t ions to geometr ic-opt ical theory for LF, V L F propagation between the ionosphere and the ground, Radio Sci. J . R e s . , NBS/USNC- URSI, - 68D, No. 1, pp. 67-78, January 1964.

Johler , J . R . , "Zonal ha rmon ics in low frequency t e r r e s t r i a l rad io wave propagation, Nat. Bur. Stand. (U. S. ) Tech. Note 335, Apr i l 13, 1966.

Johler , J . R . , "Theory of propagation of low frequency t e r r e s t r i a l radio waves - -mathemat ica l interpretat ion of D-region propagation s tudies , I t ESSA Tech. Repor t IER48-ITSA 47, August 1967.

Johler , J . R. , and Mellecker , C . , "Theoret ical LF , V L F field calculations with spher ica l wave functions of integer o r d e r , ESSA Tech. Report , ERL165-ITS 106, Apr i l 1970.

Debye, P . , "Der l ichtdruck auf kugeln von beleibigem mate r i a l , (English t ranslat ion: "The p r e s s u r e of light on sphe res made of any mater ia l . ' I ) , Ann. Physik (Leipzig), - 30, pp. 57-136, 1909.

Lord Rayleigh, "On the acoust ic shadow of a sphere, I ' with Appendix giving the values of Legendre ' s functions f r o m P 0 Pz0 a t in te rva ls of 5 degrees by Prof . A. Lodge, Phil . Trans . Roy. SOC. , London, A203, pp. 87-110, 1904.

to

Joh le r , J . R., "Ground wave propagation in a no rma l and a n ionized a tmosphere , ESSA Tech. Report , ERL121-ITS 85, 1969a.

Deeks, D. G. , "D-region e lec t ron distributions in middle lati tudes deduced from the ref lexion of long rad io waves, I t P r o c . Roy. SOC., A291, pp. 413-437, 1966. - Bain, W. C . , and May, B. R . , "D-region electron-densi ty dis t r ibut ions f r o m propagation data, P r o c . IEE, - 114, No. 11, pp. 1593-1597, November 1967.

[21] Fey, L., and Looney, C. H . , J r . , "A dual frequency VLF timing sys tem, IEEE Trans . Instrum. and Meas . , IM-15. No. 4, pp. 190- 195, December 1966.

2 2

A P P E N D I X

In a s e r i e s of pape r s , Johler has combined the zonal harmonic

ser ies with the geometr ic s e r i e s and by extracting the ground wave

f r o m the total field, great ly reduced the number of t e r m s required

for convergence of the se r i e s .

dix i s an attempt to condense this theory.

The ma te r i a l presented in this Appen-

To gain insight into this application of zonal harmonics we wi l l

f i r s t consider the case of a sharply bounded isotropic ionosphere and

then general ize to an anisotropic ionosphere with a continuously va ry -

ing electr ical makeup.

For the isotropic case , and par t icular ly for ver t ica l e lec t r ic

polarization, the zonal harmonic representat ion i s

I o P is the intensity of the electr ical source , a point dipole, which for

convenience may be taken to be 1.

(4n x

a i s the radius of the ea r th and k

p o is the permeabili ty of space 8

henry /me te r ) and c is the speed of light (2 .997925~10 m / s ) .

is the wave number of a i r . P ( z ) i s 1 n

the solution of Legendre’s differential equation. R and T a r e the n n

ground and ionospheric reflection coefficients respectively (the sub-

scr ip t denotes that the reflection coefficients m u s t be recomputed for

r! ” ’ i s the spherical wave function and a = - each n). la

2 3

The geometr ic s e r i e s may be introduced by noting that the denomi-

nator of eq (1) can be expressed a s a geometr ic s e r i e s .

[ l-RnTn]' l m [RnTn] j

j = l

Substituting into (1) and interchanging the o r d e r of summation yields

m

+E E r , j = E

r r , o E

j = 1

where

and

( 3 )

and F ( n ) = n(n t1 )

At th i s point

2 n t l ) P ( c o s B ) . n

an analogy may be drawn with geometr ic optics.

E . i s a wave which has been ref lected

f r o m the ionosphere j t imes, Because of l a t e ra l displacement at the

ionosphere, and a l so at the ground, the wave is not reflected f r o m a

point but r a the r f r o m a region. The l a r g e s t portion of the reflection

does occur a t o r nea r the point predicted by geometr ic optics.

actual angle of incidence at the ground, T., o r a t the ionosphere, vi,

i s the ground wave and E r , o r , J

The

1

2 4

for each of the n waves is given by

with the convention that the s ine = 1 when

g rea t e r than one,

The spherical wave functions may easi ly be evaluated f r o m the

r e c u r r e n c e relat ion given (z = k a ) and ( l Y 2 ) - pq (z) - 1 l a n

where ,

and

( z ) - ( z ) 2 n t l ( 1 ~ 2 )

n n - i (z) = - t; j ( L 2 )

n t l Z ( 7 )

( 9 1 ( z ) = exp [* iz]. 5" $ 2 ) -1

Simi la r ly the Legendre function can be found for in tegra l n f r o m

the r e c u r r e n c e relat ion

p ( z ) P ( z ) = P ( z ) - - (2n - l ) z n-1 n n n -1 n n-2

2 5

where

P,(z) = 1

and

Note:

a given distance.

With z = cosf3, 8 is the central angle of the sphere subtended by

F o r the case of an anisotropic ionosphere, eq ( 5 ) m u s t be modified

to r ead ,

where C. i s the “effective reflection coefficient.”

cally evaluated by analogy with geometr ic optics,

C . can be graphi- J J

C, = T ee 2

C z = R T t R T T e ee m e m m e

C , = Z R R T T T t R 2 T 3 e ee ~ R ’ T m mm T e m T m e (12) e m ee e m m e

o r f r o m

26

where

A = R T 1 m mm

A = R T tR T 2 e e e m mm

A = R R f T T 3 e m [ - T ee mm m e e m

The ground reflection coefficients are defined by,

and,

where

27

Note that

Since m o s t of the reflection takes place near the points predicted

by geometr ic optics the concept of local reflection coefficients may be

introduced in the expression for C.. J

ground p a r a m e t e r s along the propagation path may be included in the

field equation.

Tha t i s , changes in ionospheric o r

The convergence of the zonal harmonic s e r i e s ( 1 ) i s notoriously

slow pr imar i ly because of the inclusion of the groundwave in this

expression. Equation ( 3 ) , however, s epa ra t e s the groundwave, E r , 0,

f r o m the skywaves.

groundwave, the number of t e r m s requi red for convergence may be

reduced by a factor of approximately 15.

skywave s e r i e s occurs rapidly as n approaches k, a ( s in qi -+ l ) ,

whereas for the groundwave 15 k , a t e r m s a r e required.

the contribution of t e r m s with small angles of incidence, 'pi < 30 , a r e

near ly negligible so that for f requencies up to 20 kHz, only a few hun-

d red t e r m s may be required for convergence.

By using other methods of calculation for the

That i s , convergence of the

F u r t h e r m o r e , 0

2 8

TABLE 1

LIST O F CALCULATIONS

Magnetic Azimuth (Degrees )

10.20 10.20 10.20 10.20 10 ,20 10.20

12.20 12.20

12.25 12.25

12.30 12.30

12. 50 12. 50 12, 50 12. 50 12. 50 12. 50 12. 50 12. 50 12.50 12. 50

12.70 12.70 12.70 12.70 12.70 12.70 12.70 12.70 12,70 12.70

9 0 90

180 180 27 0 270

90 9 0

90 90

90 9 0

90 90

135 135 150 180 180 225 270 270

9 0 9 0

135 135 150 180 180 225 270 270

P r o f i l e Identification

Normal Day Normal Night Norma l Day Normal Night Normal Day Normal Night

Norma l Day Normal Night

Normal Day Normal Night

Norma l Day Normal Night

Norma l Day Normal Night Norma l Day Normal Night Norma l Day Normal Day Normal Night Normal Day Normal Day Normal Night

Norma l Day Normal Night Norma l Day Normal Night Normal Day Normal Day Normal Night Norma l Day Normal Day Normal Night

2 9

TABLE 1 (Continued)

Frequency

(kHz)

13. 60 13.60 13. 60 13.60 13.60 13.60

19.90 19.90 19.90 19.90 19.90 19.90

20,OO 20.00 20.00 20.00 20.00 20.00

20. 50 20. 50 20. 50 20. 50 20. 50 20. 50

20.90 20.90 20,90 20.90 20.90 20.90

10.20 12. 50 12.70 20.00

Magnetic Azimuth (Degrees)

9 0 90

180 180 270 270

90 90

180 180 270 270

90 90

180 180 270 270

90 90

180 180 270 270

90 9 0

180 180 270 27 0

90 90 90 90

P r o f i l e Identification

Normal Day Normal Night Norma l Day Normal Night Norma l Day Normal Night

Norma l Day Normal Night Norma l Day Normal Night Norma l Day Normal Night

Norma l Day Normal Night Norma l Day Normal Night Norma l Day Normal Night

Normal Day Normal Night Norma l Day Normal Night Norma l Day Normal Night

Norma l Day Normal Night Norma l Day Normal Night Normal Day Normal Night

Deeks 1200 Deeks 1200 Deeks 1200 Deeks 1200

30

TABLE 1 (Continued)

1 0 . 2 0 1 2 . 5 0 12.70 2 0 . 0 0

10.20

12. 50

12.70

2 0 . 0 0

12.20

12.20

12.20

12.20

12 .30

12.30

12.30

12.30

Magnetic Azimuth (Degrees)

90 90 90 90

9 0

90

90

90

90

90

90

90

90

90

90

90

Profi le Identification

Bain & May Bain & May Bain & May Bain & May

Normal Day (Sea W a t e r ) Normal Day (Sea Water ) Normal Day (Sea W a t e r ) Normal Day (Sea Water )

Normal Day (Raised 2. 5 k m )

Normal Day (Lowered 2. 5 k m )

Normal Night (Raised 2. 5 km)

Normal Night (Lowered 2. 5 km)

Normal Day (Raised 2. 5 km)

Normal Day (Lowered 2. 5 km)

Normal Night (Raised 2. 5 km)

Normal Night (Lowered 2, 5 km)

31

In

0 N \

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "

N N N N N N ~ N N N N N N N N N N N N ~

. . o o o o o o d d d d d d d d d d d d o o o o o o o m

c,

d .* 2 c,

d cd 0 a d k c,

5

2 a, (I]

a

32

d

d

9 m

0 N,

W

Ln M co N,

m 00 Ln M

N

0 ri

d 0 2 $

0 a

M w

3 3

References for Table 2

1. W , D. Westfall, "Diurnal Changes of P h a s e and Group Velocity of V L F Radio Waves, I ' Radio Science, Vol. 2 (New S e r i e s ) , No. 1 , January 1967.

2. B. E. Blair and A . H. Morgan, "Control of W W V and WWVH Standard Frequency Broadcas ts by V L F and LF Signals, Science J. of Res. NBS/USNC-URSI, Vol 69D, No. 7, July 1965,

Radio

3 . Yoshiyuki Yasuda, pr iva te communication.

4. P o B. Rao and W. A. Teso , "An Investigation of Propagat ion P h a s e Changes at V L F , " The Radio and Electronic Engineer, November 19 66.

5. A . L. el Sayed, "Comparison of W W V L and the Local Standard, P r o c . of the Mathematical and Phys ica l Society, U . A . R. , 1969.

6. Measurements m a d e by NBSBL.

7. J . H. Roeder , unpublished report .

34

r- m m m N

.rl u a, k

r- N H

0

0 cv

0

0 N

0 0 0 N N N

d X w

0 0 0 * e a

ln N 3

m 0 4

0 0 0 “ N Gc

0 z 0 E? d 4

0 u 9 4 4 4 > > >

3 3 3 3 3 3

4 > 4 > 3 3

3 3 \

C

35

P

N m m b

v 9

m N

d

cr) M

cr) cr) Ln 4

0 0 r-

b m L n N cr)

m N

N 4

0

Ln v

0

F 0 d

m 9

cr, N 0 * N N

Lo

* co

N

* Ln d

co a 0 d

b u E; w d Pi

J

3 E 2

\

C

4

3 L 2

\ C

36

Lo r- 6 Ln 9 M 9 0 m N

a 0

* co M 9 3 9 3 N

N 0

N d r- 3

6 * A N

0

Q

m 3

0

V 6 d 3

0 N Lo M

* aJ 3 r- N

V

3 3

N

M V

M M \o 6 N

3

r- M N

M N M ?I N 4

J F + \ z 3 c 3

F z \

C

o o m m m r - 6000" 3 N N N 4 3

0 0 0 . 0 0

O \ o m o \ m r - 6000" 3 N N N 3 3

. e - . * .

(I)

k e, 5

E 2 01

2 tf

37

b

m r- m Lo N

co a 0 d

m o N U 7 d * N

O D

* a m N

4

0

r- 0 d

m a . . m N o w N N

a a .d k

: 38

Ld k k a, P G Ld u

c

a, V

2

q .A v 3

" m .d

" - a, a 0 a, U

a a,

4

0 0- r- M

N 4

r- 4 N

* .

Z M M d '

O M a m N

0 0

39

k a, c, c,

3 (I) " rd

b k

m c r ) w c o 4 P - N

. e

0

a Ln 4

* 4 4 N

z $ c 3 \

40

N O R M A L D A Y P R O F I L E

h

V u \ v, z 0 m I- o W -J W u

t I-

m z W

Y

n

4 0 60 80 1 0 0 H E I G H T ( k m )

F i g u r e 1.

D E E K S 1 2 0 0 P R O F I L E

h

V

\ U 2 m z 0 m I- 0

w u

t I-

m

W

c-.l

z o n

- 1 4 0 6 0 8 0 100

H E I G H T ( k m ) F i g u r e 3.

7 5 1 0 0 1 2 5 2 0 0 H E I G H T ( k m )

F i g u r e 2.

B A I N & M A Y P R O F I L E

41 H E I G H T ( k m )

F i g u r e 4.

DI URNAL PHASE 2 0 k H z 1 8 0 " A z

-1oc

lor

\

- T H E O R E T I C A L

a E X P E R I M E N T A L

US

- 2 0

- 3 0

- 4 0 1 I I I I I I I 1 0 0 2 0 0 300 400 5 0 0 600 7 0 0

F i g u r e 5.

40 r 30

20

RELATIVE GROUP DELAY N O R M A L D A Y

2 0 . 0 k H z 1 8 0 " A z 0

0 - T H E O R E T I C A L -1 o E X P E R I M E N T A L

0 0

- 1 0 0 5 0 0 1 , 0 0 0 1 , 5 0 0 2,000

D I S T A N C E ( k m ) F i g u r e 6.

42

1 3 . 6 k H z

9 0 " A z

2 7 0 "

N O R M A L N I G H T

1 8 0 "

RELATIVE PHASE N O R M A L D A Y

1 0 . 2 k H z 9 0 " A z

1 1 I I 1 I 1 I I I 0 2 0 0 0 4 0 0 0 6000 8 0 0 0 1 0 0 0 0

Figure 8.

1 0 . 2 k H z 1 8 0 " A z

1 1 1 1 1 I 1- 0 2 0 0 0 4 0 0 0 6000 8 0 0 0 1 0 0 0 0 -81

D I S T A N C E ( km)

Figure 9.

44

2

0 - v, z Q

4: CT

H

I 3 - 2

v - - 4 v, 4 I a

- 6

-8


1 0 . 2 k H z 2 7 0 " A z

1 I I I 1 1 1 I I J 0 2000 4 0 0 0 6000 8 0 0 0 1 0 0 0 0

F i g u r e 10.

1 2 . 2 k H z 9 0 " A z

w - 2 1 v,

- 4 -1 0 2 0 0 0 4 0 0 0 6 0 0 0 8000 1 0 0 0 0

2 1 I , , I I ,

D I S T A N C E ( k m )

Figure 11

4 5


I a

- 4

1 2 . 2 5 k H z 9 0 " A z

2r

I I I I I I 1 1 1 I

1 2 . 3 k H z 9 0 " A z

4 I a

I 1 I 1 1 I 1 I I 1 0 2000 4000 6000 8000 10000

- 4

Figure 13.

1 2 . 5 k tiz 9 0 " A z z 2r z Q

n Q E

H

v

w - v, 4: I a

- 41 I I I 1 I I I I 1 I 0 2000 4000 6000 8000 10000

D I S T A N C E ( k m ) Figure 14.

46


v, Q I a

1 2 . 5 k H z 1 3 5 " A z

Q I a

- v, 2r

1 2 . 5 k H z 1 5 0 " A z

U

v, w - 2 1

1 2 . 5 k H z 1 8 0 " A z

*r

Q I n - 4 I I I I I 1 I I 1 1

0 2000 4000 6000 8000 10000

D I S T A N C E ( k i n )

Figure 17.

47


4 I a

1 2 . 5 k H z 2 2 5 " A z

I I I I I I I 1 1 1

r

W

5 I n

m - 2 -

- 4

I I 1 I I I I I I I 6000 8000 100 0 2000 4 0 0 0

I I I I I 1 I 1 I I

Figure 18.

00

1 2 . 7 kHz 9 0 " A z


Figure 20.

48


w - 2 - m 4 I n

1 2 . 7 kHz 1 3 5 "Az

1 I I I 1 1 I I I

z 4

r : o 4 ry: v

w - 2 v, Q I a - 4 1 I I I 1 1 I 1 I 1 J

0 2000 4000 6000 8000 100 Figure 21.

- 2 v, z 4:

z o

; - 2

4 ry: v

4 I n - 4

1 2 . 7 kHz 1 5 0 " A z -

00

1 I 1 I 1 1 I 1 I I 0 2000 4000 6000 8000 10000

Figure 22.

1 2 . 7 k H z 1 8 0 " A z


Figure 23.

49


w - 2 -

a - 4

v, 5 I

1 2 . 7 kHz 2 2 5 " A z

1 I 1 I I 1 I I 1 I

Figure 24.

1 2 . 7 k H z 2 7 0 " A z

I 1 I 1 I I I I 1 -I 0 2000 4000 6000 8000 10000

Figure 25.

1 3 . 6 k H z 9 0 " A z

I 1 I I 1 1 I I I 0 2000 4000 6000 8000 10000


Figure 26.

5 0


1 3 . 6 k H z 1 8 0 " A z

2 - Q

Q I a I 1 I 1 I 1 I I I I

4000 6000 8000 10000 - 2 0 2000

F i g u r e 27.

13.6kHz 2 7 0 " A z

I 1 1 I I I 1 2 - a 0 2 0 0 0 4000 6 0 0 0 8000 1 0 0 0 0 - 21

D I S T A N C E (km) Figure 28.

51


19.9kHz 1 8 0 " A z

1 I 1 I I 1 I d - 0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0


Figure 29.

52


1 9 . 9 k H z 9 0 " A Z

- 61 I 1 I I 1 I 1 I I 1 0 2000 4000 6 0 0 0 8000 1 0 0 0 0

Figure 30.

1 9 . 9 k H z 2 7 0 0 ~ ~

- 61 I 1 I 1 I I 1 2 - 0 2000 4000 6000 8000 10000


Figure 31.

53


2 0 . OkHz 9 0 " A z

1 1 1 1 1 I 1 1 I I 0 2 0 0 0 4 0 0 0 6 0 0 0 8000 1 0 0 0 0

Figure 32.

20. OkHz 1 8 0 " A z

I 1 I I I I 1 2 - 0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0


Figure 3 3 .

54

4

- 2 m z Q

r : o Q CT v

w - 2 m 4 1 a - 4

-6


2 0 . 0 k H z 2 7 0 " A z

-

I 1 1 I 1 I I I I J 2 0 0 0 4000 6 0 0 0 8000 1 0 0 0 0 0

Figure 34.

2 0 . 5 k H z 9 0 " A z

U L U U U s u u u o u u u o v v v I uuuu


Figure 35.

55


4

n 2 m z Q

z o Q w v

w - 2 m Q I a - 4

-6

2 0 . 5 k H z -

-

1 8 0 " A z

I I I 1 1 I I I 1 I 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

Figure 36.

4

- 2 m z < E o

w - 2

a w v

m Q I a - 4

- 6

2 0 . 5 kHz -

2 7 0 " A z

I 1 I I 1 I 1-

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

D I S T A N C E (km)

Figure 37.

56


2 0 . 9 k H z 9 0 " A z

1 1 1 1 I I I 1 I I 0 2000 4 0 0 0 6 0 0 0 8000 1 0 0 0 0

Figure 38.

2 0 . 9 k H z 1 8 0 " A z

I 1 1 I 1 - 6' 1 1- 0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0


57

2 0 . 9 k H z


2 7 0 " A z

-6 I 1 I I 1 1 1 I I I 0 2000 4000 6000 8 0 0 0 1 0 0 0 0

D I S T A N C E (k in )

Figure 40.

58

1 0 . 2 k H z

z Q - - 2 - n Q Ly: v

-4 W Ln Q I a - 6 -

- 8

'r

-

1 1 I I I 1 1 I I 1

RELATIVE PHASE N O R M A L N I G H T

9 0 " A z

Figure 41.

1 0 . 2 k H z 1 8 0 " A z

I 1 I I I I I 1 I I 0 2000 4000 6 0 0 0 8 0 0 0 10000


Figure 42.

5 9


1 0 . 2 k H z 2 7 0 " A z

I 1 I 1 I I I I I I 4000 6000 8000 10000

-8 1 0 2000

Figure 43.

1 2 . Z k H z Y U " A z

I 1 I I 1 I I I 1 1 2 0 0 0 4000 6000 8000 10000 0

DISTANCE ( km)

Figure 44.

60

1 2 . 2 5 k H z


9 0 " A z

-81 I 1 I 1 1 1 1 I 1 I 0 2 0 0 0 4000 6000 8000 10000

Figure 45.

2

0 h

Ln z Q

4 e

- 2

v

- 4 w m 4: I a - 6

-8

1 2 . 3 k H z

-

9 0 " A z

0 2 0 0 0 4000 6000 8000 10000

D I S T A N C E (km)

Figure 46.

61


1 2 . 5 k H z 9 0 " A z

2,

- v, z 4 H

n 4 m v

w v, 4 I a

I I 1 1 I I I 1 I I 4000 6000 8000 1 0 0 0 0 0 2000

Figure 47.

1 2 . 5 k H z 1 3 5 " A z

1 1 I I 1 I I I I I 0 2 0 0 0 4000 6000 8000 10000

D I S T A N C E (I" F i g u r e 48.

62


1 2 . 5 k H z 1 8 0 " A z

-81 I 1 I 1 1 I 1 I I 1 0 2 0 0 0 4 0 0 0 6000 8000 1 0 0 0 0

Figure 49.

1 2 . 5 k H z 2 7 0 " A z

I I I I I I I I I I 0 2 0 0 0 4 0 0 0 6 0 0 0 8000 10000


Figure 50.

6 3


- 4

- 6

1 2 . 7 k H z 9 0 " A z

-I W v, Q I n

I I I 1 I I I I I I 0 2000 4000 6000 8000 10000 - 8 I

Figure 51.

2

0 n m z <

ct cr:

U

-2 v

- 4 m Q I n

- 6

-8

1 2 . 7 k H z 1 3 5 " A z

-

-

-

-

1 1 I I 1 1 I 1 I I 0 2000 4000 6000 8000 10000


64

2

0 cn z Q - - 2 n Q & v

-4 W cn Q I a - 6

-8

2

- 0 v, z 4: H

n - 2 4: & v

w -4

n

m Q I

- 6

-8


1 2 . 7 k H z 1 8 0 O A z

I I I I I I I I I I 0 2000 4000 6000 8000 10000

Figure 53.

1 2 . 7 k H z 2 7 0 " A z

1 I 1 1 1 1 I 1 1 J I 2000 4000 6000 8000 10000


Figure 54.

6 5


1 3 . 6 k H z 9 0 " A z

0 h

m z Q U

- 2 Q CT v

m -4 Q I a

- 6

-8 I

0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0

Figure 55.

2

- 0 m z Q H

n - 2 Q CT v

w -4 m Q I Q

- 6

-8

1 3 . 6 k H z 1 8 0 " A z

I 1 I 1 1 I I I I I 0 2000 4000 6 0 0 0 8000 10000


Figure 56.

66


2

- 0 v, z Q

Q CY

CI

a - 2

v

w -4 v, a 1 a - 6

-8

6

4

2 - v, z 4

G O 4 CY v

- 2 W v, 4 I

-4

- 6

- 8

1 3 . 6 k H z 270'AZ

I 1 1 I I I I I I I 4 0 0 0 6000 8000 1 0 0 0 0 0 2 0 0 0

Figure 57.

1 9 . 9 k H z 9 0 " A z

I 1 I I I I 0 2000 4 0 0 0 6000


Figure 58.

6 7

- 8000 10000


- 2

n

m z 4: H

n 4: CL v

w v, 4: I a

n

v, z Q

c3 4: e

+-I

v

w m Q I a

1 9 . 9 k H z 180"AZ

8

6

4

2

0

- 2

1 9 . 9 k H z

Figure 59.

2 7 0 " A z

- 4 I 1 I 1 1 I I I I I - 0 2000 4 0 0 0 6000 8000 10000

DISTANCE ( k m )

Figure 60.

6 8


4

2

h

* o z 4

c3 H

2 - 2 v

W m - 4 C t

a - I

- 6

- 8

2 0 . 0 k H z 9 0 " A z -

1C

E

- E m z 4

E 4 Q lx v

w 2 * 5 I a C

- 2

-4

I 1 I I 1 1 I I I I 0 2 0 0 0 4 0 0 0 6000 8 0 0 0 10000

Figure 61. -

2 0 . 0 k H z 1 8 0 " A z

1 I I 1 I I I I I I 0 2 0 0 0 4 0 0 0 6000 8000 1 0 0 0 0


Figure 62.

69


20.0kHz 2 7 0 " A z

8r

I 1 I 1 1 1 I I 1 I 0 2000 4000 6000 8 0 0 0 10000

Figure 63.

2 0 . 5 k H z 9 0 " A z

4

2

0

-2

- 4

- 6

- a I I I I 1 I I 1 I I 0 2000 4 0 0 0 6000 8000 1 0 0 0 0

DISTANCE ( k m ) F i g u r e 64.

70


I 1 I I I I 1 I 4000 6000 8 0 0 0 1 0 0 0 0 2 0 0 0

1 0

8

- 6 m z Q H

Q n 4

- 2 m

CT v

Q I a

0

-2

- 4

Figure 65. -

0

2 0 . 5 k H z 2 7 0 " A z

I I 1 I I I I 1 I I 0 2000 4000 6000 8000 1 0 0 0 0


Figure 66.


0

-2

- 4 n v, z 4: - -6 n Q e v

-8 w v, 4: I n- - 1 0

- 1 2

- 1 4

20.9kHz 90"Az

Figure 67.

20.9kHz 1 8 0 " A z

I 1 I I 1 I I I I 1 0 2000 4000 6000 8000 10000

00


Figure 68.

72

1C

E

E h

m z Q

z 4 Q @L v

2 W m Q I a c

- I


I I 1 1 1 1 I I I I 0 2 0 0 0 4 0 0 0 6000 8000 1 0 0 0 0

Figure 69.

7 3

(D

I

0 7

N 4 0 0 m

N I Y N

0 c

I 0 -

m I 0 -

I 0 7

I 0 7

( W A ) 3aniiidww 74

0 0 0 0 7

0 0 0

0 0 7

0 0 1 -

0 I

7

0 0 0 0 -

0 0 0 7

0 0 7

0 - I 0 -

N 4: 0 0 m

N I Y N

(u 7

,n I 0 7

t. I

0 7

a,

I 0 7

N 4: 0 0 h N

N I Y N

0 7

1 I I m W r.

I 0 7

0 7

I

0 -

0 0 0 0 7

0 0 0 7

0 0 7

3 m -

0 I -

0 0 0 0 7

0 0 0 7

3 3 -

3 -

h

E 24 v

w V z 4: I- m H

n

h

E Y v

W V L Q I- m u n

I 0 7

rr) r- a,

2 M

.d

Gc

N 4: 0 0 In

N I Y pr)

N -

N 4:

0 m 0

N I Y Lo N

N -

0 0 0 0 7

0 0 0 7

0 0 7

I I I PI m

0

I 0 7

1

0 7

I

0 -

h

E Y v

W V z U I- v,

0 Y

h

E Y v

W V z Q: I- v,

0 CI

N 4 0

m M - N I Y m

N 7

(0

I

0 7

l- I 0 - m

I

0 7

N 4: 0

0 m

N I Y LrJ

N - 1 I I

I W b (D

0 - 0 7

0 7

0 0 0 0 -

0 0 0 7

0 0 -

0 m -

0 I - 0 0 i;l 0 7

0 0 0 -

0 0 -

0 -

n

Y E v

w V L U I- v, U n

n

Y E v

W V z 4 I- v) U n

0 -

N 4

0 a3

0

7

N I Y LD

N 7

N 4 0 0 In 7

N I 24 LD

N 7

(D

I

0 - b

I

0 c

m I 0 7

0

0 II 3

m -

0 I

7

II 3

II 3

I I 1 (0 PI m

I I C

0 - 0 c

0 - 7 8

0 0 c, 0 7

0 0 0

0 0 7

0 - 0

h

E Y U

W V z Q: I- v, U

n

CI

E Y U

W V z 4 I- v,

0 U

0 0

W r n e =>a

N 4 0 0 h N

N I Y U J

N c

I I I 9 I 0 7

t. I

0 - m I

0 c

N 4 0 m cu N

N I Y Lo

cu 7

L I I W r- m

1 I

0 7

0 .- 0 7

N Q 0 In m - N I Y h

N ?

N 4: 0 0 m

N I Y h

N -

0 0 0 0 7

0 0 0 7

0 0 -

1 I I 3

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m r. (D

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BETWEEN 1 0 . 2 & 1 2 . 5 kHz J 90" A z

280 1

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

F i g u r e 129.

BETWEEN 1 0 . 2 & 1 2 . 5 k H z

1 8 0 " Az

-

- I I I

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0


F i g u r e 130.

104

RELATIVE GROUP DELAY NORMAL D A Y

28C

24C

200

1 6 0

U s 1 2 0

80

40

0

280

240

200

1 6 0

us 120

80

40

0

BETWEEN 10.2 & 12.5 kHz 270" Az

BETWEEN 1 0 . 2 & 12.7 kHz 9 0 " Az

2000 4000 6000 8000 10000

F i g u r e 131.

1 1 0 0 0 0


F i g u r e 132.

1 0 5


2 8 0

2 4 0

2 0 0

1 6 0

P S

1 2 0

8 0

4 0

0

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

B E T W E E N 1 0 . 2 1 8 0 " Az

I 1 I I I I 1 1

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

F i g u r e 133.

- BETWEEN 1 0 . 2 & 1 2 . 7 k H z

2 7 0 " Az -

-

-

-

-

- I

I 1 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0

- BETWEEN 1 0 . 2 & 1 2 . 7 k H z

2 7 0 " Az -

-

-

-

-

- I

I 1 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

D I S T A N C E ( k i n )

F i g u r e 134.

106


280

240

200

1 6 0

1 2 0

80

40

0

280

240

200

1 6 0

1-1s

1 2 0

80

40

0

I- B E T W E E N 1 0 . 2 & 1 3 . 6 k H z

90" Az

-

2000 4000 6000 8000 10000 1

if

B E T W E E N 1 0 . 2 & 1 3 . 6 k H z r 1 8 0 " Az

I 1 I I 2000 4000

1 10000

F i g u r e 135.

00 D I S T A N C E ( k m )

F i g u r e 136.

1 0 7


2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

B E T W E E N 1 0 . 2 & 1 3 . 6 kHz r 2 7 0 " Az

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

i I I I 1 I I I I I J 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

F i g u r e 137.

B E T W E E N 1 2 . 5 & 1 2 . 7 kHz

9 0 " Az

2 8 0 -

2 4 0 -

2 0 0 -

1 6 0 -

1 2 0 -

2 0 0 0 4 0 0 0 6000 8 0 0 0 1 0 0 0 0 J 000


F i g u r e 138;

108


u s

280

240

200

1 6 0

120

80

40

0

r BETWEEN 1 2 . 5 & 1 2 . 7 k H z 1 3 5 " Az

U I 1 I 1 I 1 1 I I 1 2000 4000 6000 8000 10000

F i g u r e 139,

280 - BETWEEN 1 2 . 5 & 12.7 k H z 1 5 0 " Az 240 -

200 -

1 6 0 -

120 - 8 0 -

2000 4000 6000 8000 10000 D I S T A N C E ( k m )

F i g u r e 140,

109


2 8 0

2 4 0

200

1 6 0

1 2 0

8 0

40

0 h

B E T W E E N 1 2 . 5 & 1 2 . 7 k H z

1 8 0 " Az

I 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0

I 1 I I I I I I 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0

I ' I

F i g u r e 141.

0

u s


F i g u r e 142.

110

,

40

0

280

240

200

1 6 0

lis

120

80

40

0


B E T W E E N

2 7 0 " A z

V I I I I I 1 I I J 2000 4000 6 0 0 0 8000 10000

F i g u r e 143.

- B E T W E E N 1 2 . 5 & 1 3 . 6 k H z

90" A z -

I ; / 1 I 1 1 I I 1 1 1 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 2000 D I S T A N C E ( k m )

Figure 144.

111


2 8 0

2 4 0

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1 6 0

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8 0

4 0

0

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

c

BETWEEN 1 2 . 5 & 1 3 . 6 k H z

1 8 0 " Az

\ J 1

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0

F i g u r e 145.

00

- BETWEEN 1 2 . 5 & 1 3 . 6 k H z

2 7 0 " A z

\ I I

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0

r BETWEEN 1 2 . 5 & 1 3 . 6 k H z

0

DISTANCE ( k m )

F i g u r e 146.

112

us

RELATIVE GROUP DELAY N O R M A L D A Y 280r BETWEEN 12.7 & 1 3 . 6 kHz

240

200

160

120

8 0

40

0

280

240

2 0 0

1 6 0

1 2 0

8 0

40

0

Figure 147.

BETWEEN 12.7 & 1 3 . 6 k H z 1 8 0 " A z

I I 1 I 1 I 1 1 1 2 0 0 0 4000 6 0 0 0 8 0 0 0 1 0 0 0


113

0


1s

" O r BETWEEN 1 2 . 7 & 1 3 . 6 k H z

240

200

160

120

80

40

0 2000 4000 6000 8000 1 0 0 0 0

F i g u r e 149.

BETWEEN 1 9 . 9 & 2 0 . 0 k H z

280 r A z

240 t 200

160

120

80

40

0 1. 1 I I I 1 1 I I 1 1 2000 4000 6000 8000 10000


F i g u r e 150.

114

280

240

200

1 6 0

120

80

40

0


B E T W E E N 1 9 . 9 & 2 0 . 0 k H z

180" A z

280

240

200

1 6 0

us 120

80

40

0

F i g u r e 151. -

B E T W E E N 1 9 . 9 & 2 0 . 0 k H z 1 2 7 0 " A z

I I I I I I I 1 6000 8000 1000

I , 2000 4000


F i g u r e 152.

1 1 5

0

0


BETWEEN 1 9 . 9 & 2 0 . 5 kHz

9 0 " Az 240

200

1 6 0

120

8 0

40

0

1

0

F i g u r e 153.

BETWEEN 1 9 . 9 & 2 0 . 5 kHz

280 r . 1k3O Az 240

200

1 6 0

120

80

40

n 4 0 0 0

v -

2000 0 D I S T A N C E ( k m )

F i g u r e 154.

116


280 r B E T W E E N 1 9 . 9 & 2 0 . 5 kHz

1 6 0

1 2 0

80

40

0

F i g u r e 155.

B E T W E E N 1 9 . 9 & 2 0 . 9 k H z

280 c A z

1 6 0

1 2 0

8 0

40

0


F i g u r e 156.

117

U S

200

1 6 0

120

80

40


-

-

-

-

-

B E T W E E N 1 9 . 9 & 2 0 . 9 kHz 1 8 0 " Az

240

I I I I I 1 I 1 I I 1 0 0 0 0 0 1 2000 4000 6 0 0 0 8000

F i g u r e 157.

280 r BETWEEN 1 9 . 9 & 2 0 . 9 k H z

2 4 0

200

1 6 0

120

8 0

40

0


F i g u r e 158.

118


B E T W E E N 2 0 . 0 & 2 0 . 5 kHz

90" Az

200

1 6 0

120

80

40

0

2 8 0

240

200

1 6 0

1 2 0

8 0

40

0

2

F i g u r e 159.

B E T W E E N 2 0 . 0 & 2 0 . 5 kHz

, 1 8 0 " Az

2000 4000 6000 D I S T A N C E ( k m )

F i g u r e 160.

119

0

8000 1 0 0 0 0

280

2 0 0


B E T W E E N 20.0 & 20.5 k H z

2 7 0 " A z

1 6 0 - F.rs

1 2 0 -

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 0

F i g u r e 161. 280r B E T W E E N 20.0 & 20.9 k H z

9 0 " Az 2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0 L 6 0 0 0 8000

I 1 0 0 0 0


120

lJs


BETWEEN 2 0 . 0 & 2 0 . 9 kHz

1 8 0 " Az 2 4 0 2 a o F 2 0 0

1 6 0

1 2 0

a 0

40

0

280

2 4 0

200

1 6 0

1 2 0

a 0

40

0

Figure 163.

BETWEEN 2 0 . 0 t i ' 2 0 . 9 k H z r 2 7 0 " A z -

-

-

-

- -

4

I I I I 1 I I I 4000 6000 8000 1 0 0 0 0 2 0 0 0 DISTANCE ( k m )

Figure 164.

121


-

-

BETWEEN 2 0 . 5 & 2 0 . 9 kHz

9 0 " Az 2 8 0 r 240

200

1 6 0

1 2 0

8 0

4 0

0

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

40

0

F i g u r e 165.

BETWEEN 2 0 . 5 & 2 0 . 9 kHz

1 8 0 " Az

0


F i g u r e 166.

1 2 2


B E T W E E N 2 0 . 5 & 20.9 k H z 2 7 0 " A z

240

200

1 b o

D S

1 2 0

80

40

0

Figure 167.

0 0

1 2 3

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

80

40

0

RELATIVE GROUP DELAY NORMAL N I G H T

B E T W E E N 1 0 . 2 & 1 2 . 5 kHz

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

40

0

I I I I

0 2 0 0 0 4 0 0 0 6 0 0 0

I . 1 , I

8 0 0 0 1 0 0

F i g u r e 168.

r B E T W E E N 1 0 . 2 & 1 2 . 5 k H z

00

I 1 I ' I I 1

0 2 0 0 0 4 0 0 0 6 0 0 0 I I I I

8000 1 0 0 0


F i g u r e 169.

1 2 4

0

u s

280

2 4 0

200

1 6 0

1 2 0

80

40

280

240

200

1 6 0

1 2 0

80

40

0

-

-

-

-

-

-

RELATIVE GROUP DELAY N O R M A L N I G H T

B E T W E E N 1 0 . 2 & 1 2 . 5 k H z [ I 2 7 0 " Az

0 1. I I I I I I 1 I I I

/

I 1 I I

0 2000 4000 6 0 0 0 8000 Figure 170.

1 0 0 00

1 2 5

120

40

280 r 240

200

1 6 0

120

80

40

0


0

F i g u r e 172.

B E T W E E N 10.2 & 1 2 . 7 kHz

2 7 0 " A z

F i g u r e 172.

B E T W E E N 10.2 & 1 2 . 7 kHz

2 7 0 " A z


126

280

240 1


0

Figure 174.

B E T W E E N 1 0 . 2 & 1 3 . 6 k H z

200

1 6 0

1 2 0

8 0

40

0 0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0


127

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

40

0

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

40

0


/- B E T W E E N 1 0 . 2 & 13.6 kHz r 2 7 0 " Az

I I I I I

0 2 0 0 0 4 0 0 0 6 0 0 0 I 1

Figure 176.

B E T W E E N 1 2 . 5 & 1 2 . 7 kHz

8 0 0 0 1 0 0 0 0

I I I I I I I 1 I

8 0 0 0 1 0 0 0 2 0 0 0 4 0 0 0 6 0 0 0 D I S T A N C E ( k m )

Figure 17'7.

1 2 8

0 0

RELATIVE GROUP DELAY N O R M A L NIGHT

BETWEEN 12.5 & 12.7 kHz

240

200

1 6 0

1 2 0

80

40

n

280

240

200

1 6 0

P S 120

8 0

40

0

- -

-

-

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L

00 Figure 178.

BETWEEN 12.5 & 12.7 kHz 1 8 0 " A z

I ' 1 I I I 1 I I I 1 0 0 0 0 2000 4000 6000 8000


129


280

240

200

1 6 0

I-IS

120

80

40

0

u s

280

240

200

1 6 0

120

80

40

0

B E T W E E N 1 2 . 5 & 1 2 . 7 k H z

2 7 0 " A z

.I\ I I I I I I I I 1

I

I 2000 4000 6000 8000 100 I 2000 4000 6000 8000 100 F i g u r e 180.

B E T W E E N 1 2 . 5 8 1 3 . 6 k H z r 00


130

RELATIVE GROUP DELAY N O R M A L NIGHT

u s

B E T W E E N 12.5 & 13.6 kHz 280 r 240

200

160

120

80

40

0 U

F i g u r e 182.

B E T W E E N 12.5 & 13.6 kHz

00

270" Az

0 0 2000 4000 6000 8000 10000

DISTANCE ( k m )

F i g u r e 183.

13 1


- BETWEEN 1 2 . 7 & 1 3 . 6 k H z

9 0 " A 2 -

-

-

I 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0

:l'l.l I I I I , I , ,

0

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

80

4 0

0

2 8 0

2 4 0

200

1 6 0

P S 1 2 0

8 0

4 0

0 -

-

-

-

-

-

-

-

4 0 0

F i g u r e 184.

BETWEEN 1 2 . 7 & 1 3 . 6 k H z

1 8 0 " A z

8 0 0 0 1 0 0 0 0 2 0 0 0 4 0 0 0 6 0 0 0 I


F i g u r e 185.

1 3 2


I

280

240

200

1 6 0

LJS

1 2 0

80

40

B E T W E E N 1 2 . 7 & 1 3 . 6 k H z

2 7 0 " A z

280

240

200

1 6 0

us 1 2 0

80

40

0

I

2000 4000 6000 8000 10000 0

F i g u r e 186.

B E T W E E N

9 0 " A 2

1

0 2 0 0 0 4000 6 0 0 0 8000 1 0 0 0 0


133

RELATIVE GROUP DELAY NORMAL NIGHT

2 8 0

2 4 0 1 200

1 6 0

1 2 0

80

4 0

0

BETWEEN 1 9 . 9 & 2 0 . 0 kHz I

A Z

4 F i g u r e 188.

BETWEEN 1 9 . 9 & 2 0 . 0 kHz

2 8 0 r 2 7 0 " Az

8 0 0 0 10000

2 4 0 -

2 0 0 -

I 1 8 0 0 0 1 0 0 0 0 0 2 0 0 0 4 0 0 0 6000

I'

DISTANCE ( k m )

Figure 189.

1 3 4

u s


280

240

200

1 6 0

120

80

40

0 0 2000 4000 6000 8000 10000

F i g u r e 190.

B E T W E E N 1 9 . 9 & 2 0 . 5 k H z

2 8 0 r 1 8 0 " A z 240

200

1 6 0

80

40

0 0 2000 4000 6000 8000 10000


F i g u r e 191.

135


u s

2 8 0

2 4 0

2 0 0

1 6 0

1 2 0

8 0

4 0

0

1 B E T W E E N 1 9 . 9 & 2 0 . 5 kHz r 2 7 0 " Az

t I dl""

0 2000 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0

F i g u r e 192.

9 0 " Az I - 7 9 0 t

I

4 :I \

- 7 5 0 ~ B E T W E E N 1 9 . 9 & 2 0 . 9 kHz

0

I I I I I 1 I 1 I I 10000

- 1 0301 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0


136

- 1 6 6 0 -


B E T W E E N 19.9 & 20.9 k H z

1 8 0 " Az

F i g u r e 194.

B E T W E E N 1 9 . 9 & 2 0 . 9 k H z 2 7 0 " Az

40

0 0 2 0 0 0 4000 6000 8 0 0 0 1 0 0 0 0


137

280 9 0 " Az I

2 4 a t 200

1 6 0

120

80

40

n


280

240

200

1 6 0

P S 120

80

40

0

- 0 2000 4000 6000 8000 1 0 0 0 0

F i g u r e 196.

BETWEEN 20.0 & 20.5 k H z

1 8 0 " Az

0 2000 4000 6000 8000 10000

DISTANCE ( k m )

F i g u r e 197,

138


B E T W E E N 20.0 ti 20.5 k H z 2 7 0 " A z

280 -

2 4 0 -

200 -

cis

1 2 0

80

40 -'.

I 0 0

us

2000

B E T W E E N 90" A z

I

4000 6000 8000 10000

F i g u r e 198.

20.0 84 20.

4 - 1 1 1 0

8000 10000 0 2000 4000 6000 D I S T A N C E ( k m ) F i g u r e 199.

1 3 9


2 4 0

2 0 0

1 6 0

BETWEEN 2 0 . 0 & 2 0 . 9 k H z 1 8 0 " Az

-

-

-

- 2 0 2 0 I-

F i g u r e 200.

BETWEEN 2 0 . 0 & 2 0 . 9 kHz

I I I I I I 1 8 0 0 0 1 0 0 0 0 4 0 0 0 6 0 0 0


F i g u r e 201.

140


B E T W E E N 20.5 & 20.9 k H z 9 0 " A z

I

-24

- 24

- 2 5 0 2000 4000 6000

Figure 202.

B E T W E E N 20.5 & 20.9 k H z

8000 10000

-50001 I I 1 I 1 I 1 I I 1 0 2000 4000 6000 8000 10000


Figure 203.

141

280

240

200

1 6 0

1 2 0

80

40

0


B E T W E E N 20.5 & 2 0 . 9 k H z 2 7 0 " Az

00

Figure 204.

142

D I U R N A L PHASE

r 9 0 " A z 1 0 . 2 kHz

L!S

I - 1 2 0 I I 1 I I 1 I I I 1 0 2000 4000 6000 8000 10000

Figure 205.

40 r 1 8 0 " A z 10.2 k H z

20 c LS

0

-20

-40

- 6 0

- 8 0

- 1 00 10000 0 2000 4000 6000 8000


F i g u r e 206.

143

DIURNAL PHASE

2 7 0 " Az 1 0 . 2 kHz

4 0 r

4 0

2 0

0

- 2 0

P S - 4 0

- 6 0

-80

- 1 oc

F i g u r e 207.

9 0 " Az 1 2 . 2 kHz

I I I I I I 1 I I I 2000 4000 6000 a o o o 10000 0


144

DIURNAL PHASE

40r 9 0 " Az 1 2 . 2 5 k H z

-80

- 1 o o L I I I 1 I 1 1 I I 1 2000 4000 6000 8000 10000 0

Figure 209.

9 0 " Az 1 2 . 3 k H z

I I I

- I U U I I I I I 1 I I 1 1 10000 0 2000 4000 6000 8000


Figure 21 0.

145

DIURNAL PHASE

9 0 " . Az 1 2 . 5 k H z

us

I I I I I I I I I I 4000 6000 8000 1 0 0 - 1 00 I

0 2000

F i g u r e 211.

1 3 5 " Az 1 2 . 5 k H z

u s

9 0 " . Az 1 2 . 5 k H z 40-

- 2 0 -

-40 -

-60 -

-80 - I I I I I I I I I I

0 2000 4000 6000 8000 1 0 0 - 1 00

F i g u r e 211.

1 3 5 " Az 1 2 . 5 k H z 40 -

20 - 1

-20 -

-40 -

-60 -

-80 -

00

I I I 1 I I I I I I 2000 4000 6000 8000 10000 - 1 00

0 D I S T A N C E ( k m )

F i g u r e 212.

146

DIURNAL PHASE

2 7 0 " Az 1 2 . 5 kHz

40

20

2 o

1 8 0 " Az 1 2 . 5 kHz -

-

t

- 1 001 I 1 1 I 1 I I I I I 0 2000 4000 6000 8000 10000

2 0

2 7 0 " Az 1 2 . 5 kHz

-

- 1 0 0 1 I 1 I 1 1 I I I I I 0 2000 4000 6000 8000 10000

DISTANCE ( k m )

F i g u r e 214.

147

u s

40

20

0

- 2 0

-40

-60

- 8 0

- 1 0 0

DIURNAL PHASE

9 0 " Az 1 2 . 7 kHz

I I 1 I I I I I I 1 cl 2000 4000 6000 8000 10000

Figure 21 5.

40

20

0

- 2 c

- 4 c

-6C

-8C

40r - 1 3 5 " Az 1 2 . 7 kHz 1 3 5 " Az 1 2 . 7 kHz

- 1 001 I I I 1 I I 1 I I I 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0


Figure 21 6.

148

DIURNAL PHASE

4 0 r 20 I-

O

- 2 0

-60

-80

-100

4 0

2 0

0

- 2 0

u s -40

-60

-80

- 1 0 0

180" A z 1 2 . 7 kHz

F i g u r e 217.

2 7 0 " Az 1 2 . 7 k H z

I I 1 1 I 1 I I I 1 10000 0 2000 4000 6000 8000


F i g u r e 218.

149

40

20

0

-20

-40

-60

-80

- 1 00

40

20

0

- 2 c

1J.S

- 4 c

-6C

-8C

- 1 01

D I U RNAL PHASE

9 0 " A z 1 3 . 6 k H z

0

F i g u r e 219. -

1 8 0 " Az 1 3 . 6 k H z

I I I 1 I I I I I I 2000 4000 6000 8000 10000 0


F i g u r e 220.

150

D I U R N A L PHASE

-80

- 1 0 0 .

270" A z

-

I I I I I I I I 1 1

1 3 . 6 k H z

6 0

40

0

90" Az 1 9 . 9 k H z

-

-

-20 U S

-40

-40

-60

-

151

u s

1 0 0

6 0

D I URNAL PHASE

1 8 0 " Az 1 9 . 9 k H z

40

20

0

1 0 0

8 0

6 0

40 US

20

0

-20

-40

F i g u r e 2 2 3 .

2 7 0 " Az 1 9 . 9 kHz

I I I I I I I I I I 2000 4000 6000 8000 1 0 0 0 0 0


F i g u r e 224.

152

DIURNAL PHASE

r 9 0 " Az 2 0 . 0 kHz

-

-

-

- I

I 1 I I I I I I I 1

80

60

40

20

0

-20

-40

- 6 0

100

8 0

6 0

40

20

0

-20

-40 0

- 1 8 0 " Az 2 0 . 0 kHz

I 2000

I I I I I 4000 6000 8000


153

I 10000

DIURNAL PHASE

1 0 0 -

8 0

60

40

2 7 0 " Az 2 0 . 0 kHz

-

-

-

-40 I I I I I I I 1 I 1 I 0 2000 4000 6000 8000 10000

c 90" Az 2 0 . 5 kHz

-

-

us

-

I 1 I 1 I I I 1 I 1

8 0

60

40

2 0

0

- 2 0

-40

-60

D I U R N A L PHASE

- 2 0

1 8 0 " Az 2 0 . 5 kHz

60

- - 2 0 -

00

10000 0 2000 4000 6000 8000 D I S T A N C E ( k m )

F i g u r e 230.

155

D I U RNAL PHASE

u s

1 0 0

80

60

40 U S

20

0

-20

-40

DIURNAL PHASE

2 7 0 " P,z 20.9 k H z

I 1 I I 1 I I I I 1

1 5 7

- 2

Q

0 Q @L

H

v

w v,

U n o Q @L v

0 4 - I I 1 I I I I I d

w - 2 v, Q I

RELATIVE PHASE N o r m a l Day ( lowered 2. 5 k m )

- 1 2 . 3 k H z 9 0 " A z

a 1 I I 1 I I 1 I I I 0 2000 4000 6 0 0 0 8000 10000 - 4 I

Figure 234.

RELATIVE PHASE N o r m a l Day ( r a i s e d 2. 5 k m )

RELATIVE PHASE N o r m a l Night (raised 2. 5 k m )

2

0 h

v, z Q - 2 n

- - 4

H

Q e

W VI < I -6 n

- 8

- 1 2 . 2 0 k H z 9 0 " Az

I 1 1 I 1 I I I I I 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

F i g u r e 236,

- 1 2 . 3 0 k H z 9 0 " A z

1 1 1 I 1 I I I I I 0 2 0 0 0 4 0 0 0 6000 8000 10000


F i g u r e 237.

159

RELATIVE PHASE N o r m a l Day (sea w a t e r )

1 0 . 2 kHz 'r 9 0 " Az

- 0 m z Q

Q

H

n - 2 -

w - 4 - m 5 I a

- 6 -

I 1 1 1 I I I 1 1 I -8 6000 8000 10000 -

0 2000 4 0 0 0 F i g u r e 238.

I 1 1 1 I I I 1 1 I -8 6000 8000 10000

r i g u r e 238.

RELATIVE PHASE N o r m a l Day ( lowered 2. 5 km)

- 2 m

e W

w - 2 m Q I a -4

1 2 . 2 kHz 9 0 " Az r

I I I I 1 1- 4000 6000 8000 100 0 2000 F i g u r e 239.

00

RELATIVE PHASE N o r m a l Day ( r a i s e d 2. 5 km)

1 2 . 2 0 kHz 9 0 " Az m z 2 - 4

n

e o

m 1 I I--- 5 - 2

H

4

W

w - -

I O 2000 4000 6000 8000 10000 a

DISTANCE ( k m )

F i g u r e 240.

160

RELATIVE PHASE Normal Day ( s e a w a t e r )

1 2 . 5 kt iz 9 0 " A 2

-4

0 n

m z Q

- 2 n < CY v

-4 w m Q I a - 6

1 I I 1 1 I I I I I 0 2000 4000 6000 8000 100

F i g u r e 241. RELATIVE PHASE

Bain and May P r o f i l e

-

-

00

- 8 8 u - i d 0 2000 4000 6000 8000 10000

F i g u r e 242.

1 0 . 2 k H z 9 0 " A z RELATIVE PHASE

D I S T A N C E ( k n i )

F i g u r e 243.

161

RELATIVE PHASE N o r m a l Day ( s e a w a t e r )

- 2 - z

1 2 . 7 kHz 9 0 " Az

I I 1 I I 1 I 1 I 1 6000 8000 10000 -4 I

0 2000 4 0 0 0

F i g u r e 244.

h

v, z 4

0 Q e

U

V

w m 4 I a

1 2 . 5 kHz 9 0 " Az RELATIVE PHASE

0

- 2

- 4 L L J 0 2000 4000 6000 8000 10000

m

Q z 2

e o

4 - 2

U

n 4

V

w m

F i g u r e 245.

- RELATIVE PHASE 1 2 . 5 kHz 9 0 " Az Deeks 1200 P r o f i l e

2-

I I 1 I 1 I I I 1 I 2000 4000 6000 8000 10000 I O a


F i g u r e 246.

1 6 2

R EL A TI V E P EM S E Normal Day (sea wate r )

20.0 KHz 90" A 2 'r * 3 z 4

w

5 * -4

- 2 w

1 2 . 7 k H z 90" A z RELATIVE; PHASE

F i g u r e 248.

- 1 2 . 7 k H z 90" P,z R E L A T I V E PHASE Decks i z o o P ro f i i e *- ------ - .-

D I S T A N C E ( A r r i )

F i g u r e 249.

163

RELATIVE PHASE Bain and May Profile

20.0 kHz 90" Az

F i g u r e 250.

RELATIVE PHASE Deeks 1200 P r o f i l e

20.0 k H z 9 0 " A z l o r

0 2000 4000 6 0 0 0 8 0 0 0 1 0 0 0 0


F i g u r e 251.

164

RELATIVE C R O U P DEX,A.( N o r m a l Day (sea w a t e r )

280

240

200

1 6 0

i i s 120

80

40

0

280

240

200

1 6 0

lis 1 2 0

80

40

0

1 2 . 5 t o 1 2 . 7 k H z

2000 4000 6000 8000 10000 F i g u r e 252,

RELATIVE GROUP DELAY Deeks 1200 Profile

1 2 . 5 t o 1 2 . 7 k H z

9 0 " A z -

-

-

-

2000 4000 6000 8000 10000 D I S T A N C E ( k i n )

F i g u r e 253.

165

280

240

200

1 6 0

U S

1 2 0

80

40

0

R E L A T I V E GROUP DELAY Bain and May Profile

1 1 1 1 I 1 I 1 1 I 2000 4000 6000 a o o o 1 0 0 0 0

F i g u r e 254.

166

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