1. Introduction
This is not a new topic. East-west asymmetry in VLF (Very Low Frequency;
3-30 kHz) propagation in the Earth-Ionosphere Waveguide had been
inferred as early as the 1920’s [see the historical review byCrombie , 1958]. The geomagnetic control over VLF propagation is
expected to depend strongly on two orientational parameters
[Budden , 1985; Piggott et al. , 1965; Pitteway ,
1965; Wait and Spies , 1960; Wait and Spies , 1964;Yabroff , 1957]. One is the dip angle of the geomagnetic field,
and the other is the propagation magnetic azimuth of the VLF wavefield.
Along any long-range propagation Great Circle Path, both of these
orientational parameters can widely vary. Thus, e.g., it is only very
approximate to characterize the propagation magnetic azimuth ”of the
path” by its value at a path endpoint. The research results we review
below can be broadly separated as to whether they just grossly consider
the whole path together, or whether they dissect the path into small
segments and use a different propagation azimuth and magnetic dip within
each segment. The former we will call ”bucket” approaches, in that they
just characterize the entire path as being effectively at one
propagation magnetic azimuth. By contrast, the model comparisons which
consider the local nature of the two orientational parameters will be
called ”local” approaches.
All studies of the azimuthal asymmetry of VLF propagation prior to the
present have been based on observing the effect of magnetic propagation
azimuth on received amplitudes. This is equally true when the signals
received were from narrow-band artificial beacons [e.g., Bickel
et al. , 1970; Pappert and Hitney , 1988] or when derived from
lightning strokes [e.g., Hutchins et al. , 2013; Jacobson
et al. , 2021; Taylor , 1960]. In the already-published
[Jacobson et al. , 2021] first half of the present study,
henceforth referred to as ”JHB1”, we followed the amplitude-comparison
approach. However, we reached a cul-de-sac with that approach, when we
tried to test a particular non-intuitive though impactful prediction of
our model [Jacobson et al. , 2010; Jacobson et al. , 2009;Jacobson et al. , 2012]. The prediction is that for propagation
at low dip angle, e.g. in the range -30 to +30 deg, propagation toward
the magnetic West is deeply attenuated during dark-path conditions
(night), relative to sunlit-path (day) conditions . Curiously,
this counter-intuitive effect had not been overtly remarked prior to
JHB1, though the physics package of the comprehensive, state-of-the-art
path simulator, LWPC [Pappert and Ferguson , 1986], certainly
contains all the relevant physics.
We found in JHB1 that the sought-after dark-path conditions apparently
caused such a dearth of numerically sufficient lightning detections at
the pertinent stations, so that amplitudes could not be determined with
statistical accuracy. Thus JHB1 could not test its most interesting
model prediction. ”No detection, no amplitude”.
This shortcoming of JHB1 motivated the present study, which is the
second part of the study begun by JHB1. We completely change strategy in
this paper. Rather than comparing amplitudes, we examine observed
statistical patterns of detection/non-detection from ten selected
stations. We compare those patterns to predictions of the model. The
stations are chosen to represent all longitude sectors and all Universal
Times, and to include many diverse paths from the lightning locations to
the stations, in such a manner as to provide compelling statistical
evidence on the model’s predictions. The number of paths included
exceeds 15-billion. Each of these paths is then dissected into 50 path
segments, for a grand total exceeding 750-billion path segments. At each
path segment, the geomagnetic dip angle and magnetic propagation azimuth
are calculated, along with the instantaneous solar zenith angle, are
combined to predict the modeled contribution of that path segment to the
overall integrated attenuation for that path.