2a. Prior observations of east-west asymmetry of VLF
propagation
Here we review the carefully documented work that began in the 1950’s.
Crombie described new measurements performed in New Zealand during 1957
[Crombie , 1958], one purpose of which was to investigate the
asymmetry earlier hinted at by the scattered results of the 1920’s. The
16.6-kHz signal from a powerful transmitter (”GBR”) in Rugby, UK was
received by a magnetic loop and a vertical aerial at Wellington, NZ. The
receiver and the transmitter were nearly antipodal. By rotating the loop
antenna, Crombie was able to select separately the signal arriving on
either Great Circle Path, from respectively NNW or SSE (reckoned at
Wellington.) The signal strength on each orientation of the loop was
measured versus time during three multi-day periods. The results
confirmed not only that the signal arriving from the NNW had 10-15 dB
stronger amplitudes than the path arriving from the SSE, but also that
the diurnal variations were dissimilar between the two paths. Crombie
attributed this difference to the east-west components of each path,
although this was left notional. The detailed variation of the magnetic
azimuth along each path was not presented or addressed, so that
Crombie’s work was in the ”bucket” category. The diurnal variation was
not explained, but the gross difference between eastward and westward
propagation was noted.
Shortly after the work by Crombie, there was a systematic attempt to use
geolocated lightning to observe the zonal asymmetry of long-range
broadband VLF propagation [Taylor , 1960]. Whereas Crombie had
relied on a discrete, narrow-band, man-made beacon, Taylor exploited the
powerful broadband emissions of lightning return strokes. Attention was
focused on daytime conditions, with most of the paths over seawater. VLF
receiver stations in the western United States and in Hawaii, triggering
off common lightning strokes, were used to crudely geolocate the
lightning, at least within <10% of the path length, by
triangulating the direction found at each station. Each station measured
and recorded the vertical electric field with a vertical mast, and also
provided the direction of arrival from comparing signals on two
vertical-magnetic-loop antennas. As was necessary in that era, data were
recorded for off-line analysis using oscilloscopes and cameras. The
east-to-west attenuation from twenty lightning discharges was used to
determine a mean spectral attenuation (dB/1000km) for that direction of
propagation. The spectral attenuation was determined for the entire VLF
band. Similarly, the spectral attenuation for west-to-east attenuation
was determined using sixteen lightning discharges. All observations were
for entirely-daylit paths. It was found that attenuation east-to-west
exceeded attenuation west-to-east, by approximately 3 dB/1000km for f
< 8 kHz and by approximately 1 dB/1000km for f >
10 kHz.
Taylor’s characterization of the paths as ”east to west” versus ”west to
east” [Taylor , 1960] is in the bucket category. Moreover
Taylor did not consider the control by geomagnetic dip angle; rather,
all the paths were simply tagged as ”east to west” or as ”west to east”,
regardless of magnetic dip, and then simply labeled with one
orientation. The lightning locations are not given [Taylor ,
1960], so it would not be possible to retrospectively model Taylor’s
observations with a more local approach.
In 1969, the United States Naval Ocean Systems Center conducted airborne
measurements of VLF beacon signals on Great Circle Paths from the island
of Hawaii toward San Diego and from the island of Hawaii toward Wake.
The paths were, respectively, west-to-east and east-to-west paths,
entirely over seawater, and entirely nighttime. These data were later
presented and compared [Pappert and Hitney , 1988] to
state-of-the-art, full-wave waveguide propagation calculations using the
LWPC [Pappert and Ferguson , 1986]. The fixed frequencies of
the beacons at Hawaii were discretely between 10.9 kHz (the lowest) and
28.0 kHz (the highest). The airborne receiver recorded signal amplitudes
due to the multifrequency sounder for the first ~4000 km
of each path. Thus the measurements were all done within 4000 km of
Hawaii. The VLF data were compared to a model that included detailed
tracking of the propagation azimuth and the magnetic dip angle locally
at all points along the propagation path. This was a local approach, and
was a critical advance over the bucket approach. It was found that the
eastbound (San Diego path) signal was very reproducible day-to-day, and
was essentially perfectly modeled by LWPC with a generic nighttime
profile [Pappert and Hitney , 1988]. The westbound (Wake path)
signal, by contrast, was more variable day-to-day, and this adversely
affected the agreement with the model, although on average the agreement
was satisfactory. The variability for westbound propagation was
speculated to be related to sporadic electron-density features near
altitude 90 km. We note that the sampled paths did not delve lower than
about 30 deg in dip angle.
In addition to the airborne measurements using the multifrequency
beacon, the same aircraft was also deployed to measure the signal from
the unique 23.4-kHz signal ”NPM” radiated from the area of Honolulu,
Hawaii with much higher power than the research multifrequency beacon.
The NPM signal was measured along Great Circle Paths from NPM toward
Seattle, Ontario (California), Samoa, and Wake Island. Results were
reported [Bickel et al. , 1970], similarly, out to
~4000 km range, and were entirely over seawater and at
night. The authors [Bickel et al. , 1970] used an early
predecessor of LWPC to compare with waveguide theory, and found that the
model predictions of dependence on magnetic azimuth and magnetic dip
angle were robustly confirmed at 23.4 kHz by the airborne measurements.
Their model comparison was a local approach, exactly similar to that
used for the multifrequency beacon data [Pappert and Hitney ,
1988].
A more recent entry into the observation of propagation magnetic-azimuth
asymmetry was done with the World Wide Lightning Location Network, or
WWLLN [Hutchins et al. , 2013]. It dealt with over-seawater
paths in the Pacific sector, using WWLLN stations at island locations
Suva, Tahiti, and Honolulu. This study is in the ”bucket” category. The
study used lightning strokes jointly detected by all three of those
stations (along with other stations as well.) Each lightning stroke’s
radiated VLF energy was determined with the WWLLN energy retrieval
described elsewhere [Hutchins et al. , 2012]. The candidate
strokes were selected according to the following strict limiting
criteria:
(a) The WWLLN VLF energy determination for the stroke needed to have an
estimated error less than 10% of the VLF energy.
(b) The stations participating in the location/energy determination
needed to be equally distributed east/west of the stroke location, to
within 25%.
(c) The strokes were limited to those for which the three paths to Suva,
Tahiti, and Honolulu were all either less than 5% daylitor more than 95% daylit.
The strokes were selected from those occurring from May 2009 to May
2013. With these criteria, only 0.2% of the stroke population was
accepted, that is, only 2X106 strokes were accepted.
The high-confidence energy retrievals for the 2X106accepted strokes allowed each of these stroke’s ”normalized electric
field” to be derived for each stroke, so as to use all the strokes
despite their widely differing stroke VLF energies [Hutchins et
al. , 2013]. The normalization was the rms measured electric field (in
units of µVm-1) divided by the square root of the
retrieved VLF energy (in units of J). This normalization was tabulated
for each of the strokes as the electric field in dB above 1
µVm-1J-1/2.
The 2X106 accepted strokes were grouped into
azimuth/distance bins, with eight azimuth bins, each 45 deg wide, and
distance bins 500 km wide. The azimuth was the average magnetic azimuth
over the path, which is approximate, as the azimuth actually varies
along each path. Within each bin, the bin median was used to show
variations versus distance and azimuth. In order to highlight azimuthal
variation, each attenuation rate was normalized by an ”all-azimuth”
average. Thus the normalized-attenuation data vary azimuthally with a
mean of unity. The normalized-attenuation data were compared to the
standard theory of idealized sharp-boundary reflection from a magnetized
D-layer [Wait and Spies , 1960]. The agreement between the
WWLLN results and the sharp-boundary model was rather good [see Figure
5 in Hutchins et al. , 2013]. In part this agreement may be
fortuitous. The model uses simply a sharp-boundary ionosphere, which is
a problem. Moreover, the model did not explicitly treat “day” or
“night”, but rather tried two electron densities. However, the cited
model stuck with 2X107 s-1 as the
fixed collision electron-neutral rate in the case of either of those
electron densities, so they really do not illuminate the difference
between night and day reflection conditions. Another cause for caution
at the good agreement between the model and the data is that the model
was for dip angle of 0 deg, whilst the range of dip-angle magnitude in
the paths in the WWLLN study was 0 deg to ~45 deg.
Therefore it is not ruled-out that the good agreement of the Wait model
and the WWLLN data may have been partially fortuitous.
The legacy results cited above concern direct measurements of the VLF
amplitude. We now mention a different set of observations in which
east-west asymmetry, or ”non-reciprocity”, was revealed: The several
observations of VLF modal interference for narrow-band transmissions.
Here for brevity we mention only a few of these reports, because our
case (broadband emissions from lightning) has wide enough bandwidth to
essentially wash-out any mode-interference effects. WWLLN’s passband of
useful VLF energy is roughly 5-20 kHz [see, e.g., Figure 2.2 inHutchins , 2014]. This mixes interferences of different spatial
scale, so that the net result is washed-out.
An early series of measurements on modal interference [Crombie ,
1966] documented markedly different modal-interference wavelengths for
several discrete frequencies from 18 to 24 kHz. A more recent study
[Samanes et al. , 2015] lacked westward paths and thus could
not address this non-reciprocity issue. An even more recent study
[Chand and Kumar , 2017] did not yield unambiguous results on
non-reciprocity.