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V.L.F. propagation over long paths
Journal of Atmospheric
and Terrestrial Physics, 1967, Vol. 29, pp. 73-85. Pergamon Press Ltd. Printed in Northern Ireland
V.L.F. propagation over long paths A. B. KAISER Physics and Engineering Laboratory, Department of Scientific and Industrial Research, New Zealand (Received 21 A.@/ 1966) Abstract-Cycle slips and other evidence of interference have been observed for v.1.f. signals from NPG Seattle (18.6 and 24 kc/s), WWVL Boulder (20 kc/s) and NBA Panama (18 kc/s), each approximately 12,000 km from the receiver at Lower Hutt. Phase and amplitude variations are analysed to identify the interfering signals present. Starting from Crombie’s model of mode conversion at a shadow line it is shown how cycle losses recorded during sunrise may be produced. Consistentwith the E-W non-reciprocityof v.1.f. propagationmulti-path interference is discernibleonly for NBA; it is found that the long path signal for this station caused severe interferenceincluding cycle gains at sunset.
1. INTR~DUOTI~N THE phase and amplitude of v.1.f. transmissions from several stations are recorded at the Physics and Engineering Laboratory. The technique used is that described by CROMBIE et al. (1958): the incoming signal is mixed with a signal from a local reference oscillator of slightly different frequency and the resulting beat record is analysed to give the phase variations of the received signal. This paper is concerned with signals from the stations listed in Table 1. Table 1. V.L.F. stations observed at Lower Hutt Station
Location
Approximate distance (km)
Frequency (kc/s)
Observing periods
NBA WWVL NPG
Panama Boulder Seattle
12,100 12,200 11,700
18 20 24 18.6
Periods in 1961, 1962, 1963 June 1964-December 1965 January-May 1964 September 196PDecember 1965
WAIT (1962) has described v.1.f. propagation in terms of modes in the waveguide formed by the Earth’s surface and an ionospheric reflecting layer. For propagation by the first mode along the short great-circle path, the phase of a v.1.f. signal should follow the normal trapezoid curve, advancing as the sunrise line moves along the path and retarding during the corresponding sunset transition. During the periods when the path is completely in shadow or completely sunlit (referred to here as night-time and da,ytime respectively) the phase should remain relatively constant. The phase variation for the three paths considered does show the basic trapezoidal shape, but severe interference is observed. In particular, the diurnal phase curves often give a cycle slip, that is, over a 24 hr period, the final phase is not equal to the initial phase, but differs from it by some integral multiple of 2r. This phenomenon, first described by BURTT (1963), is naturally of considerable importance as a possible
73
74
A. B. KAISER
source of error in standard frequency dissemination and navigation using v.1.f. transmissions. Deviations from the fust mode phase pattern might be produced by the following interfering signals : the higher order modes propagating along the short great-circle path between transmitter and receiver (including signals due to ‘mode conversion’ at a shadow line) ; the whistler-mode signal propagated through the magnetosphere ; the long path signal. The interference expected from each of these signals is analysed in the following section. The experimental records are then examined and show that both the ‘mode conversion’ and the long path signals may cause cycle slips at a distance of 12,000 km from the transmitter. Phase and amplitude irregularities caused by ionospheric disturbances of various kinds are not discussed in this paper. 2. EFFECTS OF INTERFERING SIGNALS
Mode conversion CROMBIE (1964) has explained the phase steps and corresponding amplitude minima he observed for v.1.f. signals during transitions by postulating that one mode of propagation is partially converted into other modes as the radio wave propagates through an ionospheric height discontinuity. Crombie considers interconversion of the first and second modes at a sunrise or sunset boundary and neglects the second mode in the sunlit portion of the Earth-ionosphere waveguide. For the short great-circle paths from the stations NBA, WWVL, NPG to Lower Hutt, the shadow lines always pass the transmitter before the receiver. While the sunrise line is moving along the path, a second mode signal may be excited at the boundary where the height of the ionosphere changes from its daytime to its night-time value. This signal would have a greater phase velocity than the unchanged first mode signal (WAIT, 1962), and so a standing wave pattern moving with the sunrise line would be formed in the night-time waveguide. Thus, according to Crombie’s model, periodic minima would be observed at the receiver. A similar mechanism could produce interference during the sunset transition. The effect on phase and amplitude of the mode conversion signal may be obtained by considering the phasor diagram. The following analysis is valid whether the shadow lines pass the transmitter or the receiver first. Let the phasor E, represent the signal due to first mode propagation throughout the path length, and E, the signal due to first mode propagation in the daytime waveguide which is converted to or from second mode propagation in the night-time waveguide. Crombie points out that the phase 6 of signal E, with respect to E, is the difference in phase delays at the receiver, so neglecting a possible constant factor and assuming a discontinuous height change of the effective reflecting layer at a shadow line,
where d, is the length of path in the night-time region, and 1, and 1, are the wavelengths of the first and second modes respectively in the night-time waveguide. Since R, is greater than 1, for the night-time ionosphere height (WAIT, 1962), the phase 13decreases during sunrise when d, is decreasing, and increases during sunset
V.L.F.
75
propagation over long paths
when d, is increasing. To obtain the total phase variation, we the variation of the phase 4 of signal E,. This first mode phase to change approximately linearly with time during sunrise and since the velocities of the shadow lines along the three paths During night-time and daytime, when there latively constant. across the path, the mode conversion signal cannot be present.
must also consider would be expected sunset transitions, considered are reis no shadow line
0
Phase advance
Fig. 1. Mode conversion interference for E, < E, at sunrise.
advance
Fig. 2. Mode conversion interference for E, >
E, at sunrise.
Figure 1 shows the sunrise case when the amplitude of the signal E, is less than that of E,. As 0 decreases, it can be seen that the amplitude of the resultant shows a sinusoidal perturbation. Further, a periodic phase variation is superimposed on the linear first mode phase increase, enhancing this increase at amplitude minima and tending to cancel it at amplitude maxima. Thus the phase change during a transition in which the mode conversion signal E, is present tends to occur in steps, each swift phase change corresponding to an amplitude minimum. Examples of this effect are shown in the experimental records, for instance, in Fig. 3 at sunrise. Figure 2 illustrates the sunrise case when the amplitude of E, is greater than that of E,. Here the resultant signal shows a rapid decrease of phase at an amplitude minimum rather than a rapid advance. Comparing the locus of the resultant phasor with the locus of the phasor E, between consecutive maxima at OA and OB, it can be seen that the resultant signal has suffered a cycle loss relative to the first mode signal. Hence when the mode conversion signal is larger than the first mode signal during sunrise, amplitude minima are accompanied by fast phase retardations, each retardation representing one cycle loss. The experimental records also show this effect, for example, in Fig. 6. Similarly, at sunset, the presence of a mode conversion signal causes the phase decrease to occur in steps, each fast phase retardation accompanied by an amplitude minimum. If the mode conversion signal becomes larger than the first mode signal, a fast phase increase occurs at the time of an amplitude minimum and a cycle gain is registered.
A. B.
76
(I).
KAISER
To calculate the period of mode conversion interference use is made of formula Between amplitude minima 0 must change by 277. Hence, Ad
A0 =2rr = 25r
N
where Ad, is the change in length of the night-time path in the time At between minima. If u is the time average velocity of the shadow line along the path during time At, AdN = uAt so At
44
=
u(A, - A,)
e.(!g_ !y
(2)
where c is the velocity of electromagnetic radiation in free space, f the frequency of the signal, V,, and V,, the night-time phase velocities of the first and second modes respectively. In many cases u may be taken as constant throughout the transition ; then At Yjd[vrTc
(3)
‘F)
where d is the total path length and T the total time for the transition. The presence of the third and higher modes in the night-time Earth-ionosphere waveguide could complicate the observed interference pattern. From an approximate formula for phase velocity given by WAIT (1959) it can be seen that V N3 ---
vmc
4!+!&)
c
where V,, is the night-time phase velocity of the third mode. Hence interference between the first mode signal and the converted third mode signal would be twice as fast as interference due to the converted second mode signal E,. The effect of the third and higher modes during transitions would be to produce fast interference. The severity of mode conversion interference depends on the attenuation of second mode compared to the first as the two modes propagate in the night-time waveguide, as well as the mode conversion efficiency at the shadow line. The presence of mode conversion interference is not dependent on the total path length; it should occur for even the longest paths when only a small length of the path is dark, provided that the shadow line mode conversion is efficient. Unconverted second and higher modes
There may be a signal obtained at the receiver due to second mode propagation throughout the path length. This signal, unlike. the shadow line mode conversion signal, would be present continuously, but should be insignificant at great distances in daytime as it is then highly attenuated. BATES and ALBEE (1965) have recently shown
that the second
mode
can propagate
strongly
over
9000 km from
NBA
77
V.L.F. propagation over long paths
(18 kc/s) to Europe. If some unconverted second mode were present during a transition it would cause interference of period At
N
Tc
(4) i
where Vn, and Vn2 are the daytime phase velocities of the first and second modes respectively. In deriving this formula the same ideal conditions as for the mode conversion case have been assumed. The unconverted second mode phase increases faster at sunrise than the first mode phase ; by considering the phasors it can be deduced that rapid phase increases at sunrise and decreases at sunset will occur at amplitude maxima, as indicated by CROMBIE(1964). Furthermore, this unconverted second mode may produce cycle gains at sunrise and cycle losses at sunset, having the opposite effect to the mode conversion signal. Since the second mode is highly attenuated in the sunlit Earth-ionosphere waveguide, the interference will be most discernible at the end of the sunset transition and the beginning of the sunrise transition. For frequencies greater than 20 kc/s and path lengths less than 10,000 km the period is comparable to the total transition time, so that this simple multi-mode interference would not be expected to be as noticeable as mode conversion interference of shorter period. As for the mode conversion case, modes of higher order than the second would be expected to produce faster interference. Whistler mode
Whistler mode signals would not be expected to be significant except perhaps where the receiver is near the magnetic conjugate of the transmitter. For the three stations monitored, this condition is most closely satisfied for the transmitter NPG Seattle, whose conjugate point is approximately 2500 km from Lower Hutt. Allcock (private communication) has received whistler mode signals at Lower Hutt from NPG (18.6 kc/s) having up to 50 per cent of the amplitude of the sub-ionospheric signal. Such high amplitudes are, however, rather rare. Since whistler mode signals have frequency shifts of up to one or two parts in 105, their effect is usually to produce small and very fast fluctuations in amplitude and phase of the total signal. Long path propagation
BURTT (1963) suggested that the irregularity of phase curves of NBA received at Lower Hutt was due to long path interference. THOMSON et al. (1963), receiving NBA at Sydney, demonstrated that the long path signal became dominant when the short path was sunlit, showing that the attenuation at 18 kc/s was greater in the sunlit than in the dark Earth-ionosphere waveguide. THOMPSON et al. point out that this long path reception, despite the long path length being nearly twice the short path length, demonstrates the non-reciprocity of E-W v.1.f. propagation proved theoretically by BARBERand CROMBIE(1959). Considering propagation by the first mode alone, both the short and the long path signals should show a trapezoidal phase variation. During daytime and nighttime over the short path the sunrise and sunset shadow lines will both be moving
A. B. KAISER
78
along the long path. While this is happening the fraction of the long path in darkness is approximately constant, so the phase of the long path signal is also constant. During short path sunset, that is, as the sunset line moves along the short path, the sunrise line moves along the long path at the same velocity. The long path phase trapezoid is therefore just the short path trapezoid inverted, both trapezoids having approximately the same depth Au. Hence at each transition the phase of the long path signal changes by 2Au with respect to the short path signal, so that 2 Au cycles of multi-path interference occur (Aa being measured in cycles). Then the time for one cycle of interference is
At=
a
2ua’
For uniform velocities of the shadow lines along the paths, this gives the period of multi-path interference during a transition as T
At = 2Aa
(‘3)
where T as before is the duration time of the transition. The presence of the long path signal may make the measurement of Aa difficult, but it can be estimated using an empirical formula given by BLACKBAND(1964), which may be put in the form
.fax
ha = ko
7.87 x 1O-9 cycles.
Here k(f) is a correcting factor depending on frequency, various values of which are listed by Blackband. Formula (5) has been derived considering only the first mode ; the presence of higher order modes would complicate the interference and render the formula invalid. In the phasor diagram the long path signal may be represented by a perturbing phasor which counter-rotates about the head of the first mode phasor during transitions. Hence multi-path interference during transitions is of the same pattern as that produced by the mode conversion signal: amplitude minima occur at the time of rapid phase changes, the direction of the phase change depending on whether the short or the long path signal is greater. 3. INTERPRETATION OF RECORDS NPa: (18.6 kc/s) The diurnal phase variation of signals from NPG (18.6 kc/s) is usually trapezoidal with some perturbation at sunrise, as shown in Fig. 3 for May 29 1965. The interfering signal must be decreasing in phase with respect to the first mode signal since the sunrise phase increase is enhanced at amplitude minima. The period observed is consistent with mode conversion interference but not with multi-path interference. For instance, in June 1965 three rapid phase advances were clearly seen at sunrise, the first two being separated by an average of about 100 min, and the last two (at the end of the transition) by about 80 min. Since for the path NPG to Lower Hutt it is reasonable to take the sunrise line velocity along the path as constant,
V.L.F. propagation over long paths
79
formula (3) may be used to calculate the period of mode conversion interference. WAIT (1962) has calculated the phase velocities of the first and second modes for a sharply bounded ionosphere and perfectly reflecting Earth, neglecting the Earth’s magnetic field which should have only a small effect on phase velocity. Taking the night-time height of the reflecting level as 90 km and the transition time as 470 min at this height, the period of sunrise mode conversion interference in June is given as 86 min.
4
Fig. 3. Phase and amplitude of NPG (18.6 kc/s). In a similar way the period for two-path interference may be estimated from formula (6). The phase change from night to day Aa is approximately 1.6 cycles, so that the period is 145 min for June. This confirms that the sunrise interference is due to mode conversion. The interference is greatest when the transition is longest (in June) and not discernible at all when it is shortest (in December), suggesting that mode conversion is most efficient at a shadow line which is normal to the direction of propagation. Since no interference of period 43 min is discernible, the excitation of the third mode at the sunrise line would seem to be negligible. occasionally a cycle loss is recorded at At 18.6 kc/s cycle slips are uncommon; about the middle of the sunrise transition where on most days a fast phase advance occurs. No clear evidence of mode conversion interference can be found at sunset even when the transition is slowest.
NPG (24 kc/s) MCNEILL and ALLAN (1965) have indicated that cycle slips are frequently observed for 24 kc/s signals from NPG. However, the offset of the local oscillator from the transmitted frequency was only about 2 parts in lo8 when these records were taken (January-May, 1964), so the interpretation of the best trace is in some As shown in Fig. 4, at sunrise there are rapid phase advances instances ambiguous. where the frequency of the received signal may temporarily become greater than
A. B.
80
KAISER
(‘overtake’) the frequency of the local oscillator. When this happens an oscillation referred to as an ‘overtaking’ beat is produced on the beat trace. This overtaking beat, which if counted produces a spurious cycle slip in the phase curve, may resemble a beat representing a genuine cycle slip. The confusion may be heightened
0
c.3 -I a? b
5
f
-2
,--_ : .I
I
h
,t-’ , May 28 1964 ,* I'
/'
Cycle loss
A-: ,
tude I 0
2
4
6
I 8
I IO
I 12
I I4
I 16
I 18
I 20
-
22
U.T.
Fig. 4. Phase and amplitude of NPG (24 kc/s).
by the large amplitude fluctuations. For the days illustrated in Fig. 4, however, a unique interpretation may be made. Since NPG ceased transmission at 24 kc/s in May 1964, further investigation at this frequency has not been possible. The interference pattern at the end of the sunrise transition (the last two amplitude minima) is well-defined during May and is consistent with mode conversion interference. It is difficult to determine the precise times of the sharp phase advances from the beat records, but averaging over 13 days in May the time between the last two sharp phase advances is 78 min. For May, the transition time T is 420 min at a height of 70-90 km, and Wait gives (V&c) - (VxJc) as 0.0055 for an ionosphere height of 90 km. This difference in phase velocities is not very sensitive to the value of night-time ionospheric height assumed. According to formula (3), therefore, the period of mode conversion interference is 82 min, which compares favourably with the experimental value above. However, the period of interference earlier in the transition is variable, usually being greater than 82 min.
V.L.F. propagation over long paths
81
According to WAIT (1962), at 24 kc/s the second order mode should be more significant than at 18.6 kc/s. Comparison of the May 1964 records at 24 kc/s with the May 1965 records at 18.6 kc/s shows that this is indeed the case. At 18.6 kc/s no cycle slips occurred in May, but at 24 kc/s several days gave a cycle loss at sunrise as shown for May 28 in Fig. 4, indicating that the second mode signal became greater than the first mode signal. In general, the interference would be expected to be most severe at the end of the transition, since the further the second mode propagates the more it is attenuated with respect to the first mode. Nonetheless, in each instance the sunrise cycle loss occurs at about mid-transition when the sunrise line, at which the second mode is excited, is about 6,000 km from the receiver. A plausible explanation is that the first mode signal reaches minimum amplitude at about mid-transition. Then the second mode propagating in the night-time waveguide with an attenuation similar to that of the first mode may produce the observed sunrise interference. BATES and ALBEE (1965) explained the low night amplitude and anomalous trapezoid depths observed for two paths in terms of destructive interference between the first and second modes at the receiver. These paths were both under 5,000 km, but in view of the strong second mode propagation at night found by BATES and ALBEE (1965), and also revealed by the timing of sunrise cycle losses for the NPGLower Hutt path, it might be expected that the effect would be observed at large The night-time decrease of amplitude which occurs for most days in distances. April and May 1964 for the 24 kc/s signals (as shown for May 12 and May 28 in Fig. 4), and which is also observed to a lesser extent on the 18.6 kc/s records, suggests that at each frequency a second mode signal destructively interferes at night with the first mode signal. This amplitude decrease is irregular and variable from day to day, but it tends to start about 2 hr after 70 km sunset at Lower Hutt and end just before sunrise at Seattle. For instance, on some days such as May 12 1965, the phase appears to stabilize at 2.4 cycles before the interfering signal decreases the These night-time changes suggest that amplitude and deepens the phase trapezoid. the ionospheric reflecting layer is still changing some time after it has ceased to be illuminated. If an unconverted second mode were present at sunrise, formula (4) gives its period of interference as about 280 min in May for 24 kc/s and 115 min for 18.6 kc/s, where phase velocity values given by WAIT (1962) for an ionosphere height of No clear evidence indicating the presence of 70 km have been used for daytime. this simple second mode signal during transitions has been found ; it seems to become significant only when the path is entirely dark. No cycle slips have been identified at sunset, but evidence of interference is found when the sunset transition is long, that is, when the sunset line makes a large angle with the path. Figure 5 shows the amplitude of beats at sunset and the time The apparent frequency shift of the received signal is between beat maxima. indicated by the shortening of the beat. Considerable variation is shown from day to day, but frequency fluctuations of similar period to those on February 7 are shown for several other days in early February. Consistently a large frequency shift (which means a rapid phase decrease) accompanied by an amplitude minimum occurs at about mid-transition. The period of the frequency fluctuations is that
A.
82
B. KAISER
expected from the presence of a mode conversion signal, and as at sunrise, the interference is most severe at about the middle of the transition. CROMBIE (1964) found that for two W-E paths interference was more pronounced at sunrise than at sunset. For these paths at sunrise, a second mode signal excited at the transmitter was converted to a first mode signal at the shadow line. Mode conversion interference is also most severe at sunrise for the E-W paths studied in this paper, although the mode conversion at sunrise is of the same type as at sunset
U.T.
Fig. 5. Length and amplitude of beats at sunset for NPG (24 kc/s) on February 7 1964.
on W-E paths. In both these cases, a first mode signal propagating in the sunlit waveguide is partially converted to a second mode signal at the shadow line. Hence mode conversion of either type is more efficient at the sunrise line. WWF_,5 (20 kc/s) Signals from WWVL and NPG show similar characteristics, since the transmitters are both at approximately 12,000 km from Lower Hutt with a difference of only 14” in their bearings. Phase and amplitude plots shown for July 16 in Fig. 6 are typical ; on a majority of days throughout the year the mode conversion signal produces a cycle loss at the middle of the sunrise transition. The period of interference between the cycle loss and the following rapid phase advance is rather longer than expected theoretically, but the period between the last two phase advances is in better agreement. This variation in period, which is also observed for NPG at both frequencies, cannot be explained using the simple bi-modal model described in Section 2. On a few days such as August 2, 1965, the mode conversion signal apparently produces an effect throughout the entire sunrise transition. As for NPG, a significant second mode signal would therefore be expected at night. In contrast to NPG, the average night amplitude for WWVL is usually greater than the day amplitude, but like NPG, the amplitude tends to be smaller at the middle of the night than just after sunset or just before sunrise. During the day when the path is entirely sunlit the amplitude is far less erratic than at night. In contrast to the night-time pattern, there is a slight tendency for the amplitude to continue to increase after sunrise and start to decrease before sunset, as though it were slightly dependent on the Sun’s zenith angle. At no time during the year is mode conversion interference clearly seen at sunset.
V.L.F. propagation over long paths
83
0
I
-I
d
-2 i
I o-
o-
4
b -I
!
-
-2 -
1. .
0
Fig. 6. Phaseand arnpliut:de of WWVL (20 kc/s). NBA
(18 kc/s)
The bearing of the transmitter NBA from Lower Hutt is 41” E of WWVL, so that from E/W non-reciprocity the long path signal from NBA should be considerably larger than that from WWVL or NPG. The oscillator used for the 1961 NBA records gave a fast beat rate, which gives good amplitude information, but poor phase plots. An amplitude record is shown in Fig. 7 for July 8-9, 1961. For the 1962 and 1963 records the local reference was an Essen-ring oscillator giving a slower beat rate. The sunset amplitude pattern is seen throughout the year, though the third minimum is sometimes indiscernible. The occurrence of a cycle gain at sunset shows that the unconverted second mode signal cannot cause the interference. The periods of interference expected from the long path and mode conversion signals in July are now calculated. The average depth of trapezoid for NBA for 12 phase curves in 1962 is l-6 cycles, and Blackband’s formula (7) predicts a depth of about 1.65 cycles. Taking the transition time as 340 min and assuming a constant velocity for the sunset line along the path, (6) gives the period of multi-path interference as 106 or 103 min. The sunset amplitude variation for July 1961 has a period of nearly 2 hr, so that it does seem likely to be multi-path interference. The greater length of the second
A. B. KAISER
84
cycle of interference is not surprising since the velocity of the shadow lines along the paths is actually somewhat greater at the beginning of the transition than at the end. Wait’s phase velocity values give the period of sunset mode conversion interference as 60 min for a transition time of 340 min, confirming that the long path signal is primarily responsible for the sunset interference. July
8-9
1961
ai : n.
Ground
w
1,
2-
January
II-12
sunset
1962
I
I
I
I
I
16
I8
20
22
24
I
I
2
4
.-\ 6
, 8
U.T.
Fig. 7. Phase and amplitude of NBA (18 kc/s).
At sunrise the position is more complex and variable. Sometimes three minima like those at sunset are observed, but usually the amplitude pattern is irregular. For July, multi-path interference should have a period of about 160 min, and mode conversion interference about 90 min. The apparent period of interference at the start of sunrise is often approximately the expected mode conversion period, as for July 8-9. It is suggested that both the long path and mode conversion signals are significant at sunrise. A typical phase plot is shown for January 11-12, 1962. Here the long path signal predominates at the first sunset minimum and a cycle gain occurs. These cycle gains are common, and on occasions a second cycle gain is recorded at the second amplitude minimum. Sunrise cycle slips appear to be far less frequent than sunset cycle gains. It is interesting to note that THOMPSON et al. (1963) also found that the long path signal tended to predominate for longer at short path sunset than at sunrise, resulting in phase accumulations for some days. A possible cause of this asymmetry of cycle slips is greater attenuation of a v.1.f. signal as it passes a sunset shadow line than a sunrise line. 4. CONCLUSIONS
Severe interference has been observed for signals from NPG (18.6 kc/s and 24 kc/s) and WWVL (20 kc/s) during the sunrise transition. This interference has been explained using Crombie’s model of mode conversion at a shadow line. It has been
V.L.F. propagation over long paths
85
shown how the mode conversion signal may produce the frequent cycle losses recorded at mid-transition. Comparison of the 18.6 kc/s and 24 kc/s records from NPG shows that mode conversion interference is more severe at the higher frequency. Mode conversion interference at sunset has been clearly identified only at 24 kc/s; comparison with CROMBIE’S(1964) results for W-E paths indicates that mode conversion is more efficient at the sunrise than the sunset shadow line. The evidence also suggests that mode conversion is most efficient when the shadow line is normal to the direction of propagation. Support is given to the conclusion of BATES and ALBEE (1965) that second mode propagation over long paths is more significant than formerly accepted; the observation that the mode conversion signal is often larger than the first mode signal when the sunrise line is about 6,000 km from Lower Hutt shows that the second mode signal propagates in the night-time waveguide with an attenuation comparable to that of the first mode for the frequencies 18.6-24 kc/s. Hence the second mode signal would be expected to be significant at night and could be a factor in causing the low night-time amplitude noticeable for NPG at 24 kc/s. However, the similarity of the night-time amplitude variations for each case also suggests a regular pattern of ionospheric change between sunset and sunrise. It is found that the unconverted second mode signal does not become significant until after completion of the sunset transition and it does not appear to produce any effect after sunrise has begun. It has been shown that during transitions the long path signal produces interference similar to that due to the mode conversion signal but of a different period. Although for NPG and WWVL the long path signal was not discerned, severe multi-path interference was observed for the NBA to Lower Hutt path. Since all three paths are of approximately the same length, the dependence of the E/W attenuation ratio on the angle between the path and the Earth’s magnetic field is clearly shown. The long path signal from NBA was observed to produce cycle gains at sunset, while at sunrise both multi-path and mode conversion signals were present to produce complex interference. REFERENCES BARBER N. F. and CROMBIE D. D. BATES H. F. and ALBEE P. R. BLACKBAND W. T. (Ed)
1959 1965 1964
BURTT G. J. CROMBIE D. D. CROMBIE D. D., ALLAN A. H. and NE-AN M. MCNEILL F. A. and ALLAN A. H. THOMPSON A. M., ARCHER R. W. HARVEY I. K. WAIT J. R. WAIT J. R.
1963 1964 1958
and
1965 1963 1959 1962
J. Atrnosph. Terra Phye. 16, 37. J. Geophys. Res. 70, 2187. Propagation of Radio Waves at Frequencies below 300 kc/s, Pergamon Press, Oxford. Proc. In&n Elect. Engrs 110,1928. J. Res. NBS/USNC-URSI 68D, 27. Proc. In&n Elect. Engrs lOSB, 301. J. Geophys. Res. 70, 731. Proc. In&n Elect. Electron. Engr8 51, 1487. Proc. Inst. Radio Engrs 47, 998. Electromagnetic Waves in Stratified Media, Pergamon Press, Oxford.
and Terrestrial Physics, 1967, Vol. 29, pp. 73-85. Pergamon Press Ltd. Printed in Northern Ireland
V.L.F. propagation over long paths A. B. KAISER Physics and Engineering Laboratory, Department of Scientific and Industrial Research, New Zealand (Received 21 A.@/ 1966) Abstract-Cycle slips and other evidence of interference have been observed for v.1.f. signals from NPG Seattle (18.6 and 24 kc/s), WWVL Boulder (20 kc/s) and NBA Panama (18 kc/s), each approximately 12,000 km from the receiver at Lower Hutt. Phase and amplitude variations are analysed to identify the interfering signals present. Starting from Crombie’s model of mode conversion at a shadow line it is shown how cycle losses recorded during sunrise may be produced. Consistentwith the E-W non-reciprocityof v.1.f. propagationmulti-path interference is discernibleonly for NBA; it is found that the long path signal for this station caused severe interferenceincluding cycle gains at sunset.
1. INTR~DUOTI~N THE phase and amplitude of v.1.f. transmissions from several stations are recorded at the Physics and Engineering Laboratory. The technique used is that described by CROMBIE et al. (1958): the incoming signal is mixed with a signal from a local reference oscillator of slightly different frequency and the resulting beat record is analysed to give the phase variations of the received signal. This paper is concerned with signals from the stations listed in Table 1. Table 1. V.L.F. stations observed at Lower Hutt Station
Location
Approximate distance (km)
Frequency (kc/s)
Observing periods
NBA WWVL NPG
Panama Boulder Seattle
12,100 12,200 11,700
18 20 24 18.6
Periods in 1961, 1962, 1963 June 1964-December 1965 January-May 1964 September 196PDecember 1965
WAIT (1962) has described v.1.f. propagation in terms of modes in the waveguide formed by the Earth’s surface and an ionospheric reflecting layer. For propagation by the first mode along the short great-circle path, the phase of a v.1.f. signal should follow the normal trapezoid curve, advancing as the sunrise line moves along the path and retarding during the corresponding sunset transition. During the periods when the path is completely in shadow or completely sunlit (referred to here as night-time and da,ytime respectively) the phase should remain relatively constant. The phase variation for the three paths considered does show the basic trapezoidal shape, but severe interference is observed. In particular, the diurnal phase curves often give a cycle slip, that is, over a 24 hr period, the final phase is not equal to the initial phase, but differs from it by some integral multiple of 2r. This phenomenon, first described by BURTT (1963), is naturally of considerable importance as a possible
73
74
A. B. KAISER
source of error in standard frequency dissemination and navigation using v.1.f. transmissions. Deviations from the fust mode phase pattern might be produced by the following interfering signals : the higher order modes propagating along the short great-circle path between transmitter and receiver (including signals due to ‘mode conversion’ at a shadow line) ; the whistler-mode signal propagated through the magnetosphere ; the long path signal. The interference expected from each of these signals is analysed in the following section. The experimental records are then examined and show that both the ‘mode conversion’ and the long path signals may cause cycle slips at a distance of 12,000 km from the transmitter. Phase and amplitude irregularities caused by ionospheric disturbances of various kinds are not discussed in this paper. 2. EFFECTS OF INTERFERING SIGNALS
Mode conversion CROMBIE (1964) has explained the phase steps and corresponding amplitude minima he observed for v.1.f. signals during transitions by postulating that one mode of propagation is partially converted into other modes as the radio wave propagates through an ionospheric height discontinuity. Crombie considers interconversion of the first and second modes at a sunrise or sunset boundary and neglects the second mode in the sunlit portion of the Earth-ionosphere waveguide. For the short great-circle paths from the stations NBA, WWVL, NPG to Lower Hutt, the shadow lines always pass the transmitter before the receiver. While the sunrise line is moving along the path, a second mode signal may be excited at the boundary where the height of the ionosphere changes from its daytime to its night-time value. This signal would have a greater phase velocity than the unchanged first mode signal (WAIT, 1962), and so a standing wave pattern moving with the sunrise line would be formed in the night-time waveguide. Thus, according to Crombie’s model, periodic minima would be observed at the receiver. A similar mechanism could produce interference during the sunset transition. The effect on phase and amplitude of the mode conversion signal may be obtained by considering the phasor diagram. The following analysis is valid whether the shadow lines pass the transmitter or the receiver first. Let the phasor E, represent the signal due to first mode propagation throughout the path length, and E, the signal due to first mode propagation in the daytime waveguide which is converted to or from second mode propagation in the night-time waveguide. Crombie points out that the phase 6 of signal E, with respect to E, is the difference in phase delays at the receiver, so neglecting a possible constant factor and assuming a discontinuous height change of the effective reflecting layer at a shadow line,
where d, is the length of path in the night-time region, and 1, and 1, are the wavelengths of the first and second modes respectively in the night-time waveguide. Since R, is greater than 1, for the night-time ionosphere height (WAIT, 1962), the phase 13decreases during sunrise when d, is decreasing, and increases during sunset
V.L.F.
75
propagation over long paths
when d, is increasing. To obtain the total phase variation, we the variation of the phase 4 of signal E,. This first mode phase to change approximately linearly with time during sunrise and since the velocities of the shadow lines along the three paths During night-time and daytime, when there latively constant. across the path, the mode conversion signal cannot be present.
must also consider would be expected sunset transitions, considered are reis no shadow line
0
Phase advance
Fig. 1. Mode conversion interference for E, < E, at sunrise.
advance
Fig. 2. Mode conversion interference for E, >
E, at sunrise.
Figure 1 shows the sunrise case when the amplitude of the signal E, is less than that of E,. As 0 decreases, it can be seen that the amplitude of the resultant shows a sinusoidal perturbation. Further, a periodic phase variation is superimposed on the linear first mode phase increase, enhancing this increase at amplitude minima and tending to cancel it at amplitude maxima. Thus the phase change during a transition in which the mode conversion signal E, is present tends to occur in steps, each swift phase change corresponding to an amplitude minimum. Examples of this effect are shown in the experimental records, for instance, in Fig. 3 at sunrise. Figure 2 illustrates the sunrise case when the amplitude of E, is greater than that of E,. Here the resultant signal shows a rapid decrease of phase at an amplitude minimum rather than a rapid advance. Comparing the locus of the resultant phasor with the locus of the phasor E, between consecutive maxima at OA and OB, it can be seen that the resultant signal has suffered a cycle loss relative to the first mode signal. Hence when the mode conversion signal is larger than the first mode signal during sunrise, amplitude minima are accompanied by fast phase retardations, each retardation representing one cycle loss. The experimental records also show this effect, for example, in Fig. 6. Similarly, at sunset, the presence of a mode conversion signal causes the phase decrease to occur in steps, each fast phase retardation accompanied by an amplitude minimum. If the mode conversion signal becomes larger than the first mode signal, a fast phase increase occurs at the time of an amplitude minimum and a cycle gain is registered.
A. B.
76
(I).
KAISER
To calculate the period of mode conversion interference use is made of formula Between amplitude minima 0 must change by 277. Hence, Ad
A0 =2rr = 25r
N
where Ad, is the change in length of the night-time path in the time At between minima. If u is the time average velocity of the shadow line along the path during time At, AdN = uAt so At
44
=
u(A, - A,)
e.(!g_ !y
(2)
where c is the velocity of electromagnetic radiation in free space, f the frequency of the signal, V,, and V,, the night-time phase velocities of the first and second modes respectively. In many cases u may be taken as constant throughout the transition ; then At Yjd[vrTc
(3)
‘F)
where d is the total path length and T the total time for the transition. The presence of the third and higher modes in the night-time Earth-ionosphere waveguide could complicate the observed interference pattern. From an approximate formula for phase velocity given by WAIT (1959) it can be seen that V N3 ---
vmc
4!+!&)
c
where V,, is the night-time phase velocity of the third mode. Hence interference between the first mode signal and the converted third mode signal would be twice as fast as interference due to the converted second mode signal E,. The effect of the third and higher modes during transitions would be to produce fast interference. The severity of mode conversion interference depends on the attenuation of second mode compared to the first as the two modes propagate in the night-time waveguide, as well as the mode conversion efficiency at the shadow line. The presence of mode conversion interference is not dependent on the total path length; it should occur for even the longest paths when only a small length of the path is dark, provided that the shadow line mode conversion is efficient. Unconverted second and higher modes
There may be a signal obtained at the receiver due to second mode propagation throughout the path length. This signal, unlike. the shadow line mode conversion signal, would be present continuously, but should be insignificant at great distances in daytime as it is then highly attenuated. BATES and ALBEE (1965) have recently shown
that the second
mode
can propagate
strongly
over
9000 km from
NBA
77
V.L.F. propagation over long paths
(18 kc/s) to Europe. If some unconverted second mode were present during a transition it would cause interference of period At
N
Tc
(4) i
where Vn, and Vn2 are the daytime phase velocities of the first and second modes respectively. In deriving this formula the same ideal conditions as for the mode conversion case have been assumed. The unconverted second mode phase increases faster at sunrise than the first mode phase ; by considering the phasors it can be deduced that rapid phase increases at sunrise and decreases at sunset will occur at amplitude maxima, as indicated by CROMBIE(1964). Furthermore, this unconverted second mode may produce cycle gains at sunrise and cycle losses at sunset, having the opposite effect to the mode conversion signal. Since the second mode is highly attenuated in the sunlit Earth-ionosphere waveguide, the interference will be most discernible at the end of the sunset transition and the beginning of the sunrise transition. For frequencies greater than 20 kc/s and path lengths less than 10,000 km the period is comparable to the total transition time, so that this simple multi-mode interference would not be expected to be as noticeable as mode conversion interference of shorter period. As for the mode conversion case, modes of higher order than the second would be expected to produce faster interference. Whistler mode
Whistler mode signals would not be expected to be significant except perhaps where the receiver is near the magnetic conjugate of the transmitter. For the three stations monitored, this condition is most closely satisfied for the transmitter NPG Seattle, whose conjugate point is approximately 2500 km from Lower Hutt. Allcock (private communication) has received whistler mode signals at Lower Hutt from NPG (18.6 kc/s) having up to 50 per cent of the amplitude of the sub-ionospheric signal. Such high amplitudes are, however, rather rare. Since whistler mode signals have frequency shifts of up to one or two parts in 105, their effect is usually to produce small and very fast fluctuations in amplitude and phase of the total signal. Long path propagation
BURTT (1963) suggested that the irregularity of phase curves of NBA received at Lower Hutt was due to long path interference. THOMSON et al. (1963), receiving NBA at Sydney, demonstrated that the long path signal became dominant when the short path was sunlit, showing that the attenuation at 18 kc/s was greater in the sunlit than in the dark Earth-ionosphere waveguide. THOMPSON et al. point out that this long path reception, despite the long path length being nearly twice the short path length, demonstrates the non-reciprocity of E-W v.1.f. propagation proved theoretically by BARBERand CROMBIE(1959). Considering propagation by the first mode alone, both the short and the long path signals should show a trapezoidal phase variation. During daytime and nighttime over the short path the sunrise and sunset shadow lines will both be moving
A. B. KAISER
78
along the long path. While this is happening the fraction of the long path in darkness is approximately constant, so the phase of the long path signal is also constant. During short path sunset, that is, as the sunset line moves along the short path, the sunrise line moves along the long path at the same velocity. The long path phase trapezoid is therefore just the short path trapezoid inverted, both trapezoids having approximately the same depth Au. Hence at each transition the phase of the long path signal changes by 2Au with respect to the short path signal, so that 2 Au cycles of multi-path interference occur (Aa being measured in cycles). Then the time for one cycle of interference is
At=
a
2ua’
For uniform velocities of the shadow lines along the paths, this gives the period of multi-path interference during a transition as T
At = 2Aa
(‘3)
where T as before is the duration time of the transition. The presence of the long path signal may make the measurement of Aa difficult, but it can be estimated using an empirical formula given by BLACKBAND(1964), which may be put in the form
.fax
ha = ko
7.87 x 1O-9 cycles.
Here k(f) is a correcting factor depending on frequency, various values of which are listed by Blackband. Formula (5) has been derived considering only the first mode ; the presence of higher order modes would complicate the interference and render the formula invalid. In the phasor diagram the long path signal may be represented by a perturbing phasor which counter-rotates about the head of the first mode phasor during transitions. Hence multi-path interference during transitions is of the same pattern as that produced by the mode conversion signal: amplitude minima occur at the time of rapid phase changes, the direction of the phase change depending on whether the short or the long path signal is greater. 3. INTERPRETATION OF RECORDS NPa: (18.6 kc/s) The diurnal phase variation of signals from NPG (18.6 kc/s) is usually trapezoidal with some perturbation at sunrise, as shown in Fig. 3 for May 29 1965. The interfering signal must be decreasing in phase with respect to the first mode signal since the sunrise phase increase is enhanced at amplitude minima. The period observed is consistent with mode conversion interference but not with multi-path interference. For instance, in June 1965 three rapid phase advances were clearly seen at sunrise, the first two being separated by an average of about 100 min, and the last two (at the end of the transition) by about 80 min. Since for the path NPG to Lower Hutt it is reasonable to take the sunrise line velocity along the path as constant,
V.L.F. propagation over long paths
79
formula (3) may be used to calculate the period of mode conversion interference. WAIT (1962) has calculated the phase velocities of the first and second modes for a sharply bounded ionosphere and perfectly reflecting Earth, neglecting the Earth’s magnetic field which should have only a small effect on phase velocity. Taking the night-time height of the reflecting level as 90 km and the transition time as 470 min at this height, the period of sunrise mode conversion interference in June is given as 86 min.
4
Fig. 3. Phase and amplitude of NPG (18.6 kc/s). In a similar way the period for two-path interference may be estimated from formula (6). The phase change from night to day Aa is approximately 1.6 cycles, so that the period is 145 min for June. This confirms that the sunrise interference is due to mode conversion. The interference is greatest when the transition is longest (in June) and not discernible at all when it is shortest (in December), suggesting that mode conversion is most efficient at a shadow line which is normal to the direction of propagation. Since no interference of period 43 min is discernible, the excitation of the third mode at the sunrise line would seem to be negligible. occasionally a cycle loss is recorded at At 18.6 kc/s cycle slips are uncommon; about the middle of the sunrise transition where on most days a fast phase advance occurs. No clear evidence of mode conversion interference can be found at sunset even when the transition is slowest.
NPG (24 kc/s) MCNEILL and ALLAN (1965) have indicated that cycle slips are frequently observed for 24 kc/s signals from NPG. However, the offset of the local oscillator from the transmitted frequency was only about 2 parts in lo8 when these records were taken (January-May, 1964), so the interpretation of the best trace is in some As shown in Fig. 4, at sunrise there are rapid phase advances instances ambiguous. where the frequency of the received signal may temporarily become greater than
A. B.
80
KAISER
(‘overtake’) the frequency of the local oscillator. When this happens an oscillation referred to as an ‘overtaking’ beat is produced on the beat trace. This overtaking beat, which if counted produces a spurious cycle slip in the phase curve, may resemble a beat representing a genuine cycle slip. The confusion may be heightened
0
c.3 -I a? b
5
f
-2
,--_ : .I
I
h
,t-’ , May 28 1964 ,* I'
/'
Cycle loss
A-: ,
tude I 0
2
4
6
I 8
I IO
I 12
I I4
I 16
I 18
I 20
-
22
U.T.
Fig. 4. Phase and amplitude of NPG (24 kc/s).
by the large amplitude fluctuations. For the days illustrated in Fig. 4, however, a unique interpretation may be made. Since NPG ceased transmission at 24 kc/s in May 1964, further investigation at this frequency has not been possible. The interference pattern at the end of the sunrise transition (the last two amplitude minima) is well-defined during May and is consistent with mode conversion interference. It is difficult to determine the precise times of the sharp phase advances from the beat records, but averaging over 13 days in May the time between the last two sharp phase advances is 78 min. For May, the transition time T is 420 min at a height of 70-90 km, and Wait gives (V&c) - (VxJc) as 0.0055 for an ionosphere height of 90 km. This difference in phase velocities is not very sensitive to the value of night-time ionospheric height assumed. According to formula (3), therefore, the period of mode conversion interference is 82 min, which compares favourably with the experimental value above. However, the period of interference earlier in the transition is variable, usually being greater than 82 min.
V.L.F. propagation over long paths
81
According to WAIT (1962), at 24 kc/s the second order mode should be more significant than at 18.6 kc/s. Comparison of the May 1964 records at 24 kc/s with the May 1965 records at 18.6 kc/s shows that this is indeed the case. At 18.6 kc/s no cycle slips occurred in May, but at 24 kc/s several days gave a cycle loss at sunrise as shown for May 28 in Fig. 4, indicating that the second mode signal became greater than the first mode signal. In general, the interference would be expected to be most severe at the end of the transition, since the further the second mode propagates the more it is attenuated with respect to the first mode. Nonetheless, in each instance the sunrise cycle loss occurs at about mid-transition when the sunrise line, at which the second mode is excited, is about 6,000 km from the receiver. A plausible explanation is that the first mode signal reaches minimum amplitude at about mid-transition. Then the second mode propagating in the night-time waveguide with an attenuation similar to that of the first mode may produce the observed sunrise interference. BATES and ALBEE (1965) explained the low night amplitude and anomalous trapezoid depths observed for two paths in terms of destructive interference between the first and second modes at the receiver. These paths were both under 5,000 km, but in view of the strong second mode propagation at night found by BATES and ALBEE (1965), and also revealed by the timing of sunrise cycle losses for the NPGLower Hutt path, it might be expected that the effect would be observed at large The night-time decrease of amplitude which occurs for most days in distances. April and May 1964 for the 24 kc/s signals (as shown for May 12 and May 28 in Fig. 4), and which is also observed to a lesser extent on the 18.6 kc/s records, suggests that at each frequency a second mode signal destructively interferes at night with the first mode signal. This amplitude decrease is irregular and variable from day to day, but it tends to start about 2 hr after 70 km sunset at Lower Hutt and end just before sunrise at Seattle. For instance, on some days such as May 12 1965, the phase appears to stabilize at 2.4 cycles before the interfering signal decreases the These night-time changes suggest that amplitude and deepens the phase trapezoid. the ionospheric reflecting layer is still changing some time after it has ceased to be illuminated. If an unconverted second mode were present at sunrise, formula (4) gives its period of interference as about 280 min in May for 24 kc/s and 115 min for 18.6 kc/s, where phase velocity values given by WAIT (1962) for an ionosphere height of No clear evidence indicating the presence of 70 km have been used for daytime. this simple second mode signal during transitions has been found ; it seems to become significant only when the path is entirely dark. No cycle slips have been identified at sunset, but evidence of interference is found when the sunset transition is long, that is, when the sunset line makes a large angle with the path. Figure 5 shows the amplitude of beats at sunset and the time The apparent frequency shift of the received signal is between beat maxima. indicated by the shortening of the beat. Considerable variation is shown from day to day, but frequency fluctuations of similar period to those on February 7 are shown for several other days in early February. Consistently a large frequency shift (which means a rapid phase decrease) accompanied by an amplitude minimum occurs at about mid-transition. The period of the frequency fluctuations is that
A.
82
B. KAISER
expected from the presence of a mode conversion signal, and as at sunrise, the interference is most severe at about the middle of the transition. CROMBIE (1964) found that for two W-E paths interference was more pronounced at sunrise than at sunset. For these paths at sunrise, a second mode signal excited at the transmitter was converted to a first mode signal at the shadow line. Mode conversion interference is also most severe at sunrise for the E-W paths studied in this paper, although the mode conversion at sunrise is of the same type as at sunset
U.T.
Fig. 5. Length and amplitude of beats at sunset for NPG (24 kc/s) on February 7 1964.
on W-E paths. In both these cases, a first mode signal propagating in the sunlit waveguide is partially converted to a second mode signal at the shadow line. Hence mode conversion of either type is more efficient at the sunrise line. WWF_,5 (20 kc/s) Signals from WWVL and NPG show similar characteristics, since the transmitters are both at approximately 12,000 km from Lower Hutt with a difference of only 14” in their bearings. Phase and amplitude plots shown for July 16 in Fig. 6 are typical ; on a majority of days throughout the year the mode conversion signal produces a cycle loss at the middle of the sunrise transition. The period of interference between the cycle loss and the following rapid phase advance is rather longer than expected theoretically, but the period between the last two phase advances is in better agreement. This variation in period, which is also observed for NPG at both frequencies, cannot be explained using the simple bi-modal model described in Section 2. On a few days such as August 2, 1965, the mode conversion signal apparently produces an effect throughout the entire sunrise transition. As for NPG, a significant second mode signal would therefore be expected at night. In contrast to NPG, the average night amplitude for WWVL is usually greater than the day amplitude, but like NPG, the amplitude tends to be smaller at the middle of the night than just after sunset or just before sunrise. During the day when the path is entirely sunlit the amplitude is far less erratic than at night. In contrast to the night-time pattern, there is a slight tendency for the amplitude to continue to increase after sunrise and start to decrease before sunset, as though it were slightly dependent on the Sun’s zenith angle. At no time during the year is mode conversion interference clearly seen at sunset.
V.L.F. propagation over long paths
83
0
I
-I
d
-2 i
I o-
o-
4
b -I
!
-
-2 -
1. .
0
Fig. 6. Phaseand arnpliut:de of WWVL (20 kc/s). NBA
(18 kc/s)
The bearing of the transmitter NBA from Lower Hutt is 41” E of WWVL, so that from E/W non-reciprocity the long path signal from NBA should be considerably larger than that from WWVL or NPG. The oscillator used for the 1961 NBA records gave a fast beat rate, which gives good amplitude information, but poor phase plots. An amplitude record is shown in Fig. 7 for July 8-9, 1961. For the 1962 and 1963 records the local reference was an Essen-ring oscillator giving a slower beat rate. The sunset amplitude pattern is seen throughout the year, though the third minimum is sometimes indiscernible. The occurrence of a cycle gain at sunset shows that the unconverted second mode signal cannot cause the interference. The periods of interference expected from the long path and mode conversion signals in July are now calculated. The average depth of trapezoid for NBA for 12 phase curves in 1962 is l-6 cycles, and Blackband’s formula (7) predicts a depth of about 1.65 cycles. Taking the transition time as 340 min and assuming a constant velocity for the sunset line along the path, (6) gives the period of multi-path interference as 106 or 103 min. The sunset amplitude variation for July 1961 has a period of nearly 2 hr, so that it does seem likely to be multi-path interference. The greater length of the second
A. B. KAISER
84
cycle of interference is not surprising since the velocity of the shadow lines along the paths is actually somewhat greater at the beginning of the transition than at the end. Wait’s phase velocity values give the period of sunset mode conversion interference as 60 min for a transition time of 340 min, confirming that the long path signal is primarily responsible for the sunset interference. July
8-9
1961
ai : n.
Ground
w
1,
2-
January
II-12
sunset
1962
I
I
I
I
I
16
I8
20
22
24
I
I
2
4
.-\ 6
, 8
U.T.
Fig. 7. Phase and amplitude of NBA (18 kc/s).
At sunrise the position is more complex and variable. Sometimes three minima like those at sunset are observed, but usually the amplitude pattern is irregular. For July, multi-path interference should have a period of about 160 min, and mode conversion interference about 90 min. The apparent period of interference at the start of sunrise is often approximately the expected mode conversion period, as for July 8-9. It is suggested that both the long path and mode conversion signals are significant at sunrise. A typical phase plot is shown for January 11-12, 1962. Here the long path signal predominates at the first sunset minimum and a cycle gain occurs. These cycle gains are common, and on occasions a second cycle gain is recorded at the second amplitude minimum. Sunrise cycle slips appear to be far less frequent than sunset cycle gains. It is interesting to note that THOMPSON et al. (1963) also found that the long path signal tended to predominate for longer at short path sunset than at sunrise, resulting in phase accumulations for some days. A possible cause of this asymmetry of cycle slips is greater attenuation of a v.1.f. signal as it passes a sunset shadow line than a sunrise line. 4. CONCLUSIONS
Severe interference has been observed for signals from NPG (18.6 kc/s and 24 kc/s) and WWVL (20 kc/s) during the sunrise transition. This interference has been explained using Crombie’s model of mode conversion at a shadow line. It has been
V.L.F. propagation over long paths
85
shown how the mode conversion signal may produce the frequent cycle losses recorded at mid-transition. Comparison of the 18.6 kc/s and 24 kc/s records from NPG shows that mode conversion interference is more severe at the higher frequency. Mode conversion interference at sunset has been clearly identified only at 24 kc/s; comparison with CROMBIE’S(1964) results for W-E paths indicates that mode conversion is more efficient at the sunrise than the sunset shadow line. The evidence also suggests that mode conversion is most efficient when the shadow line is normal to the direction of propagation. Support is given to the conclusion of BATES and ALBEE (1965) that second mode propagation over long paths is more significant than formerly accepted; the observation that the mode conversion signal is often larger than the first mode signal when the sunrise line is about 6,000 km from Lower Hutt shows that the second mode signal propagates in the night-time waveguide with an attenuation comparable to that of the first mode for the frequencies 18.6-24 kc/s. Hence the second mode signal would be expected to be significant at night and could be a factor in causing the low night-time amplitude noticeable for NPG at 24 kc/s. However, the similarity of the night-time amplitude variations for each case also suggests a regular pattern of ionospheric change between sunset and sunrise. It is found that the unconverted second mode signal does not become significant until after completion of the sunset transition and it does not appear to produce any effect after sunrise has begun. It has been shown that during transitions the long path signal produces interference similar to that due to the mode conversion signal but of a different period. Although for NPG and WWVL the long path signal was not discerned, severe multi-path interference was observed for the NBA to Lower Hutt path. Since all three paths are of approximately the same length, the dependence of the E/W attenuation ratio on the angle between the path and the Earth’s magnetic field is clearly shown. The long path signal from NBA was observed to produce cycle gains at sunset, while at sunrise both multi-path and mode conversion signals were present to produce complex interference. REFERENCES BARBER N. F. and CROMBIE D. D. BATES H. F. and ALBEE P. R. BLACKBAND W. T. (Ed)
1959 1965 1964
BURTT G. J. CROMBIE D. D. CROMBIE D. D., ALLAN A. H. and NE-AN M. MCNEILL F. A. and ALLAN A. H. THOMPSON A. M., ARCHER R. W. HARVEY I. K. WAIT J. R. WAIT J. R.
1963 1964 1958
and
1965 1963 1959 1962
J. Atrnosph. Terra Phye. 16, 37. J. Geophys. Res. 70, 2187. Propagation of Radio Waves at Frequencies below 300 kc/s, Pergamon Press, Oxford. Proc. In&n Elect. Engrs 110,1928. J. Res. NBS/USNC-URSI 68D, 27. Proc. In&n Elect. Engrs lOSB, 301. J. Geophys. Res. 70, 731. Proc. In&n Elect. Electron. Engr8 51, 1487. Proc. Inst. Radio Engrs 47, 998. Electromagnetic Waves in Stratified Media, Pergamon Press, Oxford.