- Email: [email protected]
ELF sferics
Peigamon
Recent findings on VLF/ELF M. Hayakawa,*
K. Ohta,l_ S. Shimakura$
sferics and K. Babat
* Sugadaira Space Radio Observatory, The University
of Electra-Communications. Chofu Tokyo Japan t Department of Electronic Engineering, Chubu University. Kasugai Aichi 487. Japan $ Department of Electrical and Electronic Engineering. Chiba University. Chiba 263. Japan (Rtwicrd
inJinulform
19 Mu!, 1994
; acwptetl27
Junr
I83
1994)
AbstractPmOur recent activity on VLF/ELF sferics The first is a sophisticated second part, for whistlers)
15 reviewed, and this paper is composed of two parts. new method of estimating the propagation distance and ionospheric reflection height by using signal processing for the dispersive tails of tweek sferics near the cutoff frequencies. In the we have carried out the first attempt to apply our field-analysis direction finding (developed experimental results and their interpretation are presented. to tweek sferics ; the corresponding
The present section proposes a newt method to determine, with sufficient accuracy, the ionospheric height and the characteristics of the Earth--ionosphere waveguide affecting the propagation of sferics. We discuss the effectiveness of our method by obtaining the location of sferics and ionospheric height from data simultaneously obtained at two or three observing stations.
1. INTRODL’CTlON
VLFiELF sferics are considered to be a very important component constituting the terrestrial electromagnetic environment in the lower frequency range. VLF!ELF sferics originate in lightning discharges and propagate in the Earth-ionosphere waveguide (Outsu, 1960), and they were used to study the characteristics of distant lightning and also the lower ionosphere (Al’pert et (11. 1970). Recently, an extensive investigation of the lower ionosphere has been undertaken with VLF transmitter signals, by making full use of the advantage of their known location, frequency, power, etc. The disadvantages of VLF/ELF sferics, their unknown and sporadic occurrence, were stressed, and the importance of VLF/ELF sferics seemed to be in decline. However, by giving new ideas to these old VLF/ELF sferics, the merits of VLF/ELF sferics, such as their world-wide occurrence, their wide-band structure and so on, should be stressed. In this paper, we indicate a few examples in this direction carried out by our group.
2. LOCATION BY USING
OF DISTANT THE TAILS
LIGHTNING
DISCHARGES
OF TWEEK
SFERICS
Sferics are VLF/ELF electromagnetic waves propagated in the Earth-ionosphere waveguide (Budden, 1961 ; Wait, 1972) originating in lightning. Figure I illustrates an example of the dynamic spectra of sferics and a resultant whistler. The mode equation for the Earth-ionosphere waveguide propagation is expressed by the following equation (Wait, 1972). R, (0).
R,(H)
exp (-- i2koh
cos 0) = exp
I -- ihn). (1)
This equation is based on the assumption of the model of a flat Earth and an ionosphere, of height 17, and an incidence angle, H. R,(Q) and R,(B) are the reflection coefficients from the ionosphere and ground. respectively. The ionosphere is assumed to be sharply bounded at the effective height, h (this sharp boundary approximation is good at night) ; this h is the average value over the propagation path. k,,( = C!J/C) is the propagation constant in free space. (U the angular wave frequency, and c the velocity of light; II is the mode number. Solving equation ( 1) yields
Tweek sferics are VLF/ELF waves which are observed very frequently during the night over the whole year (Outsu, 1960) ; they are utilized to investigate the lower ionosphere and to locate the lightning. However, no effective analysis method for the dispersion effect of tweeks has been developed (Outsu, 1960). and so their usage is not great. 467
M. Hayakawa E/ ul
468
Fig. 1. An example of dynamic spectra of the causative sferic (A) and the corresponding whistler (B) observed at Zhanjiang.
cose=E+ip koh
A koh cos 8
(n= 1,2,3...),
(2)
x(t)
= Ca&) k
cm { 2nfc &qJ+@~k(l’i.
with
(5)
where N, and Ng are the values of refractive index of the ionosphere and ground, respectively. We can reasonably assume that the ionosphere and ground are perfect conductors. Then, the propagation constant in the horizontal direction kOsin 0 can be expressed as follows under the condition that 2 IQ/k& < 1- (nr&h)2, k ,,sinO=k,-,[{l-($)ljl/*
-i&{l-($r”*].
(4)
Then, we are able to obtain the group velocity vg of the nth order mode of the sferic, its propagation time T, at an angular frequency w and then the instantaneous frequency at the propagation time T,. Integrating the instantaneous frequency leads to the phase Q(t) at the time t. When we take into account the temporally slowly varying amplitude a(t) and phase Qo(t), the sferic signal (in the nth order mode) propagating in the Earth-ionosphere waveguide, x(t) is given by the following equation as a sum of a few component waves :
The first term of the phase term in equation (5) represents a component with fast frequency variations in Fig. 1, while the slowly varying components, ok(t) and mok(f), correspond with spectral broadening. 2.2. Principle of estimating the ionospheric height and the propagation distance of sferics
As seen in Fig. 1, the duration of sferics is very short, in a range from a few tens of ms to about 100 ms, and the frequency change over this duration is as fast as N 10 kHz. When we apply the conventional spectrum analysis to such non-stationary signals with rapidly changing frequency, it is obvious that the spectra exhibit an apparent spectral broadening so that it is extremely difficult to estimate the spectral parameters of the received signals with sufficient accuracy. We now propose a new method. We make a pseudosferic corresponding to the observed sferic, and we mix these two signals, resulting in a nearly stationary signal for which the conventional spectrum analysis is still available. Then, we take only the lower frequency component for the parameter estimation. Figure 2 illustrates the relationship of the observed sferic signal x(t), pseudo-sferic signal R(t) and the resultant signal y(t). The propagation distance and ionospheric height are obtained by least squares fit-
VLF/ELF
sferics
I
Time
Af
Af
(4
@I
Fig. 2. Schematic illustration of the dynamic spectra of an actual sferic signal (the shaded area within the two full lines). the corresponding pseudo-sferic signal (broken line) (in the top panels) and the resultant signal (in the bottom panels).
ting; that is, determining the parameters fn, (cutoff = nc/2h), d (propagation distance) and frequency, t,, (occurrence time) of the pseudo-sferic such that &(Ajjj)’ is a minimum after measuring the error frequency 4fn, at different frequencies of the dynamic spectrum, 4’(t). Figure 3 illustrates the flow chart used to estimate the dispersion parameters of sferics based on the above principle. 2.3. Results,from data observedsimultaneously at three stutions We have been carrying out a synoptic routine observation of wide-band (O-8 kHz) VLF waves, and the
data used here are obtained at Moshiri, Sakushima and Kagoshima (Hayakawa and Tanaka, 1978) from 02.50 to 02.52 LT on 6 April 1984. Figure 1 illustrates an example of the dynamic spectra of VLF signals observed at a different station. It is clear from Fig. 1 that a strong dispersion effect occurs near the cut-off frequency (- 1.7 kHz) of the first order mode of the Earth-ionosphere waveguide. We now discuss the accuracy of the proposed method. If we indicate the error in measuring the instantaneous frequency of sferics as c!$ the errors in estimating the ionospheric height and propagation distance are deduced as follows :
Dynamic Spectra
d-ci+Ad Fig. 3. The flow chart ionosphere waveguide.
to estimate the dispersion parameters of atmospherics propagating in the EarthAfm is the difference in the instantaneous frequency between the actual and pseudosferic at a particular instant.
470
M. Hayakawa et ul.
sferics) are observed all the time and all over the world ; see Hayakawa and Shimakura (1992) and Shimakura and Moriizumi (1990) for further details. Suppose that the cut-off frequency of the 1st order mode is fnc = 1.7 kHz, the propagation distance is d = 6000 km, and also that the measuring error of the centre frequency at the instantaneous frequency of a sferic (f= 2.5 kHz) is Sf= 20 Hz, then we obtain 6h < 0.7 km and 6d < 40 km from equation (6). The root of the mean squares error of the centre frequency of the spectrum at different frequencies is actually found to be l&20 Hz, and so this method proves to be a very powerful tool to estimate the propagation distance of sferics and the ionospheric height with great accuracy. The accuracy of the present method is much higher than that used by Outsu (1960), but we then have to estimate the accuracy in locating the distant lightning by comparing the results from each pair of stations (Moshiri-Sakushima, SakushimaMoshiri, and Kagoshima-Moshiri). Figure 4 illustrates the location of several sferics estimated by each pair of stations (0 : Moshiri-Sakushima, A: Sakushima-Kagoshima, 0 : Kagoshima-Moshiri). The sferic labeled “a” originates close to the line of Japanese islands, and so the three points are separated from each other depending on the relative location of the sferics with the three observing stations. The sferits (c, d, f, h) are more suitably positioned for the exact location due to their relative relation with the observing stations. The distribution of locations of the causative sferics is then obtained, in which each point is taken as the centre of gravity of the three points so determined for each sferic. This map is compared with the corresponding map of the clouds from the Japanese meteorological satellite at 02.00 LT (about 50 min before the time of the whistler observation) and it is found that the locations of sferics fall within the active regions of lightning activity deduced from the satellite. This indicates the effectiveness of our proposed method of analysis.
2.4. Concluding remarks Sophisticated signal analysis has enabled us to deduce the propagation properties of tweek sferics with sufficient accuracy, and we will be able to locate the distant lightning sources with this method even from the simple wide-band data at a few spaced stations. This method is based on waveguide mode theory, which yields the existence of a minimum distance (- l-2 Mm) over which the present method is effective. Also, this method will be extensively utilized in estimating the large-scale D-region ionospheric irregularities on a global scale because tweeks (and/or
3. DIRECTION FINDING FOR TWEEK SFERICS AND THEIR PROPAGATION MECHANISM
Tweek sferics are known to exhibit remarkable dispersions near the cutoff frequencies of the lst- and 2nd-order mode waves, as seen in Fig. I. These dispersion effects are found to fit well with the Earth-ionosphere waveguide propagation theory (Outsu, 1960) and are utilized in Section 2. The previous investigations were all devoted to the analysis of frequencytime spectra of tweeks, and no reports have been published dealing with the detailed wave characteristics (polarization, arrival direction etc.) of tweeks. Hence, the formation mechanism of tweeks such as the reason for their long-enduring tails and the corresponding coupling of sferics to whistlers have been unsolved. The purpose of this section is to present extensive experimental results on the detailed wave characteristics of tweek sferics by means of field-analysis direction finding (Okada et al., 1977), developed for whistler mode waves. Yedemsky et al. (1992) presented some direction finding results based on an analogue system the Okada et al. (1977) method. Instead of their analogue signal analyses, we deal with a digital signal analysis. Then, the physical implications have been deduced by comparing the experimental data with the corresponding theoretical estimation of the propagation in the Earth-ionosphere waveguide, taking into account the ionospheric density profile and the effect of the Earth’s magnetic field. 3.1. VLF observations and direction.finding The VLF data used were obtained in our campaign made in South China (Hayakawa et al., 1990), and three observing stations are used ; (1) Zhanjiang (geographic coordinates 2 1.3”N ; 110.3’E ; geomagnetic latitude lO”N), (2) Guilin (25.3-N, 110.2OE; 14”N) and (3) Wuchang (30S”N, 114.6”E; 19”N). The observation was carried out continuously for 4 h from 00.00 to 04.00 LT during the period of 5-l 1 January 1988. The campaign was intended for the investigation of very low latitude whistlers (Hayakawa et al., 1990), but the data can also be utilized for the study of tweeks. Three field components (two horizontal magnetic and the vertical electric) are measured in a wide frequency range (O-10 kHz) by means of digital recorders. The outputs of three field components are digitized by an A/D converter (12 bits) with a sam-
VLF:ELI-
stems
Geographic I20”E
125
130
471
longitude 155”E
160
165
155”E
160
165
155”E
160
165
16O”E
I65
170
0
b
5
0
15YE
Fig. 4. The distribution
160
of the positions
(a f). 0. MoshiCSakushima;
I65
determined
pling speed of 40 ,ULS. Then, we make the FFT analysis by a microcomputer and we perform the field-analysis direction finding (Okada et al., 1977; Ohta et al., 1984) to estimate the amplitude ratios and phase differences among three components with a frequency resolution of 25 Hz. This field analysis direction finding is known to be effective for any elliptically polarized wave (Okada et al.. 1977).
3.2. Ohsrrcational trristic’s
results
on detailed
wave charac
gf trtreks
Figure 1 was an example of tweek sferics observed at Zhanjiang at 02.44 LT on 5 January 1988. As seen from the figure, the cutoff frequency of the lst-order mode is found to be fi, - 1.725 kHz and the frequency
for the SLXsfencs and 0. Kagoshima--Moshiri.
for each pair of rhe three stations
A, Sakushima+Kagoshima:
component below this,& corresponds to the 0th order mode. The result of field-analysis direction finding for the tweek in Fig. 1 is summarized in Fig. 5. Figure 5(b) illustrates the frequency dependence of the incidence (i) (measured from the zenith) and azimuthal (0) angles of the Ist-order mode component. while Fig. 5(c) refers to the corresponding frequency dependence of the wave polarization (u,(l). In the fieldanalysis direction finding measurement, an elliptically polarized wave is decomposed into TM and TE mode components (see Fig. 5(a)), and the wave polarization p = (u, r) is defined as the ratio of the magnetic field components of two mode waves (see Okada et ui. (1977) for further details.) A right-handed circular polarization is indicated as (u,71) = (0, 1) and 7‘> 0
412
M. Hayakawa L’Ial z (Zenith)
Wave normal
t
direction
ElYS H-1 /
.k bl
(a)
i
...
J x (East)
... ..f( %,.;
i: Incidence angle +: Azimuthal angle
3 :
s 3
2-
Y (NOW
. . . . . . ...*..
.... ??
:
.. . . .
..** . .
.
.
6 e Bl e r&
iL i . I ; .8,. : L-i_ I 45 Incident angle i (deg)
0
90
(b)
31
G
-2 9
81 P &
0
180 Azimuthal angle B (deg)
1;;
a
3 -2 6 I =
P
360
”
.......
.._.._._..........fk
1
r.2
I
O-4
I
I
-2
0 ”
I
I
2
4
6)
V
2
. . . . . . . . . . . . . . .. . . . . . . . f,e
1
O
-4
-2 -1
0
2
4
V
Fig. 5. (a) Coordinate system for direction finding. Frequency dependence of wave characteristics in Fig. 1; (b) incidence angle (i) and azimuthal angle (O), and (c) polarization (u, 0).
while 1‘c 0, indicates a right-handed polarization, left-handed. When the wave frequency is 2.5 kHz. well above the.f,_ the incidence angle (i) is found to take a large value, - 74’. and it becomes smaller with decreasing frequency toward the cutoff frequency. The further decrease of frequency approaching the ,flL is found to result in the fact that the incidence angle (i) becomes close to zero, i.e. the zenith direction (i = 0’). As far as the azimuthal direction (0) is concerned, it remains approximately at a constant value, even if the wave frequency is varied. Next, we pay attention to the result of wave polarization in Fig. 5(c). In the frequency range from 1.875 to 2.5 kHz, 2’is always negative (u < 0), which indicates left-handed elliptical polarization. The next important point is that, when the wave frequency becomes lower and approaches fiC, the wave polarization (u, u) approaches an exactly left-handed circular (u = 0, c = - 1). By contrast, the field analysis direction finding is known to be effective only for elliptically polarized waves, and it is of no use for linearly polarized waves. In the frequency range from 1.5 to 1.O kHz where the possible propagation mode is only the 0th order mode, we have measured the phase difference of the two horizontal magnetic field components, and we have confirmed that the 0th order mode wave is nearly linearly polarized. We summarize here the important findings as follows. (1) As far as the incidence angle (i) is concerned, when the frequency decreases from the cutoff frequency of the 2nd order mode, i decreases from a large value to a small one, then approaches zero when the frequency becomes extremely close tof,,. (2) The azimuth angle (0) of the lst-order mode wave remains nearly at a constant value for all frequencies. (3) For all the frequencies of the lst-order mode, the wave polarization is always left-handed. When the frequency is well above the fiC (of course, below the 2nd-order mode cutoff), the polarization is more linear, but we notice a purely left-handed circular polarization at a frequency close to thefiC. (4) The wave polarization of the 0th order mode is found to be nearly linear. 3.3. General consideration of the experimental results We discuss these experimental facts in terms of the conventional Earth-ionosphere waveguide theory. The 0th order mode is known to be the TM, (TEM) mode (Budden, 1962; Wait, 1972), which is a mode propagating horizontally in the waveguide with vertical polarization when we assume a vertical dipole
VLF&LF sferics for the lightning discharge. The experimental finding (4) seems to be in good agreement with this theoretical prediction. Next, we discuss the properties of the 1st order mode. If we suppose, as the first approximation, that both the ionosphere and ground are perfect conductors. the dispersion equation of the 1st order mode w<~ve, propagating in the waveguide, is given by. (,I2 = Pk,; +m’ (en/h)‘,
(7)
where k, is the wave number in the propagation direction (q direction), and nr is the mode number. When we assume that the initial lightning is a vertical dipole, only the TM mode can propagate. In order to make it easier to compare equation (7) with the experimental results in Fig. 5, equation (7) is written as PI,,= c,li,,:(:I = sin i,
(8)
where ,ln is the effective refractive index of the relevant tnode and i is the incidence angle of the plane wave constituting the mode. By using n4 and i, equation (7) is written as
In Fig. 5. we have plotted, as a broken line, the variation of i with frequency based on equation (9) by using the experimentally estimated cutoff frequency, fiL = 1.725 kHz. It seems to us that the agreement between the experiment and theory is rather good, but not perfect. probably because of the approximation that the ionosphere is a perfect conductor. When we discuss the wave polarization, the idealized model for the ionosphere as a perfect conductor is not sufficient so that we have to consider the inhomogeneity and anisotropy of the lower ionosphere. Namely, even if the source is a vertical dipole, we have to consider both TM and TE modes, which is closely related with the poorly understood problem on the formation of tweek tails and also the coupling of sferics to whistlers. As has already been found as an experimental fact (see finding I), the incidence angle (i) becomes very close to zero when the frequency approaches,f,, so we can study the physical mechanism of tweek formation by assuming vertical incidence (i .+ 0’). It is probably right to suppose that the ground is a perfect conductor, but it is essential to treat the ionosphere as an anisotropic medium. The reflection coefficient (R,,) of plane waves for the vertical incidence is given by (Hayakawa, 1992).
R, = (n,-l)/(n,+l),
(10)
where nP is the refractive expressed by the following approximation. II;, = 1 -X*(1
index of the ionosphere. formula assuming the QI_
-iZ+
Y,).
!lI)
where X = tui!w’. YL = UH cos &PI, % = .’ (0. C!,,, I the angular electron plasma frequency, c+, is the angular electron gyrofrequency, H is the angle between the Earth’s magnetic field and the vertical direction. and y is the collision frequency of electrons with neutrals. One characteristic mode in equation (1 I) corresponds with a right-handed circularly polarized wave (whistler mode), and the other with a left-handed circularly polarized wave. In order to have the formation of the tail of tweek sferics, a number of reflections from the ionosphere would be involved and, in order to achieve this, equations (10) and (11) suggest that either (I ) lnp/ x 1 or (2) Re (n,) = 0 (Re means the real part). Although the detailed discussions are omitted, the first condition corresponds with the case of reflection from an isotropic (Y = 0) ionosphere, and this condition IS realized for daytime conditions. During daytime, we anticipate a lot of attenuation and so this is not suitable for the formation of tweek tails. The second condition (Re(n,) = 0) is only possible for an anisotroptc ionosphere. Re (nK) = 0 is never met (n,: righthanded circularly polarized (whistler-mode) wave) but Re (nJ = 0 is possible for the left-handed CII-cularly polarized wave in the frequency range C& < 01 < GI,, (SZ, : angular ion gyrofrequency Re(n,) = 0 is the condition of total reflection and so a left-handed circularly polarized wave is totally reflected from the anisotropic ionosphere. As is found as an experimental fact (see finding 3). the wave poiarization is left-handed in the frequency range 01’the lst-order mode, which is satisfactorily interpreted by the indication that right-handed circularly polarized whistler mode waves tend to penetrate the magneto-, sphere as a dissipation of the Earth-ionosphere wax:eguide propagation and the exactly left-handed circular polarization at the cutoff frequency of the I it order mode is the consequence of the aboLe discussion. This kind of discussion may also provide us with the implication on the coupling of sfericy tcr whistlers.
The wave source is assumed to be a vertical electrto dipole located on the ground and the propagationmodes excited by this dipole in the Earthhtonosphere waveguide are based on solving the following modal equation when assuming an inhomogeneous
M. Hayakawa C[~1.
474
and anisotropic ionosphere (e.g. Budden, 1962 ; Wait, 1972) F = jR,(S)R,(S)-
I/ = 0,
(12)
where
are the reflection matrices of the ionosphere and the ground (Wait, 1972; Budden, 1985). S is the sine of the angle of incidence to the ionosphere and ground. The solution of S, (S of the nth order mode) of equation (6) is based on the calculation of R,(S) and R, (S), where R,(S) is given by the Fresnel formula assuming a homogeneous ground (e.g. Hayakawa, 1992) and R,(S) is calculated by means of the admittance matrix method (Budden, 1961) for the inhomogeneous and anisotropic ionosphere. The phase velocity of the nth order mode (V,) in the propagation direction is given by I’,, = c/Re(SJ, and the corresponding
attenuation
(13) rate (a,) is given
by tl, = -8.86 x 106k,Im(S,)
(dBjlOO0 km),
(14)
where Im indicates the imaginary part. The polarization p is defined as the ratio of magnetic field components of TE and TM mode waves (Okada et al., 1977) ; thisp can also be expressed by the reflection coefficients as follows P = ,,R,,*,,R,l(l -,RI
*iRJ.
(15)
Equation (15) indicates that the absolute value of p is the reciprocal of the polarization mixing ratio p defined by Pappert (1968). When p > 1, the wave is a quasi-TM mode, and it is quasi-TE for p < 1. The group velocity in the q-direction (propagation direction) of the Earth-ionosphere waveguide is given by ug = dwldk, where k, is wave number in the q-direction (k, = k,s). S is generally complex, and when S, = Im(S) is nearly constant and independent of wave frequency, the group velocity vg can be given by I’, = dw/d(k&), with S, = Re(S).
(16)
lo+
I o-L
10”
Id
N (cm-‘) Fig. 6. Electron density profiles and collision frequency profile.
Figure 6 illustrates typical profiles of the nighttime ionosphere and the collision frequency profile. The first density profile is an exponential profile, which is often used for calculations in the VLF band at frequencies above 10 kHz and has proved to be useful in explaining satisfactorily the observed phase and amplitude variations (Morfitt et al., 1982). Such electron density profiles are expressed by where No = 30.7 cme3, N = N,exp {B(z-z,)I, z,, = 87 km as in Morfitt et al. (1982) and p is assumed to take three values of 0.150.24 and 0.35 km-‘. These profiles are indicated by E15, E24 and E35, respectively. In particular, E24 is suggested, by Morfitt et al. (1982), to be a good model at middle latitudes and to be well suited for the wave characteristics around 10 kHz. The second one (indicated by R) is the profile proposed by Reagan et al. (1982), and it is shown that this profile is suitable for accounting for observations at ELF. Recently, this model has also been adopted in analyzing VLF wave propagation at high latitudes (Inan et al., 1988). The collision frequency profile is reasonably assumed to be independent of latitude and longitude. In the case of sferics treated in Section 3, most of their propagation is over the sea, so that the Earth is considered as a perfect conductor. The geomagnetic field is based on the real magnetic field model, the so-called IGRF (1990) model. We show the numerical results for the tweek sferics discussed experimentally in Fig. 1. By using the determination of azimuthal directions, Ohta et al. (1991) have estimated that the sources of these tweeks are located about 3000 km from the observing station. In the following, we indicate the tweek in Fig. 1 as A244
VLF!ELF
475
sferics
(b) . I
1
oo-
a-
50-
6-
A239
DIP = 29.1 o
420,
2-
I
10 -
AZ =
fu = 1.195 mHz
3
187.8”
gg?
DIP = 29.1” OIS 1
I-
I 1.5
I
I
2.5 2.0 Frequency (kHz)
:3.0
((cl
1fH = 1.195 mHz
I
5l.C)
1.5
,i (A2j9)
I 2.0 Frequency (kHz)
2.5
4 Zhanjiang
DIP = 29.1”
I
i o-
0:
:
1
-1-
-2 -
-1 -
*
Measured (oA244 (*A239
IL * * R(2)
\
0
-2 -
O*
-Measured o A244 * A239
OP*
Zhanjiang -31.o
I 1.5
I
I
2.5 2.0 Frequency (kHz)
3.0
-3l.CI
I . _ 1.3
I _^ Z.U
Frequency
I ^_ L.5
(kHz)
Fig. 7. Propagation parameters as a function of frequency at Zhanjiang. China. Electron density are r and E24 models. (a) Phase velocity, (b) Attenuation rate, (c) Polarization parameter. (d) Polarization parameter, u. The sferic A244 refers to that shown in Fig. I.
because of their corresponding azimuthal directions determined by Ohta et al. (1991). Figure 7 illustrates the computational results of the propagation parameters at Zhanjiang for the two azimuths, A244 and A239, for the two ionospheric models of E24 and R (although the results for another tweek, A239, are not shown). The frequency range is
profiles u. and
limited to lower frequencies, below 3 kHz; Fig. 7(a) gives the phase velocity, Fig. 7(b), attenuation rate and Fig. 7(c) and (d), the polarization. The number in the bracket indicates the mode number and we deal with Oth, 1st and 2nd order modes. First of all. we consider the cutoff frequency by using the characteristics of phase velocity and attenuation rate. WC
476
M. Hayakawa et al.
define the cutoff frequency as that at which the attenuation rate exceeds LX,= 30 dB/Mm when the phase velocity and attenuation rate increase abruptly as the frequency decreases. The attenuation rate at this frequency is considered to be about l&20 dB/Mm larger than that at the frequencies yielding the flat characteristic or a minimum in the attenuation rate. We have found fit = 1.55 kHz at Zhanjiang for the 1st order mode for both propagation paths, A244 and A239, whereasf,, = 1541.57 kHz for the E15-E35 models. However, it is clear that these fit values are considerably smaller than those observed in Fig. 1. We have found that the change offic with the change in the reference height z0 for E15-E35 models is only 0.018+020 kHz/km and so we have to lower the profiles by about 10 km in order to have a good match with the observation. On the contrary, the cutoff frequency is found to befit = 1.71 kHz for the R model, irrespective of the azimuth (A244 and A239), which is in good agreement with the observation. We have also confirmed that the dependence of& on azimuth is extremely small. We now discuss the polarization features in Fig. 7(c) and (d). The experimental results are also indicated by 0(A244) and *(A239). First, we deal with the 0th order mode. The value of u is found to be -0.2 to 0.1 for both profiles of E24 and R and for both propagation paths of A244 and A239, and the ionospheric model and propagation azimuth have a negligible effect on u. Also, the value of v is found to lie in the range of - 0.1-O. 1, except for the E24 profile for A239, and we find a slight increase in v with the decrease in frequency. In conclusion, the theoretical estimation indicates that the polarization is close to linear and TM, which is consistent with the observation (see finding 4). The observational facts (findings 2 and 3 in Section 3.2) for the 1st order mode indicate that u increases with the decrease in frequency and approaches zero at the cutoff frequency, while v increases and approaches - 1 with the decrease in frequency toward the cutoff frequency. As seen from Fig. 7(c) and (d), the theoretical frequency dependence of u for the 1st order mode is found to exhibit large differences depending on the propagation path (azimuth) and electron density profile. In the case of the profile E24, the value for A239 takes a larger negative value than for A244, which seems to be consistent with the observed frequency dependence (though not shown). However, the value itself was less than half the observed value. On the contrary, the value of v is found to be nearly constant at the frequency above the cutoff frequency f ,c, and v - - 1.4 at the cutoff frequency, though it
shows a slight dependence on the propagation path. Not only the value (tl) itself, but also its frequency dependence are considerably different from the observations, especially at the higher frequencies. The theoretical u value, for the 1st order mode for the R profile and A244 case, is shifted upward by 0.3 from that for E24 and A239, and so its u value is extremely small compared with the observed u. On the other hand, u = -0.24 for the 1st order mode of A239, and it is even smaller for A244. This results from the fact that the 1st and 2nd order modes are degenerate at a particular azimuth between those of A239 and A244, and as a consequence of this, the u value of the 1st order mode of A239 is small and that of the 2nd order mode is larger, as seen from the figure. Hence, the theoretical estimate is far from the observation. Furthermore, the theoretical v value of the 1st order mode approaches - 1 at the cutoff frequency, but it approaches 0 at the frequency higher than 2.3 kHz. Consequently, the theoretical lst-order mode is considered to be a quasi-TM mode. Furthermore, Fig. 7(b) shows that the attenuation rate for the 2nd order mode in this frequency range is lower than that of the 1st order mode. As far as the attenuation rate is concerned, the same thing is valid and so the 2nd order mode is propagating as well, which makes it very difficult to calculate the p value in the two-mode propagation. These points may suggest that there may exist a problem in the choice of electron density profile. Another possible problem may be the assumption that the mode is propagating with slowly changing mode characteristics, depending on the parameters along the propagation path. 3.5. Conclusion The application of our field-analysis direction finding to the digital measurement data of the waveforms of three electromagnetic field components has enabled us to obtain the frequency dependencies of the incident and azimuth angles and wave polarization of tweek sferics. These frequency dependencies for the 1st order mode are firstly interpreted in terms of the conventional Earth-ionosphere waveguide mode propagation on the assumption of a perfect conductor for both the ionosphere and ground. The experimental facts that left-handed polarization is observed for the 1st order mode, at a frequency of about fi_ are qualitatively interpreted by the leakage of sferics into the magnetosphere in the whistler mode. Furthermore, the observed value of wave polarization is suggested to be a useful quantity to study the inhomogeneity and anisotropy of the lower ionosphere. Further details will be found in Hayakawa ef al. (1994).
VLF/ELF
sferics
REFERENCES
Al’pert Ya. 1,. and Fligel D. S.
1970
Budden
K. G.
1961
Budden
K. G.
1962
Hayakawa
M.
1992
Hayakawa
M., Baba K. and Ohta K.
1994
Hayakawa
M., Ohta K. and Shimakura
Hayakawa
M. and Shimakura
Hayakawa
M. and Tanaka
Mortitt
D. G.. Ferguson
S.
1990
S.
1992
Y.
1978
J. A. and Snyder
F. P
1982
Ohta K., Hayakawa Tomomatsu T.
M., Shimakura
S. and
1990
Ohra K.. Hayakawa
M. and Tanaka
Y.
1984
Okada
T.. Iwar A. and Hayakawa
M.
1977
Propagation of‘ELF and VLF Wuaes Near the Lkrth Consultants Bureau, New York. Radio Waves in the Ionosphere. Cambridge Umversit> Press. The Waveguide Mode Theor), of’ U’UI.P Propcqcrtio,] Logos Press, London. Electromagnetic Wave En,gineerin,q. C‘orona Pub Comp. (in Japanese). On wave characteristics of tweek atmospherics deduced from direction finding measurement, .I. ,qwph l‘.r Re.\ (in press). Spaced direction finding of nighttime whistlers ar 10% and equatorial latitudes and their propagation mechanism. J. yeophqs. Res. 95, 15,091. High accuracy method of locating distant hghtning bl means of tweek atmospherics. Proc. 1I th Wroclau Symp. Exhibition on EMC, 566. On the propagation of low latitude whistlers Rw (revph!s. Space Phyx. 16, 11 I. Numerrcal modeling of the propagation medium ,tt ELF:VLF/LF. AGARD Conf. Proc. No. 305, B?. Correlation of whistlers at a low latitude wrth cauaati\c hghtnings at conjugate regions. Trams. hut. Ekwtr Inform. Comm. Eqres. Japan J.74.B-11. 216 2X4. Ducted propagation of daytime whistlers as deduced from the ground-based direction tindmg. .I. qet$r~,r RCY. 89, 7557. The measurement of Incident and azrmuthal angles and the polarization of whistlers at low latitudes. Pitrrw! Sptrcr Sci. 25, 233. Numerical study of tweeks based on waveguide mode theory. Proc. Rcs. Inst. .4tmosph . :Vqpw lit~w 7.
Outsu J.
1960
P_rippert R. A.
1968
A numerical study of VLF mode structure gation below an anisotropic ionosphere
1982
Modeling of the ambient and disturbed ronospherrc media pertinent to ELFVLF propagation. AGAR D Conf. Proc. No. 305, 33. On the method of estimating the ionosphertc hetght and propagation distance based on the dispersion effect of atmospherics.Menr. I+iccu/r. I%/., C‘hihtr I ;ttir 41. I. Ekctroma,ynetic Wuwr m Stratifred MARTIN.Pcrgamon Press, Oxford. Experimental investigatron of the twseek lieid structur.I&. Spucc Rcs. 12, 251.
5x. and prop+ R&o SCt
3,219. Reagan J. B., Meyerott lmhof W. L.. Gaines Shimakura
R. E., Gunton R. C., E. E. and Larsen T. R.
S. and Moriizumi
M.
1990
W.ait J. R. Yedemsky D. Ye., Ryabov and Yarotsky V. S.
1972 B. S., Shchokotov
Yu. A.
1992
Recent findings on VLF/ELF M. Hayakawa,*
K. Ohta,l_ S. Shimakura$
sferics and K. Babat
* Sugadaira Space Radio Observatory, The University
of Electra-Communications. Chofu Tokyo Japan t Department of Electronic Engineering, Chubu University. Kasugai Aichi 487. Japan $ Department of Electrical and Electronic Engineering. Chiba University. Chiba 263. Japan (Rtwicrd
inJinulform
19 Mu!, 1994
; acwptetl27
Junr
I83
1994)
AbstractPmOur recent activity on VLF/ELF sferics The first is a sophisticated second part, for whistlers)
15 reviewed, and this paper is composed of two parts. new method of estimating the propagation distance and ionospheric reflection height by using signal processing for the dispersive tails of tweek sferics near the cutoff frequencies. In the we have carried out the first attempt to apply our field-analysis direction finding (developed experimental results and their interpretation are presented. to tweek sferics ; the corresponding
The present section proposes a newt method to determine, with sufficient accuracy, the ionospheric height and the characteristics of the Earth--ionosphere waveguide affecting the propagation of sferics. We discuss the effectiveness of our method by obtaining the location of sferics and ionospheric height from data simultaneously obtained at two or three observing stations.
1. INTRODL’CTlON
VLFiELF sferics are considered to be a very important component constituting the terrestrial electromagnetic environment in the lower frequency range. VLF!ELF sferics originate in lightning discharges and propagate in the Earth-ionosphere waveguide (Outsu, 1960), and they were used to study the characteristics of distant lightning and also the lower ionosphere (Al’pert et (11. 1970). Recently, an extensive investigation of the lower ionosphere has been undertaken with VLF transmitter signals, by making full use of the advantage of their known location, frequency, power, etc. The disadvantages of VLF/ELF sferics, their unknown and sporadic occurrence, were stressed, and the importance of VLF/ELF sferics seemed to be in decline. However, by giving new ideas to these old VLF/ELF sferics, the merits of VLF/ELF sferics, such as their world-wide occurrence, their wide-band structure and so on, should be stressed. In this paper, we indicate a few examples in this direction carried out by our group.
2. LOCATION BY USING
OF DISTANT THE TAILS
LIGHTNING
DISCHARGES
OF TWEEK
SFERICS
Sferics are VLF/ELF electromagnetic waves propagated in the Earth-ionosphere waveguide (Budden, 1961 ; Wait, 1972) originating in lightning. Figure I illustrates an example of the dynamic spectra of sferics and a resultant whistler. The mode equation for the Earth-ionosphere waveguide propagation is expressed by the following equation (Wait, 1972). R, (0).
R,(H)
exp (-- i2koh
cos 0) = exp
I -- ihn). (1)
This equation is based on the assumption of the model of a flat Earth and an ionosphere, of height 17, and an incidence angle, H. R,(Q) and R,(B) are the reflection coefficients from the ionosphere and ground. respectively. The ionosphere is assumed to be sharply bounded at the effective height, h (this sharp boundary approximation is good at night) ; this h is the average value over the propagation path. k,,( = C!J/C) is the propagation constant in free space. (U the angular wave frequency, and c the velocity of light; II is the mode number. Solving equation ( 1) yields
Tweek sferics are VLF/ELF waves which are observed very frequently during the night over the whole year (Outsu, 1960) ; they are utilized to investigate the lower ionosphere and to locate the lightning. However, no effective analysis method for the dispersion effect of tweeks has been developed (Outsu, 1960). and so their usage is not great. 467
M. Hayakawa E/ ul
468
Fig. 1. An example of dynamic spectra of the causative sferic (A) and the corresponding whistler (B) observed at Zhanjiang.
cose=E+ip koh
A koh cos 8
(n= 1,2,3...),
(2)
x(t)
= Ca&) k
cm { 2nfc &qJ+@~k(l’i.
with
(5)
where N, and Ng are the values of refractive index of the ionosphere and ground, respectively. We can reasonably assume that the ionosphere and ground are perfect conductors. Then, the propagation constant in the horizontal direction kOsin 0 can be expressed as follows under the condition that 2 IQ/k& < 1- (nr&h)2, k ,,sinO=k,-,[{l-($)ljl/*
-i&{l-($r”*].
(4)
Then, we are able to obtain the group velocity vg of the nth order mode of the sferic, its propagation time T, at an angular frequency w and then the instantaneous frequency at the propagation time T,. Integrating the instantaneous frequency leads to the phase Q(t) at the time t. When we take into account the temporally slowly varying amplitude a(t) and phase Qo(t), the sferic signal (in the nth order mode) propagating in the Earth-ionosphere waveguide, x(t) is given by the following equation as a sum of a few component waves :
The first term of the phase term in equation (5) represents a component with fast frequency variations in Fig. 1, while the slowly varying components, ok(t) and mok(f), correspond with spectral broadening. 2.2. Principle of estimating the ionospheric height and the propagation distance of sferics
As seen in Fig. 1, the duration of sferics is very short, in a range from a few tens of ms to about 100 ms, and the frequency change over this duration is as fast as N 10 kHz. When we apply the conventional spectrum analysis to such non-stationary signals with rapidly changing frequency, it is obvious that the spectra exhibit an apparent spectral broadening so that it is extremely difficult to estimate the spectral parameters of the received signals with sufficient accuracy. We now propose a new method. We make a pseudosferic corresponding to the observed sferic, and we mix these two signals, resulting in a nearly stationary signal for which the conventional spectrum analysis is still available. Then, we take only the lower frequency component for the parameter estimation. Figure 2 illustrates the relationship of the observed sferic signal x(t), pseudo-sferic signal R(t) and the resultant signal y(t). The propagation distance and ionospheric height are obtained by least squares fit-
VLF/ELF
sferics
I
Time
Af
Af
(4
@I
Fig. 2. Schematic illustration of the dynamic spectra of an actual sferic signal (the shaded area within the two full lines). the corresponding pseudo-sferic signal (broken line) (in the top panels) and the resultant signal (in the bottom panels).
ting; that is, determining the parameters fn, (cutoff = nc/2h), d (propagation distance) and frequency, t,, (occurrence time) of the pseudo-sferic such that &(Ajjj)’ is a minimum after measuring the error frequency 4fn, at different frequencies of the dynamic spectrum, 4’(t). Figure 3 illustrates the flow chart used to estimate the dispersion parameters of sferics based on the above principle. 2.3. Results,from data observedsimultaneously at three stutions We have been carrying out a synoptic routine observation of wide-band (O-8 kHz) VLF waves, and the
data used here are obtained at Moshiri, Sakushima and Kagoshima (Hayakawa and Tanaka, 1978) from 02.50 to 02.52 LT on 6 April 1984. Figure 1 illustrates an example of the dynamic spectra of VLF signals observed at a different station. It is clear from Fig. 1 that a strong dispersion effect occurs near the cut-off frequency (- 1.7 kHz) of the first order mode of the Earth-ionosphere waveguide. We now discuss the accuracy of the proposed method. If we indicate the error in measuring the instantaneous frequency of sferics as c!$ the errors in estimating the ionospheric height and propagation distance are deduced as follows :
Dynamic Spectra
d-ci+Ad Fig. 3. The flow chart ionosphere waveguide.
to estimate the dispersion parameters of atmospherics propagating in the EarthAfm is the difference in the instantaneous frequency between the actual and pseudosferic at a particular instant.
470
M. Hayakawa et ul.
sferics) are observed all the time and all over the world ; see Hayakawa and Shimakura (1992) and Shimakura and Moriizumi (1990) for further details. Suppose that the cut-off frequency of the 1st order mode is fnc = 1.7 kHz, the propagation distance is d = 6000 km, and also that the measuring error of the centre frequency at the instantaneous frequency of a sferic (f= 2.5 kHz) is Sf= 20 Hz, then we obtain 6h < 0.7 km and 6d < 40 km from equation (6). The root of the mean squares error of the centre frequency of the spectrum at different frequencies is actually found to be l&20 Hz, and so this method proves to be a very powerful tool to estimate the propagation distance of sferics and the ionospheric height with great accuracy. The accuracy of the present method is much higher than that used by Outsu (1960), but we then have to estimate the accuracy in locating the distant lightning by comparing the results from each pair of stations (Moshiri-Sakushima, SakushimaMoshiri, and Kagoshima-Moshiri). Figure 4 illustrates the location of several sferics estimated by each pair of stations (0 : Moshiri-Sakushima, A: Sakushima-Kagoshima, 0 : Kagoshima-Moshiri). The sferic labeled “a” originates close to the line of Japanese islands, and so the three points are separated from each other depending on the relative location of the sferics with the three observing stations. The sferits (c, d, f, h) are more suitably positioned for the exact location due to their relative relation with the observing stations. The distribution of locations of the causative sferics is then obtained, in which each point is taken as the centre of gravity of the three points so determined for each sferic. This map is compared with the corresponding map of the clouds from the Japanese meteorological satellite at 02.00 LT (about 50 min before the time of the whistler observation) and it is found that the locations of sferics fall within the active regions of lightning activity deduced from the satellite. This indicates the effectiveness of our proposed method of analysis.
2.4. Concluding remarks Sophisticated signal analysis has enabled us to deduce the propagation properties of tweek sferics with sufficient accuracy, and we will be able to locate the distant lightning sources with this method even from the simple wide-band data at a few spaced stations. This method is based on waveguide mode theory, which yields the existence of a minimum distance (- l-2 Mm) over which the present method is effective. Also, this method will be extensively utilized in estimating the large-scale D-region ionospheric irregularities on a global scale because tweeks (and/or
3. DIRECTION FINDING FOR TWEEK SFERICS AND THEIR PROPAGATION MECHANISM
Tweek sferics are known to exhibit remarkable dispersions near the cutoff frequencies of the lst- and 2nd-order mode waves, as seen in Fig. I. These dispersion effects are found to fit well with the Earth-ionosphere waveguide propagation theory (Outsu, 1960) and are utilized in Section 2. The previous investigations were all devoted to the analysis of frequencytime spectra of tweeks, and no reports have been published dealing with the detailed wave characteristics (polarization, arrival direction etc.) of tweeks. Hence, the formation mechanism of tweeks such as the reason for their long-enduring tails and the corresponding coupling of sferics to whistlers have been unsolved. The purpose of this section is to present extensive experimental results on the detailed wave characteristics of tweek sferics by means of field-analysis direction finding (Okada et al., 1977), developed for whistler mode waves. Yedemsky et al. (1992) presented some direction finding results based on an analogue system the Okada et al. (1977) method. Instead of their analogue signal analyses, we deal with a digital signal analysis. Then, the physical implications have been deduced by comparing the experimental data with the corresponding theoretical estimation of the propagation in the Earth-ionosphere waveguide, taking into account the ionospheric density profile and the effect of the Earth’s magnetic field. 3.1. VLF observations and direction.finding The VLF data used were obtained in our campaign made in South China (Hayakawa et al., 1990), and three observing stations are used ; (1) Zhanjiang (geographic coordinates 2 1.3”N ; 110.3’E ; geomagnetic latitude lO”N), (2) Guilin (25.3-N, 110.2OE; 14”N) and (3) Wuchang (30S”N, 114.6”E; 19”N). The observation was carried out continuously for 4 h from 00.00 to 04.00 LT during the period of 5-l 1 January 1988. The campaign was intended for the investigation of very low latitude whistlers (Hayakawa et al., 1990), but the data can also be utilized for the study of tweeks. Three field components (two horizontal magnetic and the vertical electric) are measured in a wide frequency range (O-10 kHz) by means of digital recorders. The outputs of three field components are digitized by an A/D converter (12 bits) with a sam-
VLF:ELI-
stems
Geographic I20”E
125
130
471
longitude 155”E
160
165
155”E
160
165
155”E
160
165
16O”E
I65
170
0
b
5
0
15YE
Fig. 4. The distribution
160
of the positions
(a f). 0. MoshiCSakushima;
I65
determined
pling speed of 40 ,ULS. Then, we make the FFT analysis by a microcomputer and we perform the field-analysis direction finding (Okada et al., 1977; Ohta et al., 1984) to estimate the amplitude ratios and phase differences among three components with a frequency resolution of 25 Hz. This field analysis direction finding is known to be effective for any elliptically polarized wave (Okada et al.. 1977).
3.2. Ohsrrcational trristic’s
results
on detailed
wave charac
gf trtreks
Figure 1 was an example of tweek sferics observed at Zhanjiang at 02.44 LT on 5 January 1988. As seen from the figure, the cutoff frequency of the lst-order mode is found to be fi, - 1.725 kHz and the frequency
for the SLXsfencs and 0. Kagoshima--Moshiri.
for each pair of rhe three stations
A, Sakushima+Kagoshima:
component below this,& corresponds to the 0th order mode. The result of field-analysis direction finding for the tweek in Fig. 1 is summarized in Fig. 5. Figure 5(b) illustrates the frequency dependence of the incidence (i) (measured from the zenith) and azimuthal (0) angles of the Ist-order mode component. while Fig. 5(c) refers to the corresponding frequency dependence of the wave polarization (u,(l). In the fieldanalysis direction finding measurement, an elliptically polarized wave is decomposed into TM and TE mode components (see Fig. 5(a)), and the wave polarization p = (u, r) is defined as the ratio of the magnetic field components of two mode waves (see Okada et ui. (1977) for further details.) A right-handed circular polarization is indicated as (u,71) = (0, 1) and 7‘> 0
412
M. Hayakawa L’Ial z (Zenith)
Wave normal
t
direction
ElYS H-1 /
.k bl
(a)
i
...
J x (East)
... ..f( %,.;
i: Incidence angle +: Azimuthal angle
3 :
s 3
2-
Y (NOW
. . . . . . ...*..
.... ??
:
.. . . .
..** . .
.
.
6 e Bl e r&
iL i . I ; .8,. : L-i_ I 45 Incident angle i (deg)
0
90
(b)
31
G
-2 9
81 P &
0
180 Azimuthal angle B (deg)
1;;
a
3 -2 6 I =
P
360
”
.......
.._.._._..........fk
1
r.2
I
O-4
I
I
-2
0 ”
I
I
2
4
6)
V
2
. . . . . . . . . . . . . . .. . . . . . . . f,e
1
O
-4
-2 -1
0
2
4
V
Fig. 5. (a) Coordinate system for direction finding. Frequency dependence of wave characteristics in Fig. 1; (b) incidence angle (i) and azimuthal angle (O), and (c) polarization (u, 0).
while 1‘c 0, indicates a right-handed polarization, left-handed. When the wave frequency is 2.5 kHz. well above the.f,_ the incidence angle (i) is found to take a large value, - 74’. and it becomes smaller with decreasing frequency toward the cutoff frequency. The further decrease of frequency approaching the ,flL is found to result in the fact that the incidence angle (i) becomes close to zero, i.e. the zenith direction (i = 0’). As far as the azimuthal direction (0) is concerned, it remains approximately at a constant value, even if the wave frequency is varied. Next, we pay attention to the result of wave polarization in Fig. 5(c). In the frequency range from 1.875 to 2.5 kHz, 2’is always negative (u < 0), which indicates left-handed elliptical polarization. The next important point is that, when the wave frequency becomes lower and approaches fiC, the wave polarization (u, u) approaches an exactly left-handed circular (u = 0, c = - 1). By contrast, the field analysis direction finding is known to be effective only for elliptically polarized waves, and it is of no use for linearly polarized waves. In the frequency range from 1.5 to 1.O kHz where the possible propagation mode is only the 0th order mode, we have measured the phase difference of the two horizontal magnetic field components, and we have confirmed that the 0th order mode wave is nearly linearly polarized. We summarize here the important findings as follows. (1) As far as the incidence angle (i) is concerned, when the frequency decreases from the cutoff frequency of the 2nd order mode, i decreases from a large value to a small one, then approaches zero when the frequency becomes extremely close tof,,. (2) The azimuth angle (0) of the lst-order mode wave remains nearly at a constant value for all frequencies. (3) For all the frequencies of the lst-order mode, the wave polarization is always left-handed. When the frequency is well above the fiC (of course, below the 2nd-order mode cutoff), the polarization is more linear, but we notice a purely left-handed circular polarization at a frequency close to thefiC. (4) The wave polarization of the 0th order mode is found to be nearly linear. 3.3. General consideration of the experimental results We discuss these experimental facts in terms of the conventional Earth-ionosphere waveguide theory. The 0th order mode is known to be the TM, (TEM) mode (Budden, 1962; Wait, 1972), which is a mode propagating horizontally in the waveguide with vertical polarization when we assume a vertical dipole
VLF&LF sferics for the lightning discharge. The experimental finding (4) seems to be in good agreement with this theoretical prediction. Next, we discuss the properties of the 1st order mode. If we suppose, as the first approximation, that both the ionosphere and ground are perfect conductors. the dispersion equation of the 1st order mode w<~ve, propagating in the waveguide, is given by. (,I2 = Pk,; +m’ (en/h)‘,
(7)
where k, is the wave number in the propagation direction (q direction), and nr is the mode number. When we assume that the initial lightning is a vertical dipole, only the TM mode can propagate. In order to make it easier to compare equation (7) with the experimental results in Fig. 5, equation (7) is written as PI,,= c,li,,:(:I = sin i,
(8)
where ,ln is the effective refractive index of the relevant tnode and i is the incidence angle of the plane wave constituting the mode. By using n4 and i, equation (7) is written as
In Fig. 5. we have plotted, as a broken line, the variation of i with frequency based on equation (9) by using the experimentally estimated cutoff frequency, fiL = 1.725 kHz. It seems to us that the agreement between the experiment and theory is rather good, but not perfect. probably because of the approximation that the ionosphere is a perfect conductor. When we discuss the wave polarization, the idealized model for the ionosphere as a perfect conductor is not sufficient so that we have to consider the inhomogeneity and anisotropy of the lower ionosphere. Namely, even if the source is a vertical dipole, we have to consider both TM and TE modes, which is closely related with the poorly understood problem on the formation of tweek tails and also the coupling of sferics to whistlers. As has already been found as an experimental fact (see finding I), the incidence angle (i) becomes very close to zero when the frequency approaches,f,, so we can study the physical mechanism of tweek formation by assuming vertical incidence (i .+ 0’). It is probably right to suppose that the ground is a perfect conductor, but it is essential to treat the ionosphere as an anisotropic medium. The reflection coefficient (R,,) of plane waves for the vertical incidence is given by (Hayakawa, 1992).
R, = (n,-l)/(n,+l),
(10)
where nP is the refractive expressed by the following approximation. II;, = 1 -X*(1
index of the ionosphere. formula assuming the QI_
-iZ+
Y,).
!lI)
where X = tui!w’. YL = UH cos &PI, % = .’ (0. C!,,, I the angular electron plasma frequency, c+, is the angular electron gyrofrequency, H is the angle between the Earth’s magnetic field and the vertical direction. and y is the collision frequency of electrons with neutrals. One characteristic mode in equation (1 I) corresponds with a right-handed circularly polarized wave (whistler mode), and the other with a left-handed circularly polarized wave. In order to have the formation of the tail of tweek sferics, a number of reflections from the ionosphere would be involved and, in order to achieve this, equations (10) and (11) suggest that either (I ) lnp/ x 1 or (2) Re (n,) = 0 (Re means the real part). Although the detailed discussions are omitted, the first condition corresponds with the case of reflection from an isotropic (Y = 0) ionosphere, and this condition IS realized for daytime conditions. During daytime, we anticipate a lot of attenuation and so this is not suitable for the formation of tweek tails. The second condition (Re(n,) = 0) is only possible for an anisotroptc ionosphere. Re (nK) = 0 is never met (n,: righthanded circularly polarized (whistler-mode) wave) but Re (nJ = 0 is possible for the left-handed CII-cularly polarized wave in the frequency range C& < 01 < GI,, (SZ, : angular ion gyrofrequency Re(n,) = 0 is the condition of total reflection and so a left-handed circularly polarized wave is totally reflected from the anisotropic ionosphere. As is found as an experimental fact (see finding 3). the wave poiarization is left-handed in the frequency range 01’the lst-order mode, which is satisfactorily interpreted by the indication that right-handed circularly polarized whistler mode waves tend to penetrate the magneto-, sphere as a dissipation of the Earth-ionosphere wax:eguide propagation and the exactly left-handed circular polarization at the cutoff frequency of the I it order mode is the consequence of the aboLe discussion. This kind of discussion may also provide us with the implication on the coupling of sfericy tcr whistlers.
The wave source is assumed to be a vertical electrto dipole located on the ground and the propagationmodes excited by this dipole in the Earthhtonosphere waveguide are based on solving the following modal equation when assuming an inhomogeneous
M. Hayakawa C[~1.
474
and anisotropic ionosphere (e.g. Budden, 1962 ; Wait, 1972) F = jR,(S)R,(S)-
I/ = 0,
(12)
where
are the reflection matrices of the ionosphere and the ground (Wait, 1972; Budden, 1985). S is the sine of the angle of incidence to the ionosphere and ground. The solution of S, (S of the nth order mode) of equation (6) is based on the calculation of R,(S) and R, (S), where R,(S) is given by the Fresnel formula assuming a homogeneous ground (e.g. Hayakawa, 1992) and R,(S) is calculated by means of the admittance matrix method (Budden, 1961) for the inhomogeneous and anisotropic ionosphere. The phase velocity of the nth order mode (V,) in the propagation direction is given by I’,, = c/Re(SJ, and the corresponding
attenuation
(13) rate (a,) is given
by tl, = -8.86 x 106k,Im(S,)
(dBjlOO0 km),
(14)
where Im indicates the imaginary part. The polarization p is defined as the ratio of magnetic field components of TE and TM mode waves (Okada et al., 1977) ; thisp can also be expressed by the reflection coefficients as follows P = ,,R,,*,,R,l(l -,RI
*iRJ.
(15)
Equation (15) indicates that the absolute value of p is the reciprocal of the polarization mixing ratio p defined by Pappert (1968). When p > 1, the wave is a quasi-TM mode, and it is quasi-TE for p < 1. The group velocity in the q-direction (propagation direction) of the Earth-ionosphere waveguide is given by ug = dwldk, where k, is wave number in the q-direction (k, = k,s). S is generally complex, and when S, = Im(S) is nearly constant and independent of wave frequency, the group velocity vg can be given by I’, = dw/d(k&), with S, = Re(S).
(16)
lo+
I o-L
10”
Id
N (cm-‘) Fig. 6. Electron density profiles and collision frequency profile.
Figure 6 illustrates typical profiles of the nighttime ionosphere and the collision frequency profile. The first density profile is an exponential profile, which is often used for calculations in the VLF band at frequencies above 10 kHz and has proved to be useful in explaining satisfactorily the observed phase and amplitude variations (Morfitt et al., 1982). Such electron density profiles are expressed by where No = 30.7 cme3, N = N,exp {B(z-z,)I, z,, = 87 km as in Morfitt et al. (1982) and p is assumed to take three values of 0.150.24 and 0.35 km-‘. These profiles are indicated by E15, E24 and E35, respectively. In particular, E24 is suggested, by Morfitt et al. (1982), to be a good model at middle latitudes and to be well suited for the wave characteristics around 10 kHz. The second one (indicated by R) is the profile proposed by Reagan et al. (1982), and it is shown that this profile is suitable for accounting for observations at ELF. Recently, this model has also been adopted in analyzing VLF wave propagation at high latitudes (Inan et al., 1988). The collision frequency profile is reasonably assumed to be independent of latitude and longitude. In the case of sferics treated in Section 3, most of their propagation is over the sea, so that the Earth is considered as a perfect conductor. The geomagnetic field is based on the real magnetic field model, the so-called IGRF (1990) model. We show the numerical results for the tweek sferics discussed experimentally in Fig. 1. By using the determination of azimuthal directions, Ohta et al. (1991) have estimated that the sources of these tweeks are located about 3000 km from the observing station. In the following, we indicate the tweek in Fig. 1 as A244
VLF!ELF
475
sferics
(b) . I
1
oo-
a-
50-
6-
A239
DIP = 29.1 o
420,
2-
I
10 -
AZ =
fu = 1.195 mHz
3
187.8”
gg?
DIP = 29.1” OIS 1
I-
I 1.5
I
I
2.5 2.0 Frequency (kHz)
:3.0
((cl
1fH = 1.195 mHz
I
5l.C)
1.5
,i (A2j9)
I 2.0 Frequency (kHz)
2.5
4 Zhanjiang
DIP = 29.1”
I
i o-
0:
:
1
-1-
-2 -
-1 -
*
Measured (oA244 (*A239
IL * * R(2)
\
0
-2 -
O*
-Measured o A244 * A239
OP*
Zhanjiang -31.o
I 1.5
I
I
2.5 2.0 Frequency (kHz)
3.0
-3l.CI
I . _ 1.3
I _^ Z.U
Frequency
I ^_ L.5
(kHz)
Fig. 7. Propagation parameters as a function of frequency at Zhanjiang. China. Electron density are r and E24 models. (a) Phase velocity, (b) Attenuation rate, (c) Polarization parameter. (d) Polarization parameter, u. The sferic A244 refers to that shown in Fig. I.
because of their corresponding azimuthal directions determined by Ohta et al. (1991). Figure 7 illustrates the computational results of the propagation parameters at Zhanjiang for the two azimuths, A244 and A239, for the two ionospheric models of E24 and R (although the results for another tweek, A239, are not shown). The frequency range is
profiles u. and
limited to lower frequencies, below 3 kHz; Fig. 7(a) gives the phase velocity, Fig. 7(b), attenuation rate and Fig. 7(c) and (d), the polarization. The number in the bracket indicates the mode number and we deal with Oth, 1st and 2nd order modes. First of all. we consider the cutoff frequency by using the characteristics of phase velocity and attenuation rate. WC
476
M. Hayakawa et al.
define the cutoff frequency as that at which the attenuation rate exceeds LX,= 30 dB/Mm when the phase velocity and attenuation rate increase abruptly as the frequency decreases. The attenuation rate at this frequency is considered to be about l&20 dB/Mm larger than that at the frequencies yielding the flat characteristic or a minimum in the attenuation rate. We have found fit = 1.55 kHz at Zhanjiang for the 1st order mode for both propagation paths, A244 and A239, whereasf,, = 1541.57 kHz for the E15-E35 models. However, it is clear that these fit values are considerably smaller than those observed in Fig. 1. We have found that the change offic with the change in the reference height z0 for E15-E35 models is only 0.018+020 kHz/km and so we have to lower the profiles by about 10 km in order to have a good match with the observation. On the contrary, the cutoff frequency is found to befit = 1.71 kHz for the R model, irrespective of the azimuth (A244 and A239), which is in good agreement with the observation. We have also confirmed that the dependence of& on azimuth is extremely small. We now discuss the polarization features in Fig. 7(c) and (d). The experimental results are also indicated by 0(A244) and *(A239). First, we deal with the 0th order mode. The value of u is found to be -0.2 to 0.1 for both profiles of E24 and R and for both propagation paths of A244 and A239, and the ionospheric model and propagation azimuth have a negligible effect on u. Also, the value of v is found to lie in the range of - 0.1-O. 1, except for the E24 profile for A239, and we find a slight increase in v with the decrease in frequency. In conclusion, the theoretical estimation indicates that the polarization is close to linear and TM, which is consistent with the observation (see finding 4). The observational facts (findings 2 and 3 in Section 3.2) for the 1st order mode indicate that u increases with the decrease in frequency and approaches zero at the cutoff frequency, while v increases and approaches - 1 with the decrease in frequency toward the cutoff frequency. As seen from Fig. 7(c) and (d), the theoretical frequency dependence of u for the 1st order mode is found to exhibit large differences depending on the propagation path (azimuth) and electron density profile. In the case of the profile E24, the value for A239 takes a larger negative value than for A244, which seems to be consistent with the observed frequency dependence (though not shown). However, the value itself was less than half the observed value. On the contrary, the value of v is found to be nearly constant at the frequency above the cutoff frequency f ,c, and v - - 1.4 at the cutoff frequency, though it
shows a slight dependence on the propagation path. Not only the value (tl) itself, but also its frequency dependence are considerably different from the observations, especially at the higher frequencies. The theoretical u value, for the 1st order mode for the R profile and A244 case, is shifted upward by 0.3 from that for E24 and A239, and so its u value is extremely small compared with the observed u. On the other hand, u = -0.24 for the 1st order mode of A239, and it is even smaller for A244. This results from the fact that the 1st and 2nd order modes are degenerate at a particular azimuth between those of A239 and A244, and as a consequence of this, the u value of the 1st order mode of A239 is small and that of the 2nd order mode is larger, as seen from the figure. Hence, the theoretical estimate is far from the observation. Furthermore, the theoretical v value of the 1st order mode approaches - 1 at the cutoff frequency, but it approaches 0 at the frequency higher than 2.3 kHz. Consequently, the theoretical lst-order mode is considered to be a quasi-TM mode. Furthermore, Fig. 7(b) shows that the attenuation rate for the 2nd order mode in this frequency range is lower than that of the 1st order mode. As far as the attenuation rate is concerned, the same thing is valid and so the 2nd order mode is propagating as well, which makes it very difficult to calculate the p value in the two-mode propagation. These points may suggest that there may exist a problem in the choice of electron density profile. Another possible problem may be the assumption that the mode is propagating with slowly changing mode characteristics, depending on the parameters along the propagation path. 3.5. Conclusion The application of our field-analysis direction finding to the digital measurement data of the waveforms of three electromagnetic field components has enabled us to obtain the frequency dependencies of the incident and azimuth angles and wave polarization of tweek sferics. These frequency dependencies for the 1st order mode are firstly interpreted in terms of the conventional Earth-ionosphere waveguide mode propagation on the assumption of a perfect conductor for both the ionosphere and ground. The experimental facts that left-handed polarization is observed for the 1st order mode, at a frequency of about fi_ are qualitatively interpreted by the leakage of sferics into the magnetosphere in the whistler mode. Furthermore, the observed value of wave polarization is suggested to be a useful quantity to study the inhomogeneity and anisotropy of the lower ionosphere. Further details will be found in Hayakawa ef al. (1994).
VLF/ELF
sferics
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1960
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