Comment on “Worldwide extremely low frequency magnetic field sensor network for sprite studies” by Toby Whitley et al.

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[1] Whitley et al. [2011, hereinafter paper 1] contains promising experimental data: the ELF records with known source (the TLEs) coordinates and the exact time of events. Pulses were recorded with the GPS time stamps at four observatories at: Eskdalemuir (Scotland): 55.3°N, 3.2°W; Pinon Flat (California): 33.6°N, 116.5°W; Canberra (Australia): 35.3°S, 149.4°E; and Sutherland (South Africa): 32.4°S, 20.8°E. The experimental setup offers a rare possibility of direct comparing of observational and computational data [e.g., Nickolaenko et al., 2008]. We tried to do this, but met problems.

[2] The TLE causing ELF transients took place over the Southern Europe (SPT) and at Africa (LTG). The coordinates of the second event might be found in the text, position of the first TLE can be estimated from the map of Figure 6 in paper 1.

[3] When comparing the model data with the waveforms (paper 1), one immediately notes the experimental early arrival times, see Figure 1 where we present computed waveforms superimposed on Figure 8 of paper 1. The lines with crosses depict computed HWE and lines with dots show the HSN field component. Obvious pulse early arrival suggests finding of relevant propagation velocity V directly from the records.

Figure 1.

Comparison of computed and measured pulses from the sprite event over Africa.

[4] One can derive the source–observer “electromagnetic” distance DE and the velocity V by using two time moments [Ogawa and Komatsu, 2007, 2009]: the arrival time of direct wave tp = DE/V and the arrival time of antipodal wave ta = (LDE)/V. Here, L denotes the Earth's circumference of 40 000 km. Time moments tp and ta from Figures 7 and 8 of paper 1 are listed in Table 1. The velocity and the “electromagnetic” source–observer distance are readily obtained by using obvious relations: V = L/(ta + tp) and DE = L/2 − V (tatp)/2. The results are collected in Table 1. As one may see, it is OK with the signal velocity: it agrees with the estimates similarly obtained from experimental data by Ogawa and Komatsu [2007, 2009] and with the model results [Nickolaenko and Hayakawa, 2002].

Table 1. Signal Velocity Vand the Source-Observer DistanceDE Found Directly From the ELF Records
Propagation Pathtp (ms)ta (ms)DE (Mm)Signal Velocity V (Mm/s)
Africa–Australia649213.846256.4
Africa–California4411111.354258.1
Europe–California4513210.169226.0

[5] Alternative estimate for the signal velocity VS is found by exploiting the “absolute” time of TLE occurrence. For this purpose, one must compute the geometric source–observer distance DG and divide it by the arrival time tp picked from the record: VS = DG/tp. Relevant data are collected in Table 2 together with the wave arrival azimuth AZ.

Table 2. Signal Velocity VS Found From the “Geometrical” Path Length DG and the Arrival Time tpa
Observatorytp (ms)DG (Mm)VS (Mm/s)AZ (deg)
  • a

    Bold font indicates that the signal velocities for the Scotland and California observatories exceed the light velocity.

South Europe TLE Event (SPT) (44.5°N and 4.6°E)
California4511.274250.056.5
Australia8016.856210.7−60.2
South Africa408.698217.5−11.7
 
African TLE Event (LTG) (11.2691°N and 12.114°W)
Scotland114.848440.7−168.5
California4414.281324.631.6
Australia6416.770262.0−138.1
South Africa226.004272.9−39.9

[6] Table 2 demonstrates problems with the LTG event: the signal velocities for the Scotland and California observatories exceed the light velocity (shown by bold font). So, it is OK with the pulse outline and relevant V, but there are problems with their onsets and relevant VS.

[7] After calculating the difference (DGD) of geometric and electromagnetic distances, we find that the value agrees with the commonly accepted accuracy of the Q-burst source location (∼1000 km) only for the Europe–California path. Deviations for the other pairs are almost three times higher.

[8] The internal contradictions in the experimental data become especially obvious when one compares the observed waveforms with computations (see Figure 1). There are records with very good agreement, while simultaneous records of the same event at other observatories do not agree with similar computations. Why?

[9] We must mention here how the waveforms were computed. The time domain solution was used for the ELF pulse propagating in the Earth–ionosphere cavity. The magnetic field waveform is [Nickolaenko and Hayakawa, 2002; Nickolaenko et al., 2004a, 2004b, 2008]:

display math

Here HA is the amplitude, g(t) = exp(it/A) is the time factor, and x = cos θ is the cosine of the source–observer angular distance. Equation (1) corresponds to the linear frequency dependence v(ω) = + B. We used in computations A = (1/6 − i/70)/2π and B = −1/3 relevant to the v(f) = (f − 2)/6 − i f/70 heuristic dependence. We find the west–east and south–north field components by using the wave arrival azimuth shown in Table 2.

[10] Figure 2 compares experimental and the model data for the LTG event (Africa) recorded at Australia. We had to apply the 16.1 Mm source–observer distance to obtain such a good correspondence. The source distance is smaller than the geometrical distance by 677 km (−4%), and particular deviation is within the recognized accuracy of the ELF distance estimates. Every pulse element is recognized in Figure 2: the direct, the antipodal and the round-the-world wave. This is the case of very good reciprocity of observations and model computations.

Figure 2.

Superposition of model and experimental data for the African sprite and Australian record.

[11] Figure 3demonstrates the other case of good correspondence between the observed and model pulses: the SPT event (South Europe) recorded at California. The geometric 11 274 km distance was applied in computations. Again, the direct and antipodal waves are readily recognized combined with some weak activity around the round-the-world arrival time. The waveforms fit well except the amplitude ratio of the field components. The wave arrival angle is 6.5° at California, and the field amplitudes must be of 1/10 ratio. This is so in the model, but it is not so in the record.

Figure 3.

Model data for European sprite and Californian record.

[12] The rest of the “same” pulses recorded at other sites (paper 1) obviously disagree with the equivalent model computations (see Figure 1). Why?

[13] Summarizing, we emphasize that observational data (paper 1) are very interesting and promising. Comparison with publications and the model computations shows sometimes an encouraging correspondence. However, it is impossible to rely on the material as it is right now: there are evident internal inconsistencies in it. Probably, additional tests, comprehensive analysis, maybe, calibrations would be necessary prior to applying the four-station network data in the environmental studies.