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.