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.