NBS MONOGRAPH 33

• J a *

An Experimental Study of Phase Variations in

Line-of-Sight Microwave Transmissions

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

THE NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astra, Director'

An Experimental Study of Phase Variations in Line-of-Sight

Microwave Transmissions

K. A. Norton, J. W. Herbstreit, H. B. Janes, K. 0. Hornberg, C. F. Peterson, A. F. Barghausen,

W. E. Johnson, P. I. Wells, M. C. Thompson, Jr., M. J. Vetter, and A. W. Kirkpatrick

National Bureau of Standards Monograph 33

Issued November 1, 1961

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington 25, D.C. - Price 55 cents
Contents

Page

1. Introduction 1

2. Description of propagation path and arrangement

of equipment 2

3. Description of data output 2

4. Analysis of short-baseline phase difference data 3

5. Analysis of long-baseline phase difference and

single-path phase data 4

6. Analysis of refractometer data 6

7. Appendix—notes on the data analysis 6

7.1. Serial correlation and power spectrum

computation 6

7.2. Estimating the power spectrum of reading

error noise 7

7.3. Elimination of trends 7

7.4. Effects of sample length on total

variance and power spectra 8

References 8

Tables 8-16

Figures 17-90

II
An Experimental Study of Phase Variations in Line-of-Sight

Microwave Transmissions*

K. A. Norton, J. W. Herbstreit, H. B. Janes, K. O. Hornberg, C. F. Peterson,

A. F. Barghausen, W. E. Johnson, P. I. Wells, M. C. Thompson, Jr., M. J. Vetter, and A. W. Kirkpatrick

During 1956 an experiment was conducted at Maui, Hawaii, to study the time

variations in the phase of arrival of microwave signals propagated over a 15-mile

line-of-sight path and the time variations in the phase difference of signals originating

at a common antenna and received at two points on a horizontal baseline normal to the propagation path. These time variations are analyzed in terms of their serial

correlation functions and power density spectra for different times of day, and for

several baseline lengths ranging from 2.2 to 4,800 feet. The slope of the power spectra

and the total variance of phase difference variations are shown to be dependent upon

baseline length. In some instances there was evidence of a diurnal cycle in total vari- ance of both phase and refractive index, with larger variances during the day time,

but in other instances this diurnal effect was not detectable. The slope of the phase

spectra appeared to be independent of time of day or meteorological conditions. The

long-term variations in single-path phase were well correlated with variations in the

mean value of refractive index measured at 5 points along the path.

1. Introduction

During the fall of 1956, the National

Bureau of Standards performed a series of

experimental measurements designed to study

the statistics of time variations in the phase of

microwave transmissions propagated over

a line-of-sight path. The purpose of the

experiment was twofold: (1) to provide

information useful in determining the error or

noise contributed by the turbulent troposphere

to any radio system using phase comparison as a means of position location; and (2) to

furnish statistics valuable in formulating and

testing tropospheric propagation theories.

The measurements were made on the island

of Maui, Hawaii, over a 15.46-mile path

extending from the 10,000-ft summit of

Haleakala to the airport at Puunene, at an

elevation of 100 ft. A major consideration in

the selection of this location was that, because

of the relatively large variations in radio

refractive index to be expected here, these data

would form a valuable supplement to similar

measurements made earlier over the Pikes

Peak—Garden of the Gods path in Colorado

[Herbstreit and Thompson, 1955]

The purpose of this report is to present an

* The research described in this Monograph was sponsored by the Air Research and Development Command, Ballistic Missile Division, U.S. Air Force, under Contract AF -04- (647) -134.

analysis of time variations in: (1) the phase

(relative to a stable phase reference) of a 9,414

Mc/s signal transmitted over this path, referred

to hereafter as single-path phase data; (2) the

phase observed at one receiving antenna

relative to that observed at an adjacent

antenna, referred to as phase difference data;

(3) atmospheric refractivity as recorded by a

microwave refractometer located at the Haleakala terminal; (4) the wind velocity at both

ends of the path, and (5) surface atmospheric

refractivity measured at 5 stations located on

or near the path.

The analysis of the phase data consists of

determining the total variance, serial correlation function, and power spectrum for samples

taken from approximately four days of almost

continuous recording. The extent to which the

total variance and power spectrum are

functions of (1) baseline length, (2) long-term

variability in atmospheric conditions (as evidenced by analysis of the meteorological data)

and (3) length of data sample is discussed.

The refractometer data from Haleakala are

analyzed in terms of variance, crossing rates,

and maximum rates. (The latter two statistics are defined in the section on refractometer

data.) The long-term variations in mean refractivity along the path are compared to the

corresponding variations in electrical length of

the path (single-path phase)

1
2. Description of Propagation Path and

Arrangement of Equipment

Figure 1 is a map showing the location of the

propagation path and the meteorological instrument shelters. Figure 2 shows an expanded

sketch of the antenna arrangement. The

antennas at Puunene were arranged along a

baseline that was approximately normal to the

propagation path at antenna B. The 9,414 Mc/s

antennas A, B, E, F, G, and H were 18-in.,

dipole-fed parabolic reflectors with half-power

beam widths of approximately 6 deg in both the

horizontal and vertical planes. The antenna

marked C-D is actually a system of two 9,414

Mc/s antennas with an effective horizontal

separation of 2.2 ft normal to the path and will

be referred to hereafter simply as the "G.E.

antenna".

A limited amount of single-path data at

1,046 Mc/s was obtained with a 10-ft dish at

the locations marked "lKMc/s" on the maps,

but this has not been analyzed for this report.

Horizontal polarization was employed throughout the experiment.

Meteorological instrument shelters were located at both path terminals and at three

intermediate points. The latter were located as near to the path as possible at altitudes of 3,000,

7,000, and 8,600 ft. Continuous recordings of

atmospheric pressure, relative humidity, and

temperature were made at each shelter.

Continuous recordings of short-term variations in refractive index, using microwave

refractometers, were made at both path

terminals. (Because of equipment troubles en- countered, the refractometer data from Puunene are considered unreliable and are not

included in this analysis.)

Figure 3 shows terrain profiles of the paths

from Haleakala to the A and H locations at

Puunene. The altitudes shown are of course

greatly exaggerated relative to the distance

scale and have been corrected for a 4/3 earth

curvature. The 6-deg beamwidths of the 9,414

Mc/s dishes at each terminal drawn on the

profile show that there was little chance of

ground reflections interferring with the measurements. At locations A, B, C, D, E, and F

there was some possibility of reflections from

foliage in the foreground. To remedy this, an

earthen wall approximately 8 ft high was

erected about 350 ft in front of these antennas

to block any such reflections.

3. Description of Data Output

The measurement techniques and circuitry

employed in this experiment are similar to those

described in other reports and hence will not be

described in detail here [Herbstreit and

Thompson, 1955; Thompson and Vetter, 1958].

In general, the radio measurements were

recorded on Esterline-Angus charts moving at

3 in. per min with occasional special recording

periods (on the order of 10 to 15 min in length)

during which the same variables were also

recorded on magnetic tape. This arrangement

permitted study of power spectral frequencies

up to 1 c/s on the charts and up to about 30 c/s

on the magnetic tapes. The phase data were of

two types. One consisted of recordings of the

variations in single-path phase. These were

made simultaneously at three of the six

antennas, A, B, E, F, G, and H. Phase difference

data were obtained from these by simply taking

the difference between the phases recorded at

two antennas. The combination of three

antennas was changed twice during the

experiment so that long baseline phase

difference data were obtained for eight baseline

lengths ranging from 42 to 4,847 ft. The other

type of data was the direct recording of phase

difference for a 2.2-ft baseline obtained from

the G.E. antenna system.

Two output circuits were used for recording

each phase variable on Esterline-Angus charts.

One contained a high-pass filter to eliminate

large, low-frequency "trends" and thereby permit amplification of the higher frequencies.

This is referred to as the "band-pass" record

because the recording meter itself limits the net

response of the circuit above about 1 c/s. The

other circuit had no high-pass filter and will be

referred to as the "low-pass" record; i.e., the

only filtering was that done by the low-pass

characteristic of the meter. Band-pass and lowpass recordings of both single-path phase and

G.E. phase difference were made simultaneously

throughout the experiment. Figure 4 shows the

frequency response characteristics of the lowpass and band-pass chart recording circuits.

Samples of the low-pass, single-path recordings,

along with the corresponding phase difference

monitor record obtained during the scaling

operation are shown in figures 5 and 6. Figure

7 shows examples of the band-pass and lowpass phase difference data obtained with the

G.E. antenna.

The refractometer data were recorded on

Esterline-Angus charts (at 3 in. per min.) at

the Haleakala site. The data output of the

airborne refractometer consisted of simultaneous low-pass Esterline-Angus and high-speed

band-pass Sanborn chart recordings. Friez

Aerovane wind measurement equipment was

operated at both path terminals and yielded a continuous chart recording (at 3 in. per min.)

of wind speed and direction. Meteorological

data were obtained at the five instrument

shelters by the use of microbarographs and

2
hygrothermographs. These instruments have a

relatively longtime constant and a correspondingly slow chart speed, so no attempt was made

to take readings from the continuous records

closer than 4 per hr.

To record cloud activity on or near the path,

a 16 mm motion picture camera was mounted

at each path terminal and aimed toward the

opposite terminal. A special timing device was

used to operate the shutter at the rate of one

exposure every 5 sec.

4. Analysis of Short-Baseline Phase

Difference Data

The principal goal of the phase data analysis

was to estimate the power spectrum1 of singlepath phase and phase difference fluctuations over as wide a power spectral frequency range

as possible and under as many conditions as

possible (e.g., different times of day, baseline

lengths, lengths of sample, etc.) The phase

difference data obtained with the 2.2-ft

baseline G.E. antenna system was analyzed first

and since this analysis differs in some important

respects from the subsequent work done on the

longer-baseline data, it will be discussed

separately.

As was mentioned earlier, the phase

variations were measured through both bandpass and low-pass filters and recorded

simultaneously on two Esterline-Angus charts.

The low-pass and band-pass recordings of the

G.E. antenna data were calibrated at 25° and

2.5°-to-5° full-scale, respectively. From the

chart samples shown in figure 7, it can be seen,

however, that the variations on the low-pass

record were small, making accurate analysis

difficult. For this reason, the main effort was

directed toward the band-pass Esterline-Angus

record. Seven periods ranging in length from

18 to 32 min were chosen, the principal criteria

used in their selection being that they were free

of discontinuities and represented different

times of the day.

The highest frequency which can properly be

represented in the sample spectrum is 1/28 c/s,

where 8 is the sampling interval. Therefore, 8 must be made sufficiently small to take into

account the highest frequencies contained within the pass-band of the recording circuit. The

values of 8 used in scaling these seven periods

are 0.341 and 0.5 sec. Since the lowest frequency

within the pass-band has a period of about 1

min, it was decided that three samples 3 to 5

min in length taken from each period would be

adequate. Table 1 contains the time, length of

sample, and total variance of each sample.

Figures 8 to 14, inclusive, show power spectra

of the G.E. antenna phase difference data for

1 The method of power spectrum analysis used is discussed in the appendix.

the seven periods along with estimates of the

reading error noise spectra.2 The ordinates are

listed in table 2. The corresponding serial

correlation functions are shown in figures 15 to

21. It will be seen that the reading error noise

seriously contaminates the spectral estimates

only at the high-frequency end in figures 8, 9,

and 10. The reduction in reading error noise in

the succeeding figures was a result of changing

from semiautomatic to manual sampling and

digitizing techniques. The frequency range of

the spectra in figures 8, 9, and 10 was extended

to lower frequencies simply by recomputing the

spectra, using every third data point. These

spectra are labeled la, 2a, 3a, etc., in the figures.

They yield some information about the power

at a frequency equal to one third of the lowest

frequency shown in the spectra labeled 1, 2, 3,

etc., but they are less reliable for two reasons. One is that the number of data points has been

reduced by a factor of three, causing increased

random fluctuation in the spectral estimates.

The other is that the high-frequency ends of

curves la, 2a, 3a, etc., are contaminated by

"aliasing", or the artificial addition to the

spectral density at these frequencies of power

which was actually present at higher

frequencies beyond the range of the analysis.

This procedure of using every third data point

was not practical after 8, had been increased to

0.5 (figs. 11 to 14), since any extension of the

spectrum to lower frequencies would have gone

out of the pass-band of the recording system.

Figure 22 shows an attempt to extend the

range of the measured spectrum by the use of

the low-pass Esterline-Angus record. Curve A,

and curves B and C are spectra obtained by

scaling the corresponding low-pass record with

8, equal to 10 sec and 1 sec, respectively. Even

ignoring curve A, which looks deceptively

horizontal because of aliasing at the highfrequency end, it still appears that the slope of

the phase difference spectrum for a 2.2-ft

baseline approaches zero as the spectral

frequency decreases over the range from 10 to

0.001 c/s. In particular, the power density in

the range 0.1 to 1.0 c/s, for which the most

information has been obtained, varies approximately as f1 - 5

, where / is the spectral frequency.

Figure 23 shows the total variance of the

G.E. phase difference (band-pass) data samples

plotted as a function of time of day. Although

the amount of data available is too limited to

draw any firm conclusions regarding diurnal

variations, it is evident that the variance was

considerably higher during the daylight hours

than during the night. It should be remembered

that these are variances of filtered data and are

therefore systematically smaller than the estimate of variance that would be obtained by

integrating the spectra, since the latter have

3 The method of estimating the reading error noise spectrum is described in the appendix.

3
been corrected for recording circuit filter

characteristics. However, there seems to be no

systematic variation in the slope of the

spectrum with time of day, so we may conclude

that the variances of these filtered data are

proportional to the variances of the data before

filtering.

5. Analysis of Long-Baseline Phase

Difference and Single-Path Phase Data

It was originally planned that the analysis of

the long-baseline phase difference and singlepath phase data would parallel the G.E. shortbaseline data analysis. That is, the minimum

data input would consist of samples chosen to

coincide in time with the G.E. data samples,

and the spectral frequency range would include

that covered in the G.E. analysis. However, the

discovery of two subtle and unanticipated

characteristics of the data resulted in a revision

of the analysis plan. As was pointed out

previously, the long-baseline phase difference

data actually consisted of pairs of simultaneous

single-path phase recordings which were scaled

by use of a semiautomatic device in the

laboratory to obtain the phase difference. This

device was designed and built at NBS by the

Data Reduction Instrumentation Section. Its

input is provided by two operators, who each

retrace a chart record with a stylus. The

angular displacement of each stylus is converted

to a d-c voltage. The difference between the two

voltages is recorded continuously on an

Esterline-Angus monitoring meter and also

sampled at a predetermined rate, digitized and

punched on IBM cards. Figures 5 and 6 show

samples of simultaneous single-path phase re- cordings along with the corresponding phase

difference monitoring chart. Provision had been

made in the design of the phase measuring

equipment to manually shift the calibration of

the recording charts a known number of

degrees to prevent the trace from going offscale. A corresponding provision was made for

changing the calibration of the scaling device

to allow for shifts in either or both charts. This

system was entirely satisfactory for studying

long-term variations in single-path phase. However, the variance of phase difference during

periods on the order of 15 min in length was so small that the error in compensating for a shift

in scale was appreciable, and showed up as a

more or less abrupt discontinuity in the

monitoring record. This difficulty limited the

number of phase difference samples having a

minimum acceptable length. It was decided that

in order to provide as complete an analysis as

possible, it should not be restricted to periods

used in the short-baseline analysis but should

include all sufficiently long periods during

which all three single-path recordings were

continuous.

4

The second difficulty which prevented direct , comparison of long and short-baseline spectra

was that one of the three phase-measuring j systems yielded single-path phase spectra that

were consistently different from those obtained

from the other two systems. Since the difference

showed up only in the frequency range above 1

c/s, it was decided that the analysis should be

restricted to the low-pass recordings. As can be

seen in the data samples in figures 5 and 6, the

scale was compressed to record large lowfrequency variations. As a consequence, although the frequency response of the low-pass

record extends to 1 c/s, the power density above | about 0.1 c/s was of the same order of

magnitude as the reading error noise, and

hence impossible to measure accurately. For

this reason, the frequency range chosen

extended from approximately 0.003 to 0.1 c/s.

It was considered desirable to maintain a uniform sample length so that a comparison of

spectra would not be confounded by possible | effects of variations in sample length. Fifteen , minutes was chosen as a reasonable compromise

between having statistically few longer samples,

or many statistically short samples. Ten to

\ thirteen such periods were selected for each of

the three combinations of baseline lengths. (In

the discussion which follows, these three major j time periods will be identified by the letter

, designations of the three antenna locations in |. use at the time at Puunene; i.e., ABH, BGH, ; BEF.)

Six or seven samples of single-path phase

record were selected from each of the periods

ABH, BGH, and BEF. In general, these samples do not coincide in time with the phase dif- j ference samples. The prime consideration in

their selection was that they be a part of a

larger sample (one-half hour or longer), so • that, although the spectra were computed for , 15-min periods, it would be possible to study i variance as a function of sample length. Tables [ 3 and 4 give the time, length of sample and \ total variance for phase difference and single- ii path samples, respectively, while tables 5 to 15, \ inclusive, list the corresponding densities computed for each sample. The serial correlation j, functions from which these spectra were computed are shown plotted in figures 24 to 34,

inclusive.3 When the individual spectra are \ plotted as curves, it is evident that no discernable characteristic (with the exception of total

variance, which will be discussed later) varied

systematically as a function of time of day, or

at least any such variation is hidden by sampling fluctuations. For this reason, the spectral

estimates for all samples at a given baseline

'

length are shown in the subsequent figures 1 simply cluster of points at each frequency.

The range of these points is determined both I

3 Not shown are serial correlation functions of samples that were

"detrended" in the way described in the appendix.
by sampling fluctuations and by more or less

long-term changes in propagation conditions

(nonstationarity) . Some measure of the relative magnitude of these two effects can be obtained by considering the distribution of spectral densities to be expected if the samples had

been taken from the same statistical population; i.e., if the time variations in phase difference constituted a stationary process. In that

case, the spectral density estimates at each

frequency would be distributed according to the

chi-squared distribution with an effective number of degrees of freedom determined by the

number (fi) of data points, the number of

frequencies (m) for which estimates are computed, and, to a very limited extent, by the slope

of the spectral density. According to the method of approximation given by Blackman and

Tukey [1958] these estimates have from 10

to 14 degrees of freedom, with an average value

of 12. In this analysis, 10 was used arbitrarily as a slightly pessimistic estimate. The solid line

in each of the figures 35 to 45 joins the median

of the ordinates at each frequency. Using these

sample medians to approximate the "true"

median, the dashed lines labeled "95 percent

stability limits" represent the bounds within

which 95 percent of all such spectral estimates

might be expected to fall if the process were

indeed stationary. It is obvious that in some

cases considerably more than 5 percent of all

the points lie outside these limits, indicating

that all of the spread cannot in these cases be

ascribed to statistical fluctuation. In particular,

it should be noted that the percentage of sample densities falling outside the stablity limits

is greater in the case of longer-baseline and

single-path data. As will be seen later, it is only

in this case that any indication of a diurnal

trend in total variance was detected. Such a trend could easily account for the increased

variance of spectral estimates. (It should also

be noted here that the slopes of the spectra become steeper with increasing baseline length,

and although the effect of very steep slopes is

to reduce the effective number of degrees of

freedom and hence increase the variance of the

spectral estimates, this effect is negligible for

the range of slopes encountered here.)

The increase in slope with increasing baseline length is best seen in figures 46, 47, and

48, where the "median" spectra are shown for

the BEF, BGH, and ABH recording periods,

respectively. Caution should be exercised in

comparing spectra obtained from different re- cording periods. The reason for this is illustrated in figure 49 which shows the median

single-path spectra for each of the three periods

and the median spectra for the 1,914-ft baseline data from the BGH and ABH periods. It can be seen that there is considerable change in

the general level of the spectra (i.e., total variance) in going from one period to another.

This long-term variability in total variance

can be seen in figure 50 in which the variance of

each sample is plotted as a function of the time

of day. On November 5 and 6, the ABH

recording period, there seemed to be a clear-cut

diurnal pattern, with higher variances during

the day than during the night. However this

pattern did not persist during the remainder of

the recording periods and it must be concluded

that if there is a tendency toward a diurnal

variance cycle, it can apparently be obliterated

by other longer-term changes in the

propagation mechanism. Evidence of such longterm changes can be seen in the single-path

phase variance which is noticeably larger

during November 8 and 9 (the BEF period)

than during the earlier periods.

Figures 51 and 52 show the single-path phase

variance versus time compared to plots versus

time of (1) long-term changes in mean singlepath phase (i.e., changes in electrical path

length) and (2) changes in a weighted4 mean

of the surface refractivity values measured at

the meteorological stations along the path. It

will be noted that the increased phase variance

on November 8 and 9 coincided with a marked

decrease in electrical path length and mean

surface refractivity. Also shown in this figure are the wind velocities at the path terminals

read from the continuous wind records. It

should be pointed out that only during the

November 8 and 9 period was the wind direction

the same (roughly normal to the path) at both

terminals with speeds as high as 15 mph.

Some examples of the time sequence pictures

of cloud activity along the path are shown in

figures 64 to 74 in the appendix. In general,

these were chosen to coincide in time as nearly

as possible with the data samples analyzed, and

the appropriate data sample numbers are listed

on the pictures. It is interesting to note that the

marked diurnal pattern of November 5 and 6

coincides with the period of widest variation in

cloudiness along the path. Only during these

two afternoons was the Haleakala site

completely enshrouded in clouds, while the

intervening night was apparently clear.

Figure 53 shows the total variance of the

phase variation samples plotted as a function of

baseline length. This includes data taken from

all three recording periods and hence the true

dependence of phase variance on baseline length

may be obscured by the long-term changes in

variance discussed above. For example, the

variances of the 1,914-ft data are in general

higher for the BGH period than for the ABH

period, and the fact that the single-path

variances from the BEF period, are in general

higher than those of the other two periods leads

4 The weighting factors are proportional to the difference in altitude of adjacent meteorological stations so that each value of refractivity was weighted in proportion to the percentage of the path over which it might be expected to apply.

5
one to suspect that the 67 and 109-ft phase

difference variances (also from the BEF

period) may also be relatively high. However,

comparisons of data taken within the same

recording period are valid because the samples

chosen were recorded simultaneously.

6. Analysis of Refractometer Data

The analysis of the microwave refractometer

recordings made at the Haleakala path terminal

consisted of determining the variance, crossing

rate and maxima rate of sixteen 15-min

samples selected from the 5 days of recording.

Figure 54 summarizes the results of this

analysis. Crossing rate is defined as the average

number of times per min that the refractivity

crossed its 15-min mean value in the positive

direction. The maxima rate is the average

number of times per minute that the trace

passes through a maximum (i.e., with first

derivative equal to zero, second derivative

negative). There is some tendency toward

higher values of all three of these statistics

during the daylight hours than during the

night, but aside from this there is no obvious

correlation between, for example, the variances

of phase and refractivity variations. This of course is not surprising in view of the fact that

the latter reflect changes in the atmosphere at

only one point of the path; while the former are determined by conditions over the entire path.

7. Appendix—Notes on the Data

Analysis

7.1. Serial Correlation and Power Spectrum

Computation

The power spectrum, or more precisely, the

power spectral density, can be defined as the

Fourier cosine transform of the autocorrelation

function of a time series. This definition is

consistent with the method used in obtaining

the spectra shown in this report. However, it

might be more satisfactory from the

engineering standpoint to look at the power

spectrum in the following way. Imagine that a

d-c voltage proportional to the time-varying

quantity being studied has been passed through

a narrow-band filter with center frequency /,

and that the variance (mean squared deviations

from the mean) of the resulting filtered data

has been measured. The ratio of this variance

to the bandwidth of the filter is a measure of

the spectral density, or variance per unit

bandwidth, at the frequency /. If this is done

for several values of /, the graph of these

spectral densities plotted versus frequency is an

estimate of the power spectrum of the variable.

The method of power spectrum estimation

used throughout this report was developed by

Blackman and Tukey [1958]. The input to the

process is a time series consisting of n

instantaneous values viU) read from a continuous recording at the rate of one reading

every S sec. The computation consists of first

determining the autocovariance function given

by:

n—k

where

and

i—1

(In most of the work reported here m=30.)

The serial correlation function, which estimates the autocorrelation function of the process, is then given by

r = k8(k = 0, 1, . . ., m),

n

r(r) r (or

The next step is to compute the finite cosine

series transform

TO- U* ( 2^8 J = 8 [R(0 > +22 R WCOSk=l

irkh

TO + R(m8)cos 7T h],

h=0, 1, 2, . . ., m.

h

U/> (~2^f) is itself a rough estimate of the

power density at the frequency c/s. However, it is as though the imaginary narrow-band

filter mentioned above had quite appreciable

sidebands so that the estimate is influenced by

variations at frequencies far removed from

2^j-. To get around this difficulty, a "refined"

estimate of power density, W(/), is computed

by the following equations for m+ 1 frequency

bands having center frequencies / =

-2mT^~

0, 1, 2...ra):

h

W(0)=1.08 Uo + 0.92 Ui

W( 2ms > =0- 46 U*-i + 1.08 Uft + 0.46 U

h = l, 2, mh W(^-) =0.92 U^x+ 1.08 Um.

W(/) is the quantity plotted in the spectrum

graphs. W(0) is not plotted because it should

properly be shown at zero frequency and also

because any estimate of the power near zero frequency based on a short data sample is of

questionable practical value.

6
7.2. Estimating the Power Spectrum of Reading Error Noise

When discrete digital values of a variable are read from a continuous record, their variance is

the sum of (1) the variance contributed by the

continuous record and (2) the variance of

random reading and rounding errors. In

interpreting sample power spectra, it is

important that some quantitative idea of the

relative magnitude of these two variances be

obtained. In this discussion, random variations

introduced by reading error and those

introduced by "rounding-off" the digitized data

to, for example, three figures, will be lumped

together and called simply reading error noise.

If the errors in reading successive points are independent, the power spectrum of the reading

error noise will be a "white noise" spectrum;

i.e., the spectral density will be essentially

constant over the range of frequencies observed.

Also, assuming that the reading error is

independent of the variable being read, the

observed spectral density at a given frequency

will be the sum of the "true" density and the

reading error noise density. It is evident from

this that, particularly if the "true" spectrum is

very steep, the power densities at some

frequencies may be of the same order of

magnitude as the reading error noise and hence

be obscured. An admittedly rough estimate of

the reading error noise spectrum was obtained

in the following way. Each chart record was

scaled twice. Then the spectrum of the n

differences between readings obtained in the

two trials was computed. If the errors made in

the two trials are independent, the total

variance of the differences will be twice the

variance of errors in either trial. Hence, the

ordinates of the difference spectrum are divided

by two to obtain the reading error noise

spectrum. Figures 55 to 58, inclusive, show

some examples of noise spectra compared to the

corresponding data spectra. It can be seen that

there is probably some contamination of the

data spectra by noise at the high-frequency end.

It was pointed out previously that 0.1 c/s was

chosen as the upper frequency limit for

spectrum analysis of the low-pass recordings

because reading error noise would dominate the

spectrum beyond that point. It should also be

noted that the data spectra for the 67-ft phase

difference are comparable in general level with

the noise spectra. This is not surprising,

however, in view of the relatively small variance

of these data (as seen in the data sample in fig.

5). For this reason, no attempt was made to

analyze phase differences with the 42-ft

baseline (E-F) antenna combination. It should

be borne in mind that these estimates tend to be

pessimistic; i.e., on the average the noise

spectral densities would probably be somewhat

lower than those shown. This is because

additional error is introduced by the small but

practically unavoidable displacement on the

time scale of the second set of readings relative

to the first.

7.3. Eliminations of Trends

As used here, the term "trend" refers to

variations occuring at spectral frequencies that are low compared to the reciprocal of the length

of sample (i.e., the fundamental frequency).

Whenever a trend contributes a large portion of

the total variance, the sample spectrum will

contain gross errors. This is because the sum of

the spectral densities (including W(0) ) multiplied by their respective bandwidths must

equal the total variance, and variance that

should properly be assigned to the "trend

frequencies" is added to the variance at the

higher frequencies.

In selecting the data samples, an effort was

made to avoid trends by picking periods where

the values of the variable at the endpoints were

similar and where visual inspection indicated

no obvious trends. This admittedly biases the

data but as will be pointed out later, this bias is

apparently very small, and in any case was

considered unavoidable.

Trends were most difficult to avoid in the

single-path and long-baseline phase difference

data and the need for some sort of filtering or "detrending" was apparent. The trend removal

method used consisted of computing the

"rough" spectrum U'h (f) of the deviations of

the individual data points from a running

average and then applying a correction to allow

for the frequency response of this "digital

filter". If c is the number of points averaged

and S is the sampling interval in seconds, then it

can be shown that the correction factor applied

to U'h(f) to obtain the "rough" detrended

spectrum Uh (f ) is given by

u»</)=uw>[i-(fS)TThe conversion of (/) to the refined estimate

W(/) is the same as was described previously.

This process was found to be satisfactory for

obtaining spectral estimates for values of c 8 f

above 1. Below this, the correction factor

changes rapidly with frequency and it was

found in repeated experiments that using the

factor for the midpoint frequency of the band

covered by Ui was not satisfactory. For this

reason, no values of W (t^) or W(^s) are

given for the detrended spectra.

In the tables of spectral densities it will be

noted that several sample spectra have

alternating positive and negative densities. This

is apparently caused by undetected trends. It

7
was found that detrending such samples

changed the negative values to positive but did

not change the other values appreciably (the

latter are, of course, the only ones shown in the

graphs)

7.4. Effect of Sample Length on Total Vari- ances and Power Spectra

In general, the long-baseline and single-path

phase variation samples analyzed were approximately 15 min long. It was mentioned

previously that the sample length was held as nearly constant as possible to avoid confusing

sample length dependence with other effects. An

investigation of this dependence with regard to

the total variance and power spectrum was

made, using those samples taken from longer

periods of continuous recording. Figure 59

shows some examples of the dependence of

single-path and phase difference variances on

sample length. The ordinate is the ratio of the

average variance of a longer sample to the

average variance of the 15-min periods

contained within that sample. The largest

increase in variance apparently occurs between

15 and 30 min with very little increase between

60 and 120 min. In none of the cases did the

variances increase by as much as a factor of 3

over the average 15-min value. Figures 60

through 63 show the power spectra of longer

samples compared to the spectra of the

component shorter periods. These indicate that

within the range of frequencies covered in this

analysis, the slope and absolute level of the

spectra remain essentially constant as the

length of sample is increased from 15 to 60 or 120 min. Apparently, most of the increase in

total variance with sample length shows up as

an increase in W(0) (not plotted) and W(^)

(plotted at 0.00306 c/s). Unfortunately, most

of the short samples shown here were detrended

and hence do not show the first two points.

However, this point is illustrated in figures 60

and 62. The total variance of the 1-hr sample

in figure 62 is 7,003 (deg) 2 and the total

variance of the one 15-min sample that was not

detrended is 1,239 (deg) 2

. Most of this

difference in variance can be accounted for in

the difference between the power densities at

0.00306 c/s. Similarly, the total variances listed

by the corresponding spectra in figure 60

indicate that only the first point in each is

clearly a function of total variance.

It should be emphasized that the dependence

of variance on sample length shown here is

necessarily biased, since it is based on periods

when the variance was small enough to permit

relatively long recordings not interrupted by

scale shifts or by the trace going off-scale. As a

consequence the variances for the long periods

j are smaller than they would have been if they

could have been selected at random from any I part of the data.

1

The experiment discussed in this report was

performed by the Radio Propagation Engineering Division, K. A. Norton, Chief. Key

personnel and their respective areas of

responsibility are as follows : J. W. Herbstreit,

general supervision of the project; K. O.

Hornberg, project manager; C. F. Peterson, ! transmitting equipment; A. F. Barghausen, re- ceiving equipment; W. E. Johnson and P. I. ! Wells, recording equipment; M. C. Thompson, | Jr., and M. J. Vetter, microwave refractometers

and design of 9,414 Mc/s equipment; A. W.

Kirkpatrick, meteorological measurements; H.

B. Janes, data analysis and preparation of this

report. E. L. Crow and M. M. Siddiqui

contributed many valuable suggestions concern- ing the statistical analysis of the data.

References

Blackman, R. B., and J. W. Tukey, The measurement

of power spectra (Dover Publications, Inc., New

York, N. Y., 1959).

Herbstreit, J. W., and M. C. Thompson, Measurements

of the phase of radio waves received over transmission paths with electrical lengths varying as a result

of atmospheric turbulence, Proc. IRE 43, No. 10,

1391-1401 (Oct. 1955).

Thompson, M. C, and M. J. Vetter, Single path phase 1 measuring system for three-centimeter radio waves,

Rev. Sci. Instr. 29, 148-150 (1958).

i

Table 1. Information relative to short-baseline phase

difference data

Baseline Length: 2.2 feet

Date and Length of Sample time * sample Variance

Nov. 5 , 1956 min dec/ 2

1 1618 3.41 0.1349

2 1625 3.41 .1634 3 1632 3.41 .1083

4 1728 3.41 .0359

5 1735 3.41 .0525 6 1742 3.41 .0302 Nov. 6 , 1956

7 0443 3.41 .0265 8 0450 3.41 .0421 9 0459 3.41 .0346 Nov. 7, 1956

10 0127 5.10 .0093

11 0135 5.15 .0137 12 0140 5.09 .0156 Nov. 8, 1956

13 0713 5.18 .1351

14 0721 5.17 .0975 15 0728 5.12 .0868 Nov. 9 ; 1956

16 0848 5.19 .0964

17 0856 5.16 .0581 18 0914 5.16 .1356

19 1502 5.17 .2896 20 1509 5.17 .1894

21 1516 5.17 .1625

* Time shown is for midpoint of sample.

f)
Table 2. Power spectral densities of short-baseline phase difference variations

Baseline length: 2.2 feet

Units: (deg.) 2/c/s

Sample

Frequency

1 2 3 4 5 6 7 8 9

c/s 0.0489 1.093( 0) 1.196( 0) 8.70H-1) 3.180(-1) A a OA / i \ O TOO / 1

\

3.728(—1; 2.679(-l) 2.961(-1) 2.884(-l)

.0978 4.434(-l) or*?/ 1 \ 6.857(-l) 3.619 2.004 2.389 1.528 1.154 2.289 1.535

.147 3.062 4.808 2.616 1.345 1.513 n O.J A 1 ON 9. 344 (-2) 8. 399 (-2) 1.748 8. 395 (-2) .196 3.221 2.773 2.318 6. 696 (-2) 1.121 7.076 6.487 8.738(-2) 6.431

.244 2.505 2.379 2.407 5.479 9.896(-2) 6.721 4.158 5.260 6.592

.293 2.015 1.742 1.753 4.167 6.637 4.637 3.648 4.914 4.983

.342 1.760 1.436 1.038 3.426 5.621 2.217 2.869 3.933 4.045

.391 1.369 1.514 6. 763 (-2) 3.634 4.938 1.603 2.039 4.156 3.697

.440 1.022 1.505 6.686 2.971 3.345 1.159 1.482 3.494 2.755

.489 8.482(-2) 1.121 6.932 1.729 2.532 1.226 1.048 2.640 2.153

.538 6.605 8. 469 (-2) 6.840 1.417 2.683 1.185 1.087 2.029 2.159

.587 4.354 6.628 5.878 1.566 2.456 8.847(-3) 1.389 1.678 2.290

.636 4.235 7.420 5.041 1.490 2.681 8.074 1.589 1.567 1.944

.684 5.775 7.376 3.287 1.081 2.762 7.635 1.121 1.744 1.461

.733 5.620 6.838 2.782 8. 071 (-3) 1.834 6.309 5. 841 (-3) 2.055 1.090

.782 3.949 5.969 3.198 6.791 1.340 6.058 5. Ill 1.550 9. 101 (-3) .831 3.559 5.928 3.141 8.064 1.141 4.490 6.572 8.366(-3) 8.676

.880 3.893 6.847 3.485 8. 156 1.096 3.934 6. 689 6.688 7.407

.929 4.451 6.890 3.355 7.176 1.084 5.061 5.368 7.965 7.046

.978 4.556 5.547 2.289 6.834 9.342(-3) 5.574 4.438 6.212 6.555

1.03 3.433 3.874 2.751 6.062 8.085 4.090 4.460 5. 124 5.756

1.08 3.145 3.287 3.498 5.819 9.269 3.044 3.352 6.774 6.417

1.12 3.986 4.040 3.657 5.284 1.00b (-2) 3.019 3.404 7.542 6.605

1.17 3.182 5.375 2.623 4.274 8.510(-3) 3.957 3.675 7.668 6.189

1.22 2.606 5.661 1.863 3.755 7.479 3.755 3.316 7.275 7.615

1.27 2.997 4.031 1.756 3.419 8.761 3.178 4.016 5.665 7.561

1.32 3.692 4.758 2.516 3.897 8.858 3.599 4.240 5.714 5.321

1.37 3.455 6.076 3.345 4.431 8.873 4.231 3.514 5.357 4.339

1.42 3.642 4.591 4.441 4.487 5.215 5.183 3.718 5.901 5.177

1.47 4.242 3.868 5.086 4.307 4.826 6.246 4.201 6.724 7.161

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 2. Power spectral densities of short-baseline phase difference variations—Continued

Baseline length: 2.2 feet

Units: (deg.) 2/c/s

Frequency

Sample

10 11 12 13 14 wmsm 16 17 18 19 20 21

c/s 0.0333

.0667

.100

.133 .167

4

152

2

902(-l) 256 337 (-2) 854

103

6.062(-l) 1.975

8.095(-2) 3.260

2.165

4.124(-1) 1.462

8. 494 (-2) 6.957 5.083

3.274( 0) 1.267

6.663(-l) 4.383 3.214

3.285C 0) 9.964(-l) 5.623

2.649

1.953

2.406( 0) 6.429(-l) 3.820

3.155

2.667

2.064( 0) 5.954(-l) 3.749 3.062

2.044

1.414( 0) 5.228(-l) 3.058

1.915 1.472

2.711( 0) 1.341

7.586(-l) 5.904 4.862

4.498( 0) 2.197

1.174

8.865C-1) 1.196( 0)

3.220( 0) 1.533

1.014

7.053(-l) 5.389

3.814( 0) 1.808

1.010

6.529(-l) 5.036

.200 .233

.267

.300 .333

1

17

7

6

655

130

632(-3)

151 954

1.864

1.390 1.296

9.022(-3) 5.343

4.711 4.156

2.709 1.530

8. 966 (-3)

3.248

3.714

2.788

1.680

1.055

2.116

1.617

1.027

9. 815 (-2) 7.945

1.768

1.471 1.504

1.008

7. 569 (-2)

1.369 1.338

1.591 1.409 1.166

1.720 1.284

8. 789 (-2) 7.028

5.303

2.897 2.500

2.189

1.894

1.516

1.117

8.058(-l) 4.921 3.247

2.376

4.334

3.106

3.148 3.422

2.401

3.559 2.898

2.269

1.364

1.158

.367

.400

.433

.467 .500

54

3

1

1

503

001 090

681 849

6.991 7.562

5.843

4.641 3.392

7.890

6.969

7.502

6.641 5.199

9.843(-2) 8.379

6.227

5.834

5.698

5.926

6.354

6.090

5.000 3.416

6.638

4.777

3.948 3.479

3.245

8. 906 (-2) 6.800

5.981

5.061 3.715

4.359 3.683

4.048

4.189

3.244

1.133

8. 415 (-2) 6.530

5.796 5.629

2.276

2.189

2.048

2.200

1.784

1.702

1.482

1.761 1.604

9. 943 (-2)

1.163 8.282(-2) 8.418

1.027(-1) 9.942(-2)

.533

.567 .600 .633

.667

2

2

1

1

1

576 498

805 800

651

3.929 4.603

4.904 4.628

4.284

5.035 5.408 3.344

2.372

2.577

4.411

5.370

6.311 5.139 3.765

2.880 3.274

3.125

2.495 2.453

2.864 2.438

2.545 3.881

4.602

5.255

7.275

8.441 7.185

4.705

2.547

1.924

1.435

1.519 2.147

5.264 4.822

3.038

2.331 2.443

1.292

8. 833 (-2) 5.793 4.719

5.438

6.574 6.440

7.423 5.863

5.914

7.339

5.227 3.534

3.136 3.332

.700

.733

.767

.800 .833

11

19

6

258 002

181 540(-4) 536

5.624

7.585 7.872

5.349

3.921

2.342

1.801 1.801 1.653

1.376

3.733

3.198

2.679 3.131

2.970

2.297

1.852

1.907 2.763 3.285

4.155

3.077

3.103 3.357

3.268

3.796 3.052

3.419

6.167

7.155

1.975 1.182

8.360(-3) 9.916

9.191

3.453

3.399

2.555

2.179

1.924

6.257

6.619

6.010

5.869

5.478

5.558 3.324

3.027

3.647

4.115

3.352

3.181 3.727

3.261

3.616

.867

.900 .933

.967 1.00

78

6

7

1

946

610

264

979

072(-3)

5.404 4.562

2.651

1.750

1.171

1.373

1.421 1.099

1.586 2.234

3.522

3.468

3.582

3.438

3.060

2.849

2.789 3.035

2.273

1.491

2.669 2.006

2.006

1.535

1.181

6.205

6.595

5.221 3.473

3.085

1.055 (-2) 1.171

8. 885 (-3) 8.781 9.230

1.639 1.768

1.499

1.914 2.182

5.346

8.021

7.807 6.227

5.988

3.205

2.799 3.870

5.636

7.051

3.383

2.167

2.023

2.823 3.153

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

9
Table 3. Information relative to long-baseline phase difference data

.Length .Lengtn Baseline Date and OI Baseline Date and of Sample length time * sample

_ _ . V ariance CI 1 bample length time * sample Variance Nov. 8, 1956 771271 aeg* /< Nov. 7 , 1956 min deg 1 104 1400 16.6 111.607 87 1520 14.5 3457.81

105 1530 1 A O 14.

0

56 . 220 OO 1845 15.8 2149.32

106 1715 17 K 1 / . O

Oft KQ7 yu . oo/ OQoy 1925 17.1 10629 .

8

107 /37/T5 "ITS 2000 1 Q O io.y 77.934 Oft yu 1 ,914(B-H) 2150 19.4 1358.56

108 2025 1 K A 10 . 4

1nz.1 O lOK iyo myi 2240 18.9 11079.9

109 2050 1ft A. lo.4 A"\ ftOQ 4i . oyo OOyz 2330 13.3 2661.22

110 2330 1 Q ft 10.0 47.909 Nov. 8, 1956 Nov. 9, 1956 noyo 0310 16.8 1371.56

111 0100 Oft 1 ZU. 1

7ft Oft ft /U.zOO 94

1

0340 14.5 893.528

112 0125 1ft o ID . Z

OI /10ft yi . 4yu OKyo 1,914(B-H) 0620 20.9 3961 . 77 113 ft7/T3 T?\ 0140 Oft ft ZU. O

1 7ft Od7 1/U. 04/ Oft yo i 0730 17.7 2674.64

114 0300 1 Q Q lo.o 90.413 Nov. 5 , 1956

115 1515 lo.O lOft AClQ izo, 4yo AQ40 1325 18.2 14248.0

110 f 1740 17 A 1/ .4 OQ ftOO yo . uzy 4Q4y 1650 16.8 4136.34 Nov. 8, 1956 50 1745 16.7 1856.60

117 1400 1ft 7 ID. / Oftft ftlQ ZUO. OlO 01 fl,914(B-H) 2000 16.9 737.643

118 1530 IKK 10.0 111 . 858 52 2015 13.7 676.319

119 1715 1 ft 7 iy . / 1Q1 7ft1 lol. /Dl KQOO 2100 14.4 446.079

1 Oft 1ZU 1ftft/"B "ITS 2000 OAZU. 11 1S7 Oftft 10/ . you K404 2130 19.2 261.034

121 2025 IKK 10.

0

1QK fiftl iyo. oyi Nov. 6, 1956 122 2050 1Q Q iy .o Iftft ftdQ 1UU. 040 00 0320 14.5 319.419

123 2330 TO Q iy .0 lft7 ftftl lU/.UOl 56 0340 18.5 653.355 Nov. 9, 1956 57 0445 18.2 1394.56

124 0100 IKK 10.0 1 ftK 1 AK 100. 140 KO00 1,914(B-H) 0505 16.4 535.305

125 0125 17 Q 1/ . O IKK OftQ 100. zoo KOoy 0550 16.4 636.727

126 109(Jt>-± ; 0140 1ft O 10, A 409 441 4yZ. 441 ou 0740 18.2 1032.71

127 0300 i/.y 1 Oft ft70 lOU.O/O Nov. 5 , 1956

128 1515 Oft o zu. z OQ7 ftKQ ZO / . U0O zz 1325 17.3 19515.7

129 1740 1ft 10.44 1AQ QOI i4y . yyi zo 1650 18.0 8964.13 Nov. 7, 1956 24 1745 16.4 3621.69

67 1520 1 K 1 10 .

QK7ft KO OOtO. OZ OKZO 3,003(A-B) 2000 17.1 1530 . 17 68 1845 1Q K iy . o lOlO 17 1Z1Z. 1/ Oft zo 2015 15.0 1296.21 69 1925 17ft 1/ . D

O^ OQ Q4 Z4y0 . 04 27 2100 14.2 1925.22

70 <70o/n tin 73o(U-JbL; 2150 1 Q K 10.

0

A1 K K7fi 410. O/O OOZO 2130 18.5 739.131

71 2240 23 4 9K4Q Z04O Kfi

. OD Nov. 6 , 1956 72 2330 1 Q Q lo.o 1401.91 z9 0320 16.0 237.649 Nov. 8, 1956 30 0340 17.5 215.370

73

1 0310 17 Q i/ . y 004 yz4. ft Kfi ooo 9iol 0445 18.4 12055.0

74 0340 1ft A ID. *

Iftft Qft1 ioy .oDi QOOZ 3,003(A-B) 0505 18.7 1550.35 75 73o(U-±iJ 1 0620 1ft A ID.

IfiKO Qft iooy . ou QQOO 0550 16.4 2102.60

76 1 0730 10.4 Ifi 4 fi7fi 0/0.0/0 Q7K. 04Q4 1 0740 21.0 4038. 13 Nov. 7, 1956 Nov. 5, 1956

77 1520 lo.o 9174 Z1/4.UUon QKOO 1325 17.8 9986.66

78 1845 1ft ft 10. u

1 Oftft 07 1 - U•

' . z / Qft OO 1650 15.2 9300.79

79 1925 17.1 KA KO OO o4oy . yz 37 1745 16.5 3290.69

80 1 ,181(Jo-Lr; 2150 1 ft K 10. O

Oft1 HKK yui . ooo Qft M,847(A-H) 2000 17.8 1649.19

81 2240 1ft A 10.

KOK1 KK OZOl . OO QOoy 2015 15.3 2006.26 82 2330 12 4 14ft.fi HQ 4U40 2100 14.7 2115.66 Nov. 8, 1956 4141 2130 15.2 916.589 83

84

0310 1Qiy 1

. i

QfiK OQQ OOO . zoo Nov. 6, 1956 0340 16.7 456.800 42 [ 0320 14.6 83.626 85

f 1,181 (B-G) 0620 18.4 979.755 43 0340 21.3 1432.45 86 0730 16.4 1245.73 44 4,847(A-H) 0445 20.8 1140.86

45 0505 16.7 4172.50 46 0550 20.2 8351.24 47 0740 20.6 4234.91

* Time shown is for midpoint of sample.

Table 4. Information relative to single-path phase data

Length

Recording Date and of Sample period time * sample Variance

Nov. 8 , 1956 min deg2

130 1400 16.9 22677.4

131 1530 17.2 7726.53

132 \ BEF 1715 14.7 8168.50

133 2000 18.1 4922.38

134 2250 19.2 7458.60 Nov. 9, 1956 135 / 0120 22.0 21243.0

136 } BEF \ 1710 16.9 3050.60 Nov. 7, 1956 97 1600 19.1 2723.70

98 BGH 1840 21.8 9043.15

99 2025 22.2 7067.35 Nov. 8, 1956 100 0000 18.5 3771.88

101 0255 16.6 1304.76

102 BOH

1 0620 16.2 9658.20

103 0820 17.3 5000.85 Nov. 5 , 1956

61 ABH 1305 19.7 12185.8 Nov. 6, 1956 62 ABH 0340 15.0 703.075 Nov. 5 , 1956 63 / 1625 16.8 5252.00

64

j

ABH

\ 1945 20.3 1268.44 Nov. 6 , 1956 65 / 0000 20.1 2382.58

66

|

ABH

\ 0720 16.4 8072.40

* Time shown is for midpoint of sample.
Table 5. Power spectral densities of long-baseline phase difference variations

Baseline length: 67 feet (B-E)

Units: (deg.) 2/c/s

Sample

r re- quency 104 105 106 107 108 109 110 111 112 113 114 115 116

0.00306

00611

!00917 .0122

.0153

7.677(3) 6.416

3l 078

1.631 1.415

3.994(3) 2.685

l!025

5.661(2) 4.105

8.049(3) 1.346

l!028

9.505(2)

1.157(3)

6.302(3) 4.014

2.246

1.475

8.697(2)

8.665(3) 4 698

2.157

1.490

1.119

1.575(3)

1 595 1.924

1.177

5.353(2)

2.887(3)

1 354 1^032

6.422(2) 6.429

6.151(3) 2.674

l!l69

1.590 1.250

5.607(3) 3.155

2^111

1.693 1.352

1.644(4) 6 486f3> 3.167

2.862

1.869

4.234(3)

4 098 3^307

2.274

1.601

152

1

1

225(4) 123(3) 138 083

040

9.830(3) 5.164

l!791 9.514(2)

1.267(3)

.0183 0214

!0244

.0275

.0306

1.525

1.153

b. 851 (2) 4.051 5.152

4.732

8 654 8^785

6.740 3.130

1.457

0 . ooy \£>) 2.786

3.011

2.575

6.057

8 616

7] 360

3.647

2.213

1.233

1 621 l!406

1.258

8.969(2)

4.685

5 101 4^280

2.544

3.796

8.326

8 068

5^275 4.739

5.566

6.222(2)

4 242 3!904 4.112

3.298

6.853(2)

7 841 8^515

9.225

1.328(3)

1.310

1 020

7i592(2) 8.170

1.053(3)

9.746(2)

1 oisni

8.585(2) 7.975 8.348

1

17

59

461 529

207(2) 017

641

1.062

5 923(21 2.205 3.152

4.399

.0336 0367

!0397

.0428

.0458

4.144

3 639

6^495

8.081 9.722

1.593

1 723 L456

1.608

1.859

1.821

1 807

2. 673 3.533

5.068

1.774

1 648 U629

2.464

2.600

6.940

4 417

6! 060 5.219

4.308

4.512

4 042

2^090 1.754

2.139

4.933

2 820

2'. 576 3.343

1.888

3.981

4.051 3^478

3.349

3.612

9.355(2) 3.094

2^515

2.186

2.091

9.142(2) 6.825 5^638

4.380

2.268

9.068 6.029

5! 035

3.441 2.905

72

2

33

474

548 952

593

219

3.074

2.498

2 [775 3.339

2.880

.0489 0519

.'0550 .0581

.0611

7.272

4 800 4^336

3.312

4.342

2.959

4 350

4^157

2.683

2.134

4.329

2 959 3i851

5.446

4.919

2.015

2 192 2^983

2.613

2.221

6.817

6 619

i. 008 2.143

2.217

2.973

2 745 2^275

2.213

2.160

1.253

1 697

1^857 1.886

1.455

3.110

1 836

l'.381 1.218

1.575

2.142

3.879

5!312

3.808

1.814

2.376 4.048

5!611 5.885 5.235

4.117 3.469

3] 231 3.779

4.215

2

22

2

4

584

626

345

279 352

2.255

2. 170 1^435 1.238

1.642

.0642

.0672 .0703

.0733

.0764

5.036

2.800

1.918 3.394

5.004

3.304

3.167

2.310 2.664 3.024

3.815

2.293

2. 100 2.126

1.741

2.665 1.684

2.161 3.559

2.931

2.040

1.962

2.703 2.483

2.104

1.573 1.032

1.808 1.788

1.035

9.128(1)

1.918(2) 2.417 1.466

6.661(1)

1.198 1.042

1.087 1.602

1.611

2.343 2.673 3.668

2.517

2.977

3.660

2.531 3.774

4.240 4.834

2.526

1.468

2.935 3.483

2.747

6

52

33

058

159

971 214

162

1.351 1.005

6.664

5.466

.0795 .0825

.0856 .0886 .0917

4.048 4.205 4.429

3.551 3.425

3.418

2.864

1.867

1.256

7.627(1)

1.802

2.547 2.312

2.040

2.970

1.799

1.518 1.886 2.062

2.658

2.027

2.181

2.901 3.042

2.569

6.330(1) 8.066

1.051(2) 1.037 1.044

7.304

1.344(2) 1.451 1.727 1.997

1.849

2.510 2.028

1.714 2.029

6.752

6.126

3.655

3.790 3.500

4.210

2.320 3.796

4.979 4.226

2.371 2.145

2.003

1.415

9.773(1)

2

1

11

1

611 595 356

617 399

3.357 4.369

5.572 8.746

1.141(2)

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 6. Power spectral densities of long-baseline phase difference variations

Baseline length: 109 feet (B-F)

Units: (deg.) 2/c/s

Sample

117 118 119 120 121 122 123 124 125 126 127 128 129

1 490(4) 8.607(3) 9 080(3) 1 560(4) 5 929(3) 4 706(3) 6.419(3) 1 655(4) 6 555(3) 5 606(4) 9 328(3) 2.134(4) 1 440(4)

1 042 4.243 2 893 6 272(3) 7 563 3 476 4.360 7 766(3) 5 098 1 630 1 039(4) 1.154 5 825(3) 5 880(3) 2.251 2 211 2 527 6 174 3 643 2.904 3 180 4 297 5 680(3) 6 391(3) 4.975(3) 3 151

5 302 1.178 1 504 3 135 4 435 2 873 1.438 4 393 3 429 6 119 3 888 2.944 2 342

3 682 7.896(2) 1 408 2 549 3 187 1 588 1.385 3 293 2 598 4 721 3 706 2.666 1 405

2 374 1.129(3) 1 576 2 298 3 865 9 582(2) 1.462 2 024 1 652 3 867 2 755 2.715 9 341(2)

1 548 1.558 1 216 2 787 3 838 1 102(3) 1.309 1 675 1 557 2 815 2 on 2.591 1 033(3)

1 358 1.728 6 780(2) 2 376 3 302 1 262 9.063(2) 8 826(2) 2 210 2 189 2 261 1.924 1 116

7 130(2) 1.323 9 864 1 750 3 211 1 195 7.320 8 172 2 649 2 017 2 392 1.207 1 095

5 557 7.222(2) 7 299 1 411 2 687 1 293 8.346 8 445 2 755 2 073 1 908 1.988 8 084(2)

8 082 7.104 6 488 1 140 1 847 9 915(2) 1.191(3) 1 016(3) 2 161 2 112 1 473 1.834 6 431

8 994 6.251 8 569 8 551(2) 1 041 7 884 9.370(2) 8 705(2) 1 215 1 554 9 983(2) 1.098 6 415

1 582(3) 4.892 1 053(3) 7 626 8 743(2) 5 043 8.374 9 807 9 063(2) 9 176(2) 8 799 1.070 3 229

1 730 6.184 1 201 4 900 6 449 3 198 9.015 1 218(3) 4 633 8 129 5 705 8.338(2) 1 813

1 484 7.140 1 142 5 133 1 091(3) 4 635 4.520 6 744(2) 4 080 9 161 3 415 6.312 2 677

9 978(2) 4.391 8 537(2) 7 130 1 463 8 059 2.682 2 307 3 454 1 059(3) 5 677 4.865 4 179 4 782 2.563 6 255 6 113 1 448 5 589 2.341 2 051 8 217 1 057 6 790 5.275 5 950

5 494 2.405 5 154 4 192 1 087 3 404 2.841 1 903 1 268(3) 1 167 5 115 4.701 4 723

6 308 2.142 5 045 3 500 5 781(2) 4 270 3.673 4 114 9 966(2) 1 044 4 306 3.523 4 307

7 619 2.081 6 175 4 135 7 207 4 807 2.840 7 416 4 809 8 505(2) 5 122 3.529 2 860

8 417 3.473 5 846 5 852 8 916 3 330 2.657 5 209 6 588 6 395 4 376 4.000 1 544

6 440 4.194 4 932 6 435 8 388 1 755 3.000 3 703 6 009 6 973 2 726 4.565 1 513

5 266 4.278 5 969 1 036(3) 7 319 2 319 3.573 3 296 5 731 1 466(3) 2 423 4.212 1 806

5 504 3.397 6 271 1 058 7 979 2 770 5.277 2 434 4 610 1 190 3 083 3.826 2 399

5 647 3.327 5 723 6 108(2) 7 073 1 545 5.477 2 487 4 362 5 895(2) 4 535 4.103 1 706

4 535 2.743 5 469 3 855 5 604 1 126 3.144 2 449 4 126 4 119 5 347 3.834 1 442

3 286 2.416 4 146 3 069 6 126 2 254 1.507 2 160 4 155 3 303 3 668 2.757 1 060

5 512 3.125 1 886 2 536 7 597 2 377 2.175 1 911 6 095 5 316 2 352 2.784 1 047

7 997 3.720 1 103 2 972 9 064 1 583 2.976 1 313 5 296 5 679 1 994 3.420 1 601

8 033 3.152 1 366 2 882 7 146 1 265 2.437 1 246 3 798 4 218 1 105 3.352 1 669

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

11
Table 7. Power spectral densities of long-baseline phase difference variations

Baseline length: 733 feet (G-H)

Units: (deg.) 2/c/s

Fre- quency

Sample

• 67 68 69 70 71 72 73 74 75 76

c/s 0.00306

.00611 .00917 .0122

.0153

4.428(5) 3.321

1.050

2.907(4) 2.495

7.687(4) 8.478

7.697

6.037 2.702

3.775(5) 1.658

2.682(4) 1.875

1.541

2.186(4) 2.122

1.428

1.605 1.632

2.407(5) 1.541 1.052

5.058(4) 3.033

1.594(5)

3.707(4) 2.677

1.573 1.090

9.892(4) 6.553

4.131 1.722

7.293(3)

1.847(4) 5.270(3) 3.410

2.724

1.588

2.421(5)

4.786(4) 1.037

1.045

7.597(3)

4.555(4) 6.409 3.972

1.573

6.039(3)

.0183

.0214

.0244

.0275

.0306

1.340

7.743(3) 5.790 3.333

3.459

5.164(3) 3.319

2.975 3.170

2.580

8.418(3) 5.641 4.365

2.055

9.488(2)

8.803(3) 7.007 4.190

2.535

2.815

2.512

1.535

1.910 1.508

6.975(3)

9.891(3) 8.262

4.197

9.013

1.037(4)

5.802

2.624

9.970(2) 4.932

3.733

8.631(2)

1.113(3) 1.199

8.423(2) 6.015

8.433

5.175

2.085

2.687

1.916

4.478 3.635

3.115

3.741 3.443

.0336

.0367

.0397 .0428

.0458

2.461

1.340

1.369 1.239

1.217

1.846

1.733

1.035

3.968(2) 7.406

7.734

5.256 3.699 3.528

3.196

1.951

1.646

1.360

6.978(2) 4.145

5.350

4.661 2.329

1.727 1.812

5.491(3) 3.115

2.264

1.296

1.750

4.949

4.567 3.930

4.208

3.217

4.245

4.821 4.514 3.418

3.241

9.723(2) 6.869

6.941 4.156

6.081

2.034

1.747

1.428

1.540

1.114

.0489

.0519

.0550

.0581

.0611

1.105 1.033

1.068

7.056(2) 5.414

9.884

6.826

2.056 2.772

3.437

1.407

7.706(1) 4.668

5.790 8.936

1.047(3) 1.170

5.474(2) 3.979

3.728

1.661 1.942

1.612

1.217

9.967(2)

1.614

1.382

6.477(2) 7.957

5.769

2.558

2.537

1.989

1.017

7.338(1)

2.490

1.049

5.723(1)

1.256(2) 1.509

7.337 6.088

2.945 3.455

1.968

6.841(2)

1.569(3) 1.741

8.665(2) 4.419

.0642

.0672 .0703

.0733

.0764

5.944 4.409

2.949

2.747 2.114

3.752

3.109

2.614

2.415 4.580

1 . oJ'.M ) 9.214(1) 6.098 8.444

1.094(2)

2.865

9.327(1)

2.498(2) 2.399

1.191

6. 112 3.612

2.043 2.744

4.315

2.824 3.083

6.472

6.253 4.426

9.922

1.207(2) 1.568

2.603

1.974

1.580

1.001

6.793(1) 7.761 8.316

1.264

1.585 2.554

1.420

2.195

5.616 6.659

5.295 3.830

2.065

.0795

.0825 .0856

.0886

.0917

1.938 3.958

5.651 5.295 4.784

4.227 3.753

3.386

3.322

2.664

5.063(1) 8.506 6.158

2.818

1.022

1.417

1.782

1.106

6.120(1) -1.685(-1)

5.590

4.623

4.331 3.489

2.075

2.453 2.983

1.920

1.520

5.760(1)

9.215(1) 6.510 6.019 3.265

2.551

5.955 7.728

6.234 3.922

3.413

2.562

2.240

8.314(1) 9.490

6.657

2.068

1.527

7.739(1) 9.109

1.789(2)

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 8. Power spectral densities of long-baseline phase difference variations

Baseline length: 1,181 feet (B-G)

Units: (deg.)Vc/s

Fre- quency

Sample

77 78 79 80 81 82 83 84 85 86

0.00306

.00611 .00917 .0122

.0153

2.586(5) 2.560

7.399(4)

1.001(5) 8.250(4) 5.317

2.921

7.556(4) 5.2755.627(5) 2.7421.942(5) 7.214(4) 2.315

1.858

9.873(3)

1.130(5) 2.123(4) 1.382

7.141(3) 4.606

5.822(4)

4.992(3) 4.143

4.025 2.792

1.193(5) 4.685(4) 1.981 1.324

1.066

8.339(4)

1.182(5) 8.580(4) 4.139

1.329

7.960(4) 1.476

8.818(3)

7.802(4) 3.910

1.584

2.090

1.890

1.936

1.940

9.961(4) 4.188

.0183

.0214

.0244

.0275 .0306

3.731

1.484 3.050

2.358

1.676

1.067

3.884(3) 2.177

1.843

1.542

6.852(3) 4.377 3.661

2.212

8.410(2)

1.943 1.917

9.743(3) 6.231 6.582

1.462

1.216

1.500

9.923(3) 4.611

1.171(4) 1.157

7.147(3) 4.534

3.348

5.008

4.178

3.050

1.406

8.547(2)

2.787 3.053

1.874

1.501 9.762(2)

9.713(3) 5.204

2.555 2.176 1.162

3.515(3) 2.843 4.564

4.949

3.818

.0336

.0367

.0397

.0428

.0458

1.212

9.385(2) 2.341 4.420

4.044

1.746

7.505(2) 4.723

2.427 5.127

7.581 7.088

5.461 5.887

7.924

3.375

1.890

1.751 1.447

6.382(2)

5.421 5.782

3.713

2.797

2.163

1.625 2.239

2.400

1.650 1.442

8.318

5.954

4.679 4.108

1.340

3.537

2.551 5.900

5.053 2.626

1.054

9.279(2) 5.465

2.535

5.410

1.649 2.012 2.003

1.644

9.826(2)

.0489

.0519 .0550

.0581

.0611

3.362

8.119(1)

2.404(2)

5.777(1) 1.289(2)

3.752

1.685

1.173

2.511 1.184

5.452

5.352

4.075

4.769

3.445

6.092

6.037

5.025 3.346

3.455

2.241 2.115

1.556

6.498(2) 3.368

1.385

1.439

1.177

8.234(2) 4.047

3.419(1) 5.318

1.209(2) 1.594

1.573

1.343 1.832

1.851

1.676

1.471

5.376 3.966

2.767

2.084

8.207(1)

7.198

7.800

5.788

3.897

3.941

.0642

.0672

.0703

.0733

.0764

1.198

2.143

-1.769(1) 7.665 -1.910

1.273 1.483

1.989

1.120 1.442

2.126

9.686(1)

1.466(2) 1.339

1.569

4.030

5.344 5.362

4.770

3.348

4.964

2.909

3.682(1)

1.054(2) 2.057

3.575

2.866

1.729

1.305 2.125

1.505

1.503 1.236

1.295

5.729(1)

1.490 1.324

1.391 1.376

7.901(1)

5.930

6.953

1.136(2) 1.091 1.346

1.955

1.469

1.165 1.633

1.123

.0795

.0825

.0856 .0886

.0917

9.654

7.254

1.707(2) 9.420(1)

2.306(2)

4.955(1) 8.482

3.938

8.250

6.480

6.255(1) 9.991

1.729(2) 2.657

2.300

4.446

4.156

4.047 2.948

2.504

1.164

1.333 2.396

2.009

7.773(1)

3.245 3.398

2.720

1.728

8.823(1)

3.022

7.032

5.047 3.819

3.099

4.446

7.483

8.386

1.633(2) 2.274

6.914(1) 5.121

1.499 3.549

2.472

1.133

2.135(1)

1.067(2) 1.723

2.381

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

12
Table 9. Power spectral densities of long-baseline phase difference variations

Baseline length 1,914 feet (B-H)

(Samples taken from BGH recording period) Units: (deg.) 2/c/s

Sample

Fre- quency 87 88 89 90 91 92 93 94 95 96

c/s 0.00306

.00611 .00917

.0122

.0153

5.009(5) 2.717

7.008(4) 1.805

5.776(3)

2.044(5) 1.807

1.106

3.678(4) 1.973

5.969(4) 4.644

2.137

1.307(5)

7.479(4) 2.239

3.667

4.543

1.473(6) 6.064(5) 2.489

1.283

4.283(4)

3.158(5) 1.540

7.355(4) 3.899

2.820

1.918(5) 3.745(4) 1.500

9.436(3) 5.954

1.222(5) 1.240(4) 7.980(3) 6.763 3.557

5.584(5) 1.862

6.280(4) 2.834

1.113

2.223(5) 2.568

1.716

6.542(4) 1.579

.0183

.0214

.0244

.0275 .0306

3.206

2.180 2.196

1.034

4.874(2)

9.887(3) 4.933

2.120 1.502

1.350

1.100

5.909(3) 3.614

2.050

1.266

2.669

1.818

1.168

5.551(3) 3.625

1.831 2.564 3.124

1.528

3.517(3)

1.210

5.424(3) 5.085 7.104

5.037

3.376

3.829

2.800

9.927(2) 4.449

2.313 3.957

2.653

8.725(2) 4.904

8.403(3) 6.512

2.662

1.714

9.504(2)

7.339(3) 6.722

5.599 3.388

2.544

.0336

.0367

.0397

.0428

.0458

3.695

3.489

1.512

8.765(1) 3.618

1.470

1.094

6.273(2) 3.618

3.451

1.340

1.691

1.581 1.505 1.474

1.031

6.187(2)

1.063(3) 1.240

7.332(2)

3.063 3.820

1.920

7.165(2) 1.589

1.652

1.746

2.440

1.146

3.091(2)

4.134

2.506

3.730

3.934

3.463

3.631

2.601

1.599

2.521 3.430

8.075

6.100

9.365 5.343 3.302

1.629

1.477

5.608(2) 1.859

7.742(1)

.0489 .0519

.0550

.0581

.0611

2.182(2) 1.988

1.973

1.355

5.517(1)

2.731 2.420

8.030(1) 7.478

6.481

1.174

1.048

1.071

8.720(2) 6.907

1.094(3) 1.107

1.009

7.287(2) 3.752

5.726

1.041(3) 1.402

1.129

1.347

7.566

1.281(3) 8.793(2) 4.430

1.660

2.315 2.282

1.051 8.806(1) 8.341

2.345

1.661 1.576

1.052

4.651(1)

3.258

3.934

2.574

2.379

4.374(1)

5.083(2) 7.747

7.897

2.898 3.066

.0642 .0672

.0703 .0733

.0764

2.937

1.905(2) 1.005

1.227(1) -2.658

2.870 -1.616

2.456

9.518(0)

1.678(1)

5.011 2.833

1.973 2.462

4.529

1.662

2.257

2.524

2.901 1.894

1.127

1.049

2.472(2)

1.112(1) -6.989

2.356

1.956 3.258

4.453 4.229

1 . 101 (2) 7.214(1)

1.002(2) 1.207

8.702(1)

3.388

5.424

8.237 4.806

5.465

1 . 2.706

3.315

1.737 2.478

Q 1 7A o . i i\J 3.741

6.115(1)

1.001(2) 5.807(1)

.0795

.0825

.0856

.0886

.0917

4.293(0)

1.515(1) 3.580

1.559(0)

1.516(1)

1.071 6.416

2.153 4.123

1.236

6.467

6.029 6.277

5.160

4.261

2.024

1.627 3.297 4.867

6.104

8.290

3.477

1.334(2) -1.433(1)

1.189(2)

2.481 1.858

8.444(1)

2.054(2) 2.460

3.536

4.629

7.802 8.375

3.500

7.883

6.828

9.886(0) 6.727 -8.054

2.018

1.931

7.907(1) 1.030(2)

2.012(1)

2.045(2)

8.953(1)

1.776(2) 4.487(1) 7.475

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 10. Power spectral densities of long-baseline phase difference variations

Baseline length: 1,914 (B-H)

(Samples taken from ABH recording period)

Units: (deg.) 2/c/s

Sample

48 49 50 51 52 53 54 55 56 57 58 59 60

1.958(6) 5.364(5) 2.695(5) 9.973(4) 6.049(4) 4.969(4) 2.484(4) 4 915(4) 1 053(5) 1 987(5) 6 545(4) 1 179(5) 7.967(5) 2.533 1.649 2.029 5.261 3.556 1.763 8 019(3) 1 618(4) 4 423(4) 5 024

863(3)

7 700(4) 2.790 9.958(4) 3.219(4) 1.073 3.881 1.965 1.064 8 726(2) 8 838(2) 1 947 1 687 8 4 031 1.837 4.803 1.361 4.929(3) 1.704 6.985(3) 4.462(3) 2 423 5 004 1 123 3 055(3) 4 343 1 182

9.711(4) 2.294 7.759(3) 1.854 7.130(3) 1.932 2.850 4 157 2 248 3 224(3) 1 266 1 933

6 032(3) 3.447 1.901 3.788 2.435 4.229 2.188 3.829 1 995 9 412(1) 5 855(2) 9 045(2) 8 211(2) 4 565

1.681 1.846 3.654 3.005 2.212 1.941 2.696 1 112 2 365(2) 7 226 9 170 8 079 3 407

6.146(3) 8.825(3) 3.254 1.777 2.253 8.719(2) 1.220 1 373 9 104(1) 6 187 8 796 6 781 2 159 6.198 7.482 1.190 8.327(2) 1.760 5.901 4.844(2) 1 120 1 336(2) R 885 6 499 2 984 1 303 7.557 5.174 4.407(2) 3.678 9.471(2) 3.183 4.009 6 072(1) -2 618(1) 3 167 5 752 1 780 6 481(2)

6.415 8.108 3.248 2.940 6.115 2.845 5.359 4 137 4 379 2 204 3 029 1 323 7 935 3.695 7.605 3.031 2.729 2.520 1.433 5.375 2 648(0) -4 440(0) -1 037(1) 2 678 1 983 5 775 4.964 3.827 3.226 2.446 4.156 1.575 3.292 2 077(1) 3 951(1) 6 084 2 524 3 311 5 366

5.262 2.565 3.304 1.523 7.739 2.872 3.241 7 844(0) -9 227(0) -7 931(0) 2 422 2 306 2 542 3.886 2.310 1.542 1.942 5.986 2.315 2.860 1 037(1) 5 918(1) 2 654(1) 1 135 1 078 3 702

1.906 1.363 1.675 1.174 2.525 5.887(1) 2.087 -1 137(0) -2 278 -1 722 1 034 1 360 3 492

2.443 6.560(2) 1.249 6.592(1) 1.515 7.363 1.331 1 086(1) 1 394 3 401 6 917(1) 1 451 2 873 2.805 4.262 2.556 3.161 3.684(1) 1.094(2) 1.285 -2 818(0) -1 834 -3 420 1 226(2) 1 244 1 386

2.249 5.074 2.299 8.454 3.774 1.361 1.036 5 181 2 276 1 476 1 330 1 122 1 381

5.269(2) 6.058 1.745 4.865 3.411 6.869(1) 8.965(1) -4 010 -1 294 -1 007 9 799(1) 1 123 1 372

9.072 6.881 1.182 2.243 1.510(2) 6.600 4.774 8 979 (-1) 1 399 1 933 5 231 1 091 1 925

1.135(3) 4.052 1.419 9.981(0) 2.579 6.911 3.689 -2 782(0) -2 265 -2 806 6 116 9 800(1) 1 256 1.428 3.004 9.341(1) 3.325(1) 2.354 6.175 2.867 8 982 1 453 2 356 6 434 6 896 1 484

5.516(2) 1.260 6.984 -1.657(0) 1.155 6.589 6.671 1 801 -4 214(0) 6 748(0) 7 014 7 042 5 496(1) 9.083 1.945 5.277 1.671(1) 1.356 8.263 5.086 5 303 1 567(1) 2 497(1) 4 743 5 975 9 830

6.276 2.355 1.033(2) -4.415(0) 1.062 6.103 2.772 5 826 (-1) -2 214 -4 833(0) 4 403 5 000 9 529 8.659 3.180 6.454(1) 3.888 3.262(1) 7.174 1.226 6 473(0) 5 733(0) 1 885(1) 2 478 3 781 1 508(2) 4.465 4.977(1) 6.268 -1.659 -2.103(0) 4.612 2.808 -4 037 -1 889(1) -2 007 4 733 2 704 9 242(1) 7.824 1.722(2) 1.947 3.602(1) 3.357(1) 3.812 3.775 5 481 1 360 -1 396(0) 3 672 1 336 1 313(2) 7.735 1.253 3.490 3.254 2.691 1.095 5.926 3 187 -8 534(0) -2 760(1) 3 004 2 265 1 150

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

13
Table 11. Power spectral densities of long-baseline phase difference variations

Baseline length: 3,003 feet (A-B)

Units: (deg.) 2/c/s

Sample

Fre- quency 22 23 24 25 26 27 28 29 30 31 32 33 34

c/s 0.00306 3 169(6) 5.756(5) 1 992(5) 16

742(5) 3 030(5) 1 121(5) 1 515(5) .00611 1 538 2.033 1 095 986(4) 6 095(4) 4 523(4) 3 584(4) .00917 1 341(5) 1 393(5) 3.801(4) 3 138(4) 1 742 8 847(3) 8 422(3) 1 080(3) 5 937(2) 6 150(3) 7 426(3) 9 615(3) 2 193(4) .0122 4 914(4) g 489(3) 1.460 1 413 1 237 9 374 5 928 3 728(2) 5 466 3 676 3 371 7 627 1 605

.0153 3 676 6 443 3.772(3) 1 212 1 254 4 671 1 726 1 240 4 043 2 066 1 188 2 796 1 536

.0183 2 778 5 643 1.236 1 041 8 997(3) We 135 2 138 1 163 2 129 1 163 6 331(2) 1 950 9 173(3) .0214 Hi 627 5 056 6.797(2) 5 501(3) 3 820 3 454 2 513 2 272 8 438(1) 1 804 9 671 1 672 5 087

.0244 i 932 5 439 2.871 2 740 1 167 1 434 1 475 1 494 1 211(2) 1 648 1 202(3) 7 749(2) 4 184

.0275 7 794(3) 1 957 l.O^lKo; 2 109 1 348 1 136 8 874(2) g 848(1) 1 305 6 085(2) g 672(2) 4 895 2 961

.0306 1 049(4) 2 667 3.527(2) 1 524 6 995(2) 7 327(2) 6 329 1 000(2) 7 472(1) 1 501 4 178 4 049 1 413

.0336 7 443(3) 4 542 4.581 1 497 7 609 7 364 4 386 5 521(1) 2 721 3 592 1 783 1 689

285(1)

7 219(2) .0367 5 095 3 571 2.074 1 599 7 732 2 652 3 030 1 852 1 614 3 803 1 830 9 5 668

.0397 4 052 1 008 6.092 1 242 5 153 4 334 1 956 2 111 2 524 1 971 1 690 1 564(2) 4 909

.0428 4 020 1 086 7.825(1) 1 007 2 654 1 646 3 476 4 535 4 934 1 930(1) 9 562(1) 1 252 4 267

.0458 3 691 A 1.044(2) 9 121(2) 1 625 3 753 3 051 3 989 4 ot>4 4 805 j 102 2 401

.0489 2 386 2 903(2) -8.251(1) 9 241 4 304(1) 2 629 9 090(1) 3 662 2 865 7 334 7 528 1 376 1 574

.0519 8 163(2) 3 984 8.088 7 023 mm 352 4 162 4 034 2 135 2 677 1 473(2) 6 081 9 549(1) 1 335

.0550 1 641(3) 9 469 -1.469(2) 4 413 5 461 1 296 6 591 2 127 3 343 9 449(1) 8 868 1 138(2) 1 756

.0581 9 137(2) 1 698 4.619(1) 3 335 2 638 1 137 6 336 1 828 3 333 4 822 9 720 1 800 1 897

.0611 3 505 H 777 -7.339 3 847 4 932 3 205(1) 6 023 1 185 3 472 2 371 6 884 1 582 1 907

.0642 4 858(1) -6 120(1) 1.237(2) 4 220 1 037(2) 1 749(2) 4 140 1 247 2 682 3 074 3 340 1 257 1 780

.0672 1 142(2) 4 278(2) -2.259(1) 5 425 7 800(1) 4 040(1) 3 475 1 456 1 364 -4 567(0) 3 906 1 325 2 200

.0703 1 793 2 210 1.240(2) 4 597 7 176 7 580 2 758 1 300 1 045 2 029(1) 3 976 9 930(1) 1 865

.0733 2 799 2 885 -9.306(0) 3 285 4 773 -2 369 4 598 1 381 1 407 1 520 5 213 8 655 1 178

.0764 -7 395(1) -6 368(1) 7.649(1) 2 954 7 303 9 875 3 470 1 254 1 548 4 592 6 635 3 308 5 742(1)

.0795 2 105(2) 2 963(2) -4.337 2 601 1 575 2 566 3 415 1 361 2 396 3 336 4 979 1 523 8 767

.0825 1 916 1 094 8.899 2 107 3 512(0) 9 189 5 160 1 273 2 239 3 702 5 131 8 406(0) 5 742

.0856 1 374 3 078 -5.155 1 902 5 002 1 626(0) 4 325 1 410 1 852 1 001 3 664 1 896(1) 3 865

.0886 2 128 1 489 5.814 2 144 8 361(1) 8 390(1) 1 611 8 382(0) 1 217 2 733 4 416 2 300 2 230

.0917 9 549 5 435 -7.168 2 148 1 127(2) -2 508(0) 9 653(0) 4 822 1 052 1 551 4 399 4 060 3 722

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 12. Power spectral densities of long-baseline phase difference variations

Baseline length: 4,847 feet (A-H)

Units : ( deg. ) 2/c/s

Sample

quency 35 36 37 38 39 40 41 42 43 44 45 46 47

0.00306 1 316(6) 1 436(6) 5 026(5) 2 113(5) 2 751(5) 3 378(5) 1 411(5) 7 995(3) 1 702(5) 6.448(5) .00611 5 416(5) 7 625(5) 2 129 1 009 1 223 8 275(4) 7 296(4) 6 587 3 937(4) 4.623(4) .00917 2 257 1 071 4 850(4) 4 062(4) 914(4) 9 235(3) 1 072 3 428 2 780(3) 1 068 1 449(4) 1 666(4) 1.725

.0122 1 566 6 410(4) WE 087 1 885 i 984 4 630 3 755(3) 1 227 1 284 5 323(3) 3 933(3) 7 057(3) 8.697(3) .0153 5 577(4) 3 151 1 135 1 031 9 669(3) 3 828 2 694 7 311(2) 5 671(2) 1 306 2 883 3 462 5.225

.0183 3 182 1 013 5 016(3) 6 235(3) 4 806 2 334 2 597 3 891 4 902 5 681(2) 2 400 1 503 3.508

.0214 3 822 3 701(3) 1 843 3 094 2 330 2 065 1 249 2 512 4 125 7 348 1 108 6 734(2) 3.025

.0244 2 424 3 682 9 290(2) 2 768 1 359 8 265(2) 1 033 1 932 1 986 7 016 6 216(2) 2 836 2.237

.0275 1 499 1 776 7 831 2 966 1 641 7 434 6 202(2) 1 811 4 112(1) 5 805 9 098 3 548 1.099

.0306 1 570 2 885 1 545 1 952 1 418 4 441 5 241 1 786 7 301 2 599 7 705 3 715 4.178(2)

.0336 1 391 1 237 145 8 824(2) 9 463(2) 5 697 3 577 1 348 8 807 3 070 5 557 3 259 9.051

.0367 5 779(3) 1 420 i 378 7 739 6 615 4 190 3 120 1 130 8 444 2 420 5 470 2 883 6.328

.0397 4 224 7 768(2) 2 591 1 072(3) 3 626 5 761 8 297(1) 1 164 6 289 1 954 2 906 1 811 5.806

.0428 3 658 1 339(3) -1 779 9 880(2) 2 949 1 113 1 476(2) 1 103 5 898 2 165(1) 1 762 1 222 1.350

.0458 1 794 6 560(2) 2 820(1) 7 518 4 781 3 777 1 332 1 025 4 316 3 731 1 179 1 078 1.184

.0489 2 217(2) 1 364(3) -7 193(1) 6 244 4 025 8 937(1) 1 583 9 741(1) 3 195 2 798 8 722(1) 1 077 -6.272(1)

.0519 1 979(3) 4 793(2) 1 528(2) 5 839 3 333 3 404(2) 1 020 1 214(2) 3 810 8 309 4 979 1 367 2.814

.0550 2 089 5 297 -6 200(0) 5 251 3 581 1 692 1 160 1 105 6 251 7 537 5 175 1 179 -3.115

.0581 1 950 6 840(1) 9 174(1) 4 254 2 318 1 710 -1 775(0) 9 610(1) 4 056 8 219 5 048 9 460(1) 1.258(2) .0611 1 457 4 315(2) -9 900 2 777 8 068(1) 2 105(1) 2 084(11 1 044(2) 1 994 1 569 5 409 1 084(2) 1.030(1)

.0642 1 981 -1 940 3 294 3 277 3 185 1 856(2) 3 991 1 003 1 291 2 757 4 162 6 722(1) 3.547

.0672 2 237 2 904 -7 446 3 872 5 459 9 739(1) 9 106 1 024 2 231 -1 555 4 207 5 282 -5.230

.0703 2 017 1 181 6 592 3 047 3 183 1 561(2) 1 274(-l) 1 005 2 177 1 307 3 017 6 852 5.111

.0733 7 604(2) 5 122 -6 789 2 150 -5 953(0) -2 042(1) 1 690(0) 1 007 2 905 2 467 2 708 4 766 -4.471

.0764 9 775 4 910(1) 4 010 2 063 1 023(1) 1 102(2) -1 332(1) 7 884(1) 2 530 4 170 3 664(0) 1 989 3.000

.0795 2 877 2 888(2) -8 043 2 190 3 909 6 266(1) 4 663 6 192 2 441 -6 590(0) 2 376(1) 1 543 1.451

.0825 2 802 2 194 3 760 2 768 JL 698 1 393(2) 3 251 5 919 8 831(0) 1 227(1) 5 313 1 742 1.287(2) .0856 1 809 4 888 -7 346 3 581 9 637 -5 005(1) 4 146 7 329 6 363 7 472(0) 5 602 1 718 4.245(1) .0886 4 400 5 996(1) 2 921(0) 3 251 9 075 4 042 -1 610 9 186 7 806 4 957(1) 4 334 3 901 6.446

.0917 6 274(1) 4 915(2) -1 178(2) 2 421 6 736 -6 512 9 811(0) 9 237 1 844(1) 4 873 4 682 6 821 3.115(-1)

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

14
Table 13. Power spectral densities of single-path phase samples taken from BEF recording period

Units: (deg.) 2/c/s

Sample

x requency

130 131 132 133 134 135 136

c/s 0.00306 3.084(6) 9 150 (5) 024(6) 5 <Jit*J\OJ 1.078(6) 3.341(6) 3.546(5) .00611 1.586 7 110 4 791 (5) 3 287 5.350(5) 5.280(5) 2.586

.00917 4.349(5) 2 970 2 452 576 1.109 4.441(4) 1.156

.0122 1.959 g 025(4) 7 675(4) 5 270(4) 3.820(4) 2.171 2.577(4) .0153 1.356 1 824 3 270 3 450 1.894 1.334 1.374

.0183 4.296(4) 2 135 2 138 2 625 9.285(3) 6.710(3) 1.169

.0214 2.387 2 170 1 691 1 550 7.205 8.950 0.000(0;

.0244 2.620 1 444 1 124 5 995(3) 9.620 8.910 4.396

.0275 2.267 9 295(3) g 520(3) 3 568 5.465 8.750 2.715

.0306 2.070 2 394 1 674 2 710 3.998 2.838 1.262

.0336 1.020 2 260 2 117 2 844 3.405 4.536 1.185

.Uoo/ 4 . 0U0 {6) 5 060 2 534 1 726 3.718 2. 187 7.740(2) .0397 4.288 5 655 4 024 2 044 2.316 2.520 6.565

.0428 3.493 2 465 x 040 1 014 1.876 8.800(2) 4.050

.0458 2.022 1 836 1 918 8 880(2) 1.402 2.064(3) 4.584

.0489 2.588 1 996 3 016 4 750 1.191 4.474(2) 3.010

.0519 2.314 2 126 2 476 1 126(3) 4.194(2) 1.181(3) 2. 284

.0550 2.990 I 204 g 035(2} 5 410(2) 9.585 7.355(2) 9.640(1)

.0581 2.734 9 945(2) I 054(3) g 215 8.105 1.662(3) 2.459(2) .0611 2.622 5 885 5 645(2) 4 564 9.525 4.881(1) 1.436

.0642 1.831 6 940 1 072(3) 5 155 3.897 4.902(2) 3.411

.0672 1.294 3 690 1 301(2) 5 610 4.885 -3.867(1) 1.414

.0703 1.073 3 593 5 275 1 202(3) -4.214(1) 1.002(3) 1.591 .0733 1.237 1 040 2 288 6 335(2) 2.876(2) -4.924(1) 8.955(1) .0764 6.100(2) 2 010 9 100 3 822 4.730 3.892(2) 2.632(2)

.0795 3.196 -3 494(1) 7 325 3 066 7.665 8.020(1) 1.156

.0825 1.260 3 490 9 915 5 475 4.221 9.105(2) 1.811 .0856 9.965 4 098 2 211 3 094 7.325 -1.040 7.390(1) .0886 9.175 3 030(2) 6 535 3 757 4.159 2.844 1.035(2) .0917 8.890 4 126(1) 1 476 1 615 5.550 -3.466 -2.062(1)

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

Table 14. Power spectral densities of single-path phase samples taken from BGH recording period

Units: (deg.) 2/c/s

Sample

r i cquency

97 98 99 100 101 102 103

0.00306 1.386(6) 1.110(6) 5.145(5) 6.070(5)

.00611 1.844(5) 3.238(5) 1.432 3.854

.00917 2.126(4) 2.829(4) 4.974(4) 4.676(4) 4.641(3) 2.526(4) 1.484

.0122 8.560(3) 1.797 1.338 4.211 1.146 1.158 8.740(4)

.0153 7.755 5.650(3) 5.095(3) 2.391 6.725(2) 8.765(3) 4.686

.0183 6.535 2.362 1.882 1.156 3.431 6.655 2.613

.0214 2.493 2.166 2.656 8.515(3) 3.840 1.920 1.890

.0244 1.180 1.296 1.461 6.155 6.120 1.104 1.322

.0275 1.178 1.631 1.895 4.308 4.992 1.032 6.245(3) .0306 1.143 9.970(2) 6.890(2) 2.485 3.568 3.534(2) 2.828

.0336 4.967(2) 8.835 1.032(3) 2.638 1.913 4.112 2.256

.0367 2.992 2.080 4.528(2) 3.058 1.357 6.640 1.904

.0397 1.352 9.475(1) 8.445 3.455 1.028 5.465 1.326

.0428 3.238 -3.935 3.348 2.611 7.935(1) 5.245 2.216

.0458 5.630 2.548(2) 6.960 1.830 2.074 4.391 2.964

.0489 3.754 2.652 2.100 1.418 3.121 2.910 1.916

.0519 1.245 2.978 4.738 1.224 3.592 1.778 9.525(2)

.0550 1.022 4.498(1) 1.404 9.420(2) 7.225 1.632 1.113(3)

.0581 7.075(1) 1.920(2) 4.520 1.159(3) 4.792 9.835(1) 9.040(2)

.0611 1.248(2) 8.480(1) 1.936 9.680(2) 2.704 8.990 9.925

.0642 6.115(1) 1.317(2) 4.145 8.235 1.442 7.185 1.156(3) .0672 4.480 3.670(1) 1.144 6.985 3.844 9.170 1.106

.0703 2.704 1.129(2) 3.470 8.350 3.586 7.215 8.305(2)

.0733 5.525 1.812(1) 1.424 8.950 3.948 6.420 7.020

.0764 3.368 1.076(2) 3.528 8.940 2.545 2.616 6.225

.0795 7.025 4.264(1) 9.505(1) 6.840 1.971 6.670 6.300

.0825 4.136 1.424(2) 3.031(2) 7.005 1.654 5.565 4.303

.0856 4.204 4.668(1) 1.216 6.255 1.822 2.774 4.791

.0886 -1.370 9.075 3.200 7.710 8.265(0) 1.216 4.842

.0917 -5.520(0) 7.230(0) 1.010 7.585 1.242(1) 3.252 7.130

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.

15
Table 15. Power spectral densities of single-path phase samples taken from ABH recording period

Units: (deg.) 2/c/s

Sample

Frequency

61 62 63 64 65 66

c/s 0.00306 1.834(6) 7.645(5) 3 602(5) .00611 o.yoU(.o; 2.740 2 685(4) .00917 4.199(4) g 5 850(3) g 000(31 .0122 2.094 Q >i AC 1.534 2 915 3 049 3 672

.0153 1.952 2.204 2.854 9 135(2) 1 422 4 634

.0183 1.670 7.590(1) 3.078 7 265 8 430(2) 4 484

a.<±\)\j\6) ft AAA 1 .886 I 104(3) 6 000 3 236

.0244 a son 7.580 d.dU0(o; g 605(2) 2 606 297

.0275 Q AAQ 1 QQA 2.985 4 138 3 064 7 935(2) .0306 1.832 6.375 3.270 2 465 2 196

.0336 2.337 2.125 3.460 1 194 3 080 1 032

AQA7 O 7ATI 1.104 1 132 1 424 g 185(2) .0397 3. 194 1.746 1 426 1 342 3 910

Ayf OC 2, 150 2.896 2.636 1 354 7 230(1) I 984

.U40o 1.064 3.378 7 285(1) 1 559(2) g 985(1)

.0489 4.462(2) 7.650(0) 2.824 6 635 8 280(1) 8 245

.0519 6. 190 3.530 1.439 5 450 7 685 6 035

.0550 6.955 4.220 6. J4o(,l) 5 570 3 314 1 034(2)

. 0581 4.917 5.905 1.766 2 934 7 435 1 451

.0611 1.864 1.274(1) 6.600 2 452 2 153 1 273

.0642 6.455(1) 1 246 1.457(2) 1 861 5 315 5 290(1) X672 -i. 540 l!028 3]373(1) 3 848 3 301 1 324

.0703 1.562(2) 1.033 -1.891(0) 3 677 7 325 2 671

.0733 1.356 9.270(0) -1.540(1) 3 273 3 601 1 296

.0764 -4.736(1) 6.640 4.278 2 110 6 150 -5 625(-l)

.0795 -5.320 4.476 1.029 2 860 4 546 1 370(1) .0825 -5.470(0) 2.892 1.059 2 379 7 345 2 864

.0856 -1.648(2) 4.764 -2.034 4 587 3 266 2 522

.0886 -1.720 4.417 1.522 5 200 4 460 2 106

.0917 -1.560 3.578 6.075(-l) 4 369 1 222 1 920

Note: Number in parentheses indicates power of 10 multiplying adjacent and following entries.
17
18
19
o

o

UJ

CO

crLd

CL

co

UJ

_J

o>-o

,(3anindiAiv 3ai±v~gu)

20
21
22
23.
Haleakala - Puunene Path Baseline Length: 2.2 Feef
Haleakala - Puunene Path Baseline Length : 2.2 heet

10

o

o

UJ

CO

<r. Ld

Q_

Ld

_JO>-o

CO

LUUJ

o

10

a-2

10"

10

10f5

0.01

^\ \

Sample N°

• • 4

6

r> oa -n

- /In -4 0

o . « 5a

. ^—^ 6a

1 Nv V \

1 i \ *

Reading Error

Noise Spectra

_ \\

N

V \ v

Hi \ /

0.1 I

CYCLES PER SECOND

Figure 9. Power spectra of 9,4-1 4. Mc/s phase difference variations.

10

25
26
27
28
Haleakala - Puunene Path Baseline Length 22 Feet

10

Sample No.

• 16

. -17

- - 18 V ~^

>

k >,<.:^

_ V

X \\

'v\ A *

My

Reading Error Noise Spectra

r v\ \\

N. \

\

VAv

\ \ X \ \ \

\ ^\ \

\

V

10'

10

,-2

-3

-4

10

10

0.01 0.1 I

CYCLES PER SECOND

Figure 13. Power spectra of 9,klU Mc/s phase difference variations.

10

29
30
HALEAKALA - PUUNENE PATH

Baseline Length : 2.2 Feet

rTo

1

1 Sample No.

1

H

ll

llll

ll

in

3

ill

ill i\t

\\ \

\ \

\ V

* ft

» \\ %\\\ s 'CPs

\

*> \ '

N

J A

0 5 10 15 20 25 30

LAG (k)

I i i i i I

' '

i 'I

0 5 10 LAG IN SECONDS (kS)

Figure 15. Serial correlation functions of 9,414 Mc/s phase difference variations.
1.0

0.8

0.6

0.4

0.2

-0.2

•0.4

-0.6

•1.0

HALEAKALA - PUUNENE PATH

Baseline Length: 22 Feet

o

1

1 Sample No.

4

ItV

ft* I

0

6

1

1

-4

\ \\ .

\\

' /

/

— -fc^i \

0

5 10 15 20 25

LAG (k)

I i i i i I i i i i I

30

5 10 LAG IN SECONDS (k8)

Figure 16. Serial correlation functions of 9,Ulh Mc/s phase difference variations.
HALEAKALA - PUUNENE PATH

Baseline Length: 2.2 Feet

\

1

1 Sample No.

7

1

I I

l\

llll

ll

O

9

11

llm

\

A

i

\

\\\

'\\

A\ ^

/ A---. /--

\

vSN s \\ / ^

/

J

V- — —

?

V —-V

' 0 5 10 15 20 25 30

LAG (k)

I

. i i I i i i i I

0 5 10 LAG IN SECONDS (k8)

Figure 17. Serial correlation functions of 9,klU Mc/s phase difference variations.
HALEAKALA - PUUNENE PATH

Baseline Length: 2.2 Feet

1.0

\

A

I

1 Sample

10

i

i

i

1 1 ,2

v\

\

"A

i V

t \\

' V

1 \

1 \

I I

1 ft

' \\

1 \\

i VA

\

\i

i

i

ii

\i \\\

\\

i \

t ,\v

\

^

\

^" \

."*' \ —— /

/

__ ^

\y

0.6

0.4

0.2

•0.2

-0.4

-0.6

-1.0

J I I L

10 15 20

LAG (k)

I i i i i I

25 30

j i i i I

LAG IN SECONDS (kS)

15

Figure 18. Serial correlation functions of 9,iH Mc/s phase difference variations.
HALEAKALA - PUUNENE PATH

Baseline Length: 22 Feet

-0.4

-0.6

-0.8

-1.0.

J L

10 15 20

LAG (k)

J i i

. , L

25 30

i i i i

5 10 LAG IN SECONDS (kS)

15

Figure 19. Serial correlation functions of 9,414 Mc/s phase difference variations.
HALEAKALA - PUUNENE PATH

Baseline Length: 2.2 Feet

-0.4

-0.6

-0.8

-1.0

J I I I I I I L

10 15 20

LAG (k)

j L

25 30

J I L.

5 10 LAG IN SECONDS (k8)

15

Figure 20. Serial correlation functions of 9,4-H Mc/s phase difference variations.
HALEAKALA - PUUNENE PATH

Baseline Length: 2.2 Feet

1

i Sample No.

19 — d{j

dl

11

11IIv

ll

11vit\i i \ i I 1 \ 1

v M 1 U » \ \

\ \ \ \

\ \ 1 \ 1 \ —\ \ IV /

//

> 7^

^ /

X \ s /

,~£^ y fx/

vf

0.8

0.6

0.4

0.2

-0.2

-0.4

-0.6

-0,8

-1.0

j i i i_

10 15 LAG (k)

J i . l_

20 25 30

j 1 1 i_

5 10 LAG IN SECONDS (k8)

15

Figure 21. Serial correlation functions of 9,414- Mc/s phase difference variations.
0NOD3S H3d 31DA0/ 2 (S33d93Q)
Haleakala - Puunene Path Baseline Length: 2.2 Feet

•

• •

••

•

• •

•

••

•

•

• •

•

•

•

•

•

• • •

•

•

•

• •

• •

•

•

•

M 2 4 6 8 10 M 2 4 6 8 10 J4 HOUR

Figure 23. Variance of phase difference versus time of day.
HALEAKALA - PUUNENE PATH

Baseline Length: 67 Feet (B-E)

30 0

LAG IN SECONDS (k8) LAG IN SECONDS (kS)

Figure 24. Serial correlation functions of 9,414 Mc/s phase difference variations.

40
HALEAKALA - PUUNENE PATH

Baseline Length: 109 Feet (B-F)

Figure 25. Serial correlation functions of 9,414. Mc/s phase difference variations.

41
HALEAKALA - PUUNENE PATH

Baseline Length: 733 Feet (G-H)

i.o

0.8

0.6

0.4

0.2

rTo

-0.2

-0.4

-0.6

-0.8

\

s

X X

ample N?

• 67

° 69

x 71

• 73

« 75

\ v1 v\ X

a a

\

\

\

)

\ \

\\ \

.\\

\

\

X —

\\\ —

-tPi

V

\

1 A

\

\\

V x

V?fc-x—*-.-

\

4 "A

\

\V

H

\

"A

\

k

1 —

-1 I l_

10 15 20 LAG (k)

i i i i 1

25 30 0

50 150 LAG IN SECONDS (kS) LAG IN SECONDS (k8)

Figure 26. Serial correlation functions of 9,AH Mc/s phase difference variations.

42
HALEAKALA - PUUNENE PATH

Baseline Length: 1,181 Feet (B-G)

Figure 27. Serial correlation functions of 9,AH Mc/s phase difference variations.

43
1.0

0.6

0.4

0.?

rT

o

0.2

04

-0.6

-1.0

HALEAKALA - PUUNENE PATH

Baseline Length: 1,914 Feet (B-H)

(Samples Taken From BGH Recording Period)

o 5

0

\ V

Sample N°

• • • 87

o o o 9

x x x 93 >A a 6 a 95

\

1

A *X^

\ -x v

\V \ *i \

N

\\

\ l \

*xv "x, v

\

"A, s, V .

XX

X

>

i A,

k > X-a. o.

* -»i

10 15 20 LAG (k)

I ' i i

i i i i i i i

25 30 0

J i

50 150 LAG IN SECONDS (kS) LAG IN SECONDS (kS)

Figure 28. Serial correlation functions of 9,414 Mc/s phase difference variations.

44
HALEAKALA - PUUNENE PATH

Baseline Length: 1,914 Feet(B-H)

1.0

0.8

0.6

0.4

0.2

T 0

-0.2

-0.4

-0.6

-0.8

v\ *\

-ml Sample N?

• • • 48

a a o 50

•-- — • 52 - c 54

A 6- o 56

x x x 58

0 o o go

X

X

x T -X k \

X1 X

>

^ \ \

v

* \\

\

X

\ —\—

\ V

\V ^ \

A.

%s

*'\

'-is-T *r

I I I L

15 20 25 LAG (k)

_i i i i I i i, i i I i

30 0

J i i_

15 20 LAG (k)

J—i—i—i I I i 50 150 0 50 150 LAG IN SECONDS (kS) LAG IN SECONDS (kS)

Figure 29. Serial correlation functions of 9,414. Mc/s phase difference variations.

45
HALEAKALA - PUUNENE PATH

Baseline Length : 3,003 Feet (A-B)

0 5 10 15 20 2 5 30 0 5 10 15 20 25 30 LAG (k) LAG (k)

I i i I i I I i j ' ' l I i I i I i i l I I i '''I' l l I I i

0 50 100 150 0 50 100 150 LAG IN SECONDS (k8) LAG IN SECONDS (k8)

Figure 30. Serial correlation functions of 9,iH Mc/s phase difference variations.

46
HALEAKALA - PUUNENE PATH

Baseline Length: 4,847 Feet (A-H)

0 5 10 15 20 25 30 LAG (k)

I i i i i I i i i i I i i i i I i 0 .50 100 150 LAG IN SECONDS (kS)

Figure 31. Serial correlation functions of

0 5 10 15 20 25 30 LAG (k)

I—i i i I I

i

I I i

i i I i

0 50 100 150 LAG IN SECONDS (kS)

Mc/s phase difference variations.

47
HALEAKALA-PUUNENE PATH

(Samples Taken From ABH Recording Period)

1.0

0.8

0.6

0.4

0.2

-0.2

-0.4

-0.6

-0.8

-A-S

(

O O

X X

a a

Sample N°

-O 61

-* 63

65

\

1

0 5 10 15 20 25 30 LAG (k)

1 i i i

i I i i i i I i i i i_—I 1

0 50 100 150 LAG IN SECONDS (kS)

Figure 32. Serial correlation functions of 5,-41-4 Mc/s single-path phase variations.
HALEAKALA-PUUNENE PATH

(Samples Taken From BGH Recording Period)

Figure 33. Serial correlation functions of 9,4.14- Mc/s single-path phase variations.
_i.o I 1 1

1 1 1

0 5 10 15 20 25 30

LAG (k)

I i i i ' I i . i i 1 1 i i i 1 1

0 50 100 150 LAG IN SECONDS (kS)

Figure 34. Serial correlation functions of 9,414 Mc/s single-path phase variations.

50

I
Haleakala - Puunene Path

^6

Baseline Length: 67 Feet (B

10

10

10*

Median spectrum

95% stability limits

•

\

. \ •:

• \

\

\

T^i :

• • •

'\. ' \ —\

** •

s, • • ^< •

• \ *X» • - • • • • \ • • • :* . v^'iA'i • •\ . ...%{. ••Vstf.Xrv:

V--»J » •

*• •••• V -t . • . . :.;•«•;

V/\J^v . ....

v v/ ••v\• /

y/

•

0.001 0.01 CYCLES PER SECOND

Figure 35. Power spectra of 9,4-14 Mc/s phase difference variations.

0.1
Halea kala - Puunene Path

io

6

i

Baseline Length; 109 Feet (B

10

0.001 0.01 CYCLES PER SECOND

Figure 36. Power spectra of 9MU Mc/s phase difference variations.

(Data samples 117 to 129, incl.)

52
10

0.01 0.1 CYCLES PER SECOND

Figure 37. Power spectra of 9,4-14 Mc/s phase difference variations.

(Data samples 67 to 76, incl.)

53
Haleakala - Puunene Path

io

6

,

Baseline Length: 1,181 Feet (B-G)

O.OOI 0.01 CYCLES PER SECOND

Figure 38. Power spectra of 9,414 Mc/s -phase difference variations.

(Data samples 77 to 86, incl.)

54
0.001 0.01 CYCLES PER SECOND

Figure 39. Power spectra of 9,U1U Mc/s phase difference variations.

(Data samples 87 to 96, incl., from ABH recording period)
CYCLES PER SECOND

Figure 40. Power spectra of 9,4.14 Mc/s phase difference variations.

(Data samples 48 to 60, incl., from ABH recording period)
0.001 0.01 0.1 CYCLES PER SECOND

Figure 41. Poiver spectra of 9,U1U Mc/s phase difference variations.

(Data samples 22 to 34, incl.)
Figure 42. Power spectra of 9,AH Mc/s phase difference variations.

(Data samples 35 to 47, incl.)
Haleakala - Puunene Path

Figure 43. Power spectra of 9,414. Mc/s single-path phase variations.

(Data samples 61 to 66 incl., from ABH recording period)
0.001 0.01 0.1

CYCLES PER SECOND

Figure 44. Power spectra of 9,U1U Mc/s single-path phase variations.

(Data samples 97 to 103 incl., from BGH recording period)

60
Haleakala-Puunene Path

0.001 0.01 CYCLES PER SECOND

0.1

Figure 45. Power spectra of 9,U1U Mc/s single^path phase variations.

(Data samples 130 to 136 incl., from BEF recording period)

61
Haleakala - Puunene Path

\

\

\

\

\

\

\

\

Baseline Length

67 feet(B-E)

« » o 109 feet (B-F)

Single Path

\\

\

\

\

\

\\

\\

\

\

\^

\

\

\

\ -o^ 1

\ >s, ^

i

0.001 0.01 0.1 CYCLES PER SECOND

Figure 46. Median phase variation spectra from BEF recording period.
Haleakala - Puunene Path

N

NN S N

\

N

Baseline Length

• • 733 feet (G-H)

° ° ° 1, 181 feet (B-G) \ x * x |,9l4feet(B-H)

« • Single Path

\\ \ \

> W

V \\

\

\WaV

\ «s.

\ \\ \

* x\ \

> lb v\

» A \ x **i

If

1I

0.001 0.01 0.1 CYCLES PER SECOND

Figure 47. Median phase variation spectra from BGH recording period.
Haleakala - Puunene Path

0.001 0.01 CYCLES PER SECOND

FIGURE 48. Median phase variation spectra from ABH recording period.

64
Haleakala - Puunene Path

10

o

o

Ld

co

rr

LJ

Q_

LJ

_lO>-o

CMCO

LJ

LJ

cniD

LJ

o

9

I0

l

10'

10*

10

10

• • • Median single path phase spectrum

from ABH recording period ——— Median single path phase spectrum

from BGH recording period

• • Median single path phase spectrum

from BEF recording period

x x x Median phase difference spectra (BH)

from ABH recording period

x ^ -* Median phase difference spectra (BH)

from BGH recording period

0.001 0.01 0.1 CYCLES PER SECOND

Figure 49. Comparison of median spectra obtained from different recording periods.

65
c

CDC

3

Q_

I _ga

j£

o

oX

c

a)

3; m

00 ._ * CO

C7>

% QJ

CTl rO o r-

• X

o

q:—Jf

>o

u.ljm

o

xo

m

o

O

c

> -oo

X

CO<

>"

,(S33W93Q)

66
22 m

(0U3Z AUVUliaaV) S33U93Q Nl 3SVHd HlVd 319NIS

>=3- "3" ro mCVJ o

us

§I—

fa

2 (S33d93Q) Nl 30NVIUVA 3SVHd HlVd 319NIS

ro Oro

ro

CXJ o

ro roOo COO oCO

CVJ r—

CNJ S1IND-N Nl AHAI13VdJ3U 3DV3dllS NV31AI

67
>

o

ooo

>

o

(0d3Z AdVdll9dV) S33d93d Nl 3SVHd HlVd 319NIS

e

"8S

s

Si

e

w

e

S5.

s

a.

8>8

8

8

ITS g

o

ro

lO

CNJ ,(S33d93Q) Nl 3DNVIdVA 3SVHd HlVd 319NIS

LO

ro ro CNJ S1IND-N Nl AHAI19Vd33d 30VJdflS NV31M

CO

oo

68
Haleakala - Puunene Path

cvi—

V)

UJ

UJ

rro

UJ

a

100,000

50,000

20,000

10,000

5,000

2,000

1,000

500

200

100

50

20

10

10 2 0 50 100 200 500 1,000 2,000

BASELINE LENGTH IN FEET

Figure 53. Variance of phase difference versus baseline length.

Single-Path Vc

1 ria — a BEF

x BGh

A ABh

O Mec

necoramg rerioa

1 Recording Period

i Recording Period

ian of Sample Variances

a

1

A

A

#

X X

0! X X

8

S

A

&

* A

< A

A

X

X

A

A

I 1

-o

X X A

A

A

A ft Ire1

X ®

B

5,000

69
0> ~~ 3 «

E -S _ E

o 2 S > o 5

O x <

Q

3d

>o

00>

UJ

Is- I-

>o

8

3inNIW/ VIAIIXV1A1

3inNllM/S9NISSOyO

(S1IND-N) Nl 30NVIUVA
10°

o

o

UJ

00

crUJ

Q_

UJ

I o

>

o

\

COCO

UJ

UJ

rrCD

UJQ

BASELINE LENGTH : 67 FEET ( B-E)

Reading Error

Noise Spectra

Sample N° —• 105

• —o 109

V

10

0.001 0.01 0.1

CYCLES PER SECOND

Figure 55. Examples of reading error noise spectra compared to corresponding phase difference spectra.
I0

6 BASELINE LENGTH: 733 FEET (G-H)

0.001 0.01 0.1

CYCLES PER SECOND

Figure 56. Examples of reading error noise spectra compared to corresponding phase difference spectra.

72
10

o

o

UJ

CO

or

Ul

Q_

UJ

I o

>

o

\

OJCO

UJ

Ul

crCD

10'

10

10'

10 -

10

0.001 0.01 0.1

CYCLES PER SECOND

Figure 57. Examples of reading error noise spectra compared to corresponding phase difference spectra.

73
0

0.001 0.01 0.1

CYCLES PER SECOND

Figure 58. Examples of reading error noise spectra compared to corresponding phase difference spectra.

74
S3~ldlAIVS 31DNIIAI-QI ±N3N0dlAI03 JO 30NVIdVA 39Vd3AV

H19N31 Q31V3IQNI 30 S3~ldlAIVS 30 33N\/ldVA 39Vd3AV

75
Haieakala-Puunene Path Baseline Length: 1,914 Feet (B-H)

0.001 0.01 0.1

CYCLES PER SECOND

Figure 60. Power spectra of phase difference variations with sample length as a parameter 9,klU Mc/s.

76
I

0.001 0.01

CYCLES PER SECOND

Figure 61. Power spectra of phase difference variations with sample length as a parameter 9,414 Mc/s.

77
Haleakala - Puunene Path Baseline Length: 4,847 Feet (A-H)

0.001 0.01 0.1

CYCLES PER SECOND

Figure 62. Power spectra of phase difference variations with sample length as a parameter 9,414 Mc/s.
9,414 Mc Haleakala - Puunene Path

2-Hour Sample, 0503 -0700,

Nov.7, 1956

0.001 0.01 0.1

CYCLES PER SECOND

Figure 63. Power spectra of single-path phase variations with sample length as a parameter.
FROM PUUNENE FROM HALEAKALA
FROM PUUNENE FROM HALEAKALA

Figure 65. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.
FROM PUUNENE FROM HALEAKALA
FROM PUUNENE FROM HALEAKALA

11/6 1655

Figure 67. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.

83
FROM PUUNENE FROM HALEAKALA

Figure 68. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.

84
FROM PUUNENE FROM HALEAKALA

11/7 15Z5

Figure 69. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.
FROM PUUNENE FROM HALEAKALA

11/8/56 0624

Samples 75, 85, 95, 102

11/8/56 0715

Samples 13, 14, 15

76, 86, 96

Figure 70. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.

I 86

i
FROM PUUNENE FROM HALEAKALA

11/8 1530

Samples 10 5, lib, 131

Figure 71. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.
FROM PUUNENE FROM HALEAKALA
Figure 73. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.
FROM PUUNENE FROM HALEAKALA

Figure 74. Photographs of Haleakala-Puunene path corresponding in time to data samples indicated.

Boulder, Colo., February 10, 1961.
U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C.,

and Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical

work. In general, each section carries out specialized research, development, and engineering in the field indicated by its title. A brief description of the activities, and of the resultant publications, appears on the

inside of the front cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-Ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment. Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standards

Reference Materials. Applied Analytical Research.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion Controls.

Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

Structure. Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal Physics.

Electrodeposition.

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth. Physical

Properties. Constitution and Microstructure.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog Systems. Applications Engineering.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Solid State Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical In- struments. Basic Instrumentation.

Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy.

Molecular Kinetics. Mass Spectrometry. Molecular Structure and Radiation Chemistry.

• Office of Weights and Measures.

BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas Liquefaction.

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Service.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter-Wave

Research. Microwave Circuit Standards.

Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

•& U.S. GOVERNMENT PRINTING OFFICE: 1961 597154 91