Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.izmiran.rssi.ru/~sova/Copies/AG_04_47.pdf Дата изменения: Sat Feb 28 14:12:58 2009 Дата индексирования: Sat Apr 9 23:34:14 2016 Кодировка: Поисковые слова: http www.astronomy.com

ANNALS OF GEOPHYSICS, VOL. 47, N. 1, February 2004

Depression of the ULF geomagnetic pulsation related to ionospheric irregularities
Valery M. Sorokin (1), Evgeny N. Fedorov (2), Alexander Yu. Schekotov (2), Oleg A. Molchanov (2) and Masashi Hayakawa (3) 1 ( ) Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN), Russian Academy of Science, Troitsk (Moscow Region), Russia (2) Schmidt United Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia (3) Department of Electronic Engineering, The University of Electro-Communications, Tokyo, Japan

Abstract We consider a depression in intensity of ULF magnetic pulsations, which is observed on the ground surface due to appearance of the irregularities in the ionosphere. It is supposed that oblique Alfven waves in the ULF frequency range are downgoing from the magnetosphere and the horizontal irregularities of ionospheric conductivity are created by upgoing atmospheric gravity waves from seismic source. Unlike the companion paper by Molchanov et al. (2003), we used a simple model of the ionospheric layer but took into consideration the lateral inhomogeneity of the perturbation region in the ionosphere. It is shown that ULF intensity could be essentially decreased for frequencies f = 0.001-0.1 Hz at nighttime but the change is negligible at daytime in coincidence with observational results.

Key words ULF ­ ionosphere ­ Alfven ­ seismicity

1. Introduction While influence of plasma irregularities is important for radio-wave propagation through the ionosphere, the same influence for ULF waves is usually neglected. In the conventional approach to many geophysical problems related to ULF magnetic pulsations (magnetospheric diagnostics, wave-particle interaction inside radiation belts and so on), the ionosphere is approximated by a layer with homogeneous con-

Mailing address: Dr. Valery M. Sorokin, Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN), Russian Academy of Science, Troitsk (Moscow Region), 142092 Russia; e-mail: sova@izmiran.rssi.ru

ductivity, which is connected with the regular conductivity profile integrated on height. However there are some indications that such a simple model is not valid even for the ULF frequency range taking into account the existence of ionospheric perturbations in reality. Alperovich et al. (2002) using both theoretical computations and laboratory experiments showed that rather small ( 10-30%) variations in plasma density can produce a several times increase in «effective» conductivity, included in consideration of ULF wave characteristics. Molchanov et al. (2003) reported the results of ULF magnetic field observations (0.003-5.0 Hz) at Kamchatka region during a long period of seismic activation. They found a remarkable and statistically reliable ULF intensity depression several days before strong seismic shocks. The effect was especially clear at nighttime and for the filter channels 0.01-0.1 Hz and it was absent at daytime. They interpreted the effect in as191


Valery M. Sorokin, Evgeny N. Fedorov, Alexander Yu. Schekotov, Oleg A. Molchanov and Masashi Hayakawa

sumption of atmospheric gravity wave intensification induced by changes in temperature and pressure near the ground due to gas and water release in a course of earthquake preparation. Mareev et al. (2002) considered gravity waves intensification in the ionosphere. An appearance of gravity waves in the ionosphere leads to depression of downgoing from magnetosphere ULF waves due to loss of coherency along the wave front (like scattering) and due to a change in effective ionospheric conductivity. Here we are going to investigate the latter process theoretically. Some results on this subject are obtained in a companion paper by Molchanov et al. (2003) in assumption of vertical stratification of the ionosphere. Here we consider the same effect in assumption of lateral inhomogeneity but for thin ionospheric layer. 2. Electromagnetic ULF field in horizontally inhomogeneous ionosphere We use a simple model, which includes the following: i) Source of the magnetic field ULF pulsations is situated in the magnetosphere and it generates downgoing Alfven waves. They propagate in a homogeneous magnetospheric medium above ionosphere along z-axis, which is coincident with the direction of the external magnetic field. The frequency of the waves <> kA, another words we consider oblique Alfven waves. ii) Ionosphere is a thin layer at z = 0 with integrated Pedersen and Hall conductivities P (x, t), H (x, t) respectively, which are time-dependent and inhomogeneous along the horizontal x-axis (see fig. 1). For simplicity, we neglect input due to ionosphere thickness h, because of kA h << 1 and present
P, H

um is completely conductive and tangential electric field disappears at the ground surface z = h. iv) For simplicity, we assume independence of the all field components on y-coordinate, i.e. /y = 0, and suppose large conductivity along z-axis for magnetosphere and ionosphere that leads to disappearance of electric field component Ez 0. Our model is about the same as was discussed in many other papers (e.g., Lyatsky and Maltsev, 1983). The only difference is assumption on lateral ionospheric inhomogeneity. Alfven wave can reflect from the ionospheric layer and transform in the isotropic mode wave (so-called fast magneto-sonic wave) inside ionosphere. Then both waves penetrate into the Earth-ionospheric cavity. As usual we consider Fourier expansion

E r (x, z, t) =

#
-3

3

dk 2r

#
-3

3

d~ E (k, z, ~) e (ikx - i~t) 2r r (2.2)

where index r = x, y, and the same for magnetic components br. In our model for Alfven wave in the magnetosphere only Ex and by exist and

B

z

1

2

x

h L
3

(x, t) =

P, H

0

+

P, H

(x, t) .

(2.1)

iii) Atmosphere below ionospheric layer is nonconductive and current-free, but the ground medi192

Fig. 1. The model used to calculate the depression of the ULF geomagnetic pulsations: 1 ­ conducting ionosphere; 2 ­ ionospheric inhomogeneities; 3 ­ Earth surface. h is the height of the lower boundary of the ionosphere; L is the spatial scale of the seismic region.


Depression of the ULF geomagnetic pulsation related to occurrence of the ionospheric irregularities

these spectral component are described by following equations: 2 2 E x (x, z, ~) 2 + k A E x (k, z, ~) = 0 2z 2 2E x (2.3) by = 1 , kA = ~ . i~ 2z CA In opposite only component Ey, bx, bz keep in the isotropic wave 2 E y (x, z, ~) + ki2 E y (k, z, ~) = 0 2z 2 2E y bx =- 1 , bz = k E y (2.4) i~ 2z k0 2 2 2 ki = k A - k , k0 = ~/c. As concerned the situation below ionosphere (at the atmosphere) we have well-known relationships 2 2 E r (x, z, ~) 2 + ^k0 - k 2h E r (k, z, ~) = 0 2z 2 2E y k (2.5) bx =- 1 =- z0 E y ik0 2z k0 2E z k ic 2E by = ~ c x = 0E 2z 2x m k z0 x
2 2 where k0 << k 2 and k z20 = k0 - k 2 - k 2. Then after matching of the magnetospheric and atmospheric fields in the ionosphere layer we obtain integral equation for the fields inside ionosphere (see Appendix for details) 2

k A = 4r A ~ c 2, A = c

2

4rC A .

Its connection with ULF magnetic field at the ground is also analyzed in Appendix, where shown bx (, h) >> by (, h) and bx (k, h, ~) =- i #k 6~ sinh ]khg@- E y (k, 0, ~). (2.7) 3. Change in the ULF spectrum on the ground induced by ionospheric perturbations Using conventional approach of perturbation theory we transform (2.6) as following: 4k ~ " -1 " -1 E (k, 0, ~) = 2k A K E) - A2 K $ c 3 " -1 l ! $ # dk l (k - k l) K (k , ~) E) . (3.1)
-3

" -1 where inverse tensor K is easy to find " -1 1 k1 K = l= -k kH 2 , l (k) = k1 (k) k2 + k H . k 2G

H

After substitution in (2.7) we have bx (k, h, ~) = 2i -i ckk A k H E (~, k) + ~l (k, ~) sinh (kh) )
3

" K (k, ~) E (k, 0, ~) = 2k A E) (k) - 4r~ $ c2 3 ! (2.6) $ # dk l (k - k l) E (k l, 0, ~)
-3

4kk A dk l " P (k - k l) $ cl (k, ~) sinh (kh) # -3 $ M 1 (k l, ~) - H (k - k l) M 2 (k l, ~), E) (~, k l) (3.2) where 1 k k (k) + k 6 2@ l (k) H 1 2 M 2 (k) = 1 k H 6k1 (k) k2 - k H@ . l (k) M 1 (k) = ULF magnetic field at the ground we find as the inverse Fourier transform of (3.2) bx (x, h, ~) = bx0 (x, h, ~) - bx1 (x, h, ~) 193

where Ex E) " k1 - k H E = = G, E) = = G, K = = Ey 0 k H k2 G ! P - H = = , k = k P + ki + ik coth (kh) H P G 1 k2 = k P + k A, k P, H = 4r P, H ~ c 2


Valery M. Sorokin, Evgeny N. Fedorov, Alexander Yu. Schekotov, Oleg A. Molchanov and Masashi Hayakawa

ick A k bx0 (x, h, ~) = r~ 2ik bx1 (x, h, ~) = rcA #

H

#
-3 3

3

dke
ikx

ikx

kE) (~, k) l (k, ~) sinh (kh)

$e

i (k - k x ) x

%e

- (k - k x )2 L2

#
-3

dke

k # l (k, ~) sinh (kh)

+e

- (kg + k - k x )2 L2 + {

A.

+ 1 7e 2

- (kg - k + k x )2 L2 - {

+

f=

#
-3

3

dk l " P (k - k l) M 1 (k l, ~) - H (k - k l) $

$ M 2 (k l, ~), E) (~, k l).

k (k ) + k2 P0 , A= 1 x sinh (k x h) A + P0 kx k B= . 2 sinh (kh) 7k1 (k) + k H k2A

(3.6)

(3.3) Finally after averaging we have for the value 2 () = the following resultant relabx bx0 tion:
b = 1 - f a Re *A ^, w xh r

In (3.3) the second term bx1 is due to presence of perturbations in the ionosphere and could be compared with bx 0. As example for solitary initial wave E* (x) = E* exp (ikxx) and E* (k) = 2E* (k + - kx). We obtain
ick A k H k x e ik x ) ~l (k x ) sinh (k x h) 3 ik k # bx1 (x, h, ~) = 4E) cA # dke ikx l (k) sinh (kh) -3 # " P (k - k x ) M 1 (k x ) - H (k - k x ) M 2 (k x ), bx0 (x, h, ~) = 2E
x

#
-3 2

3

dwB (, w) $

$ exp 7i ^w - w xh p - a 2^w - w xh A4 sinh ^w xh 2 2 w x _a1 + - w x + iw x coth ^w xhi w B= sinh ^wh_a2 + 2 - w 2 + iw coth ^whi p = x t , w = kh, w x = k x h = 2rh m x a = L h, = ~ ~ A ~ A = c 2 4r A h = C A h, a1 = 1 + 2 P0 A P0 2 0 H a2 = + . (3.7) A A^ P0 + Ah A=

(3.4) where kx = 2/ x and x is horizontal scale of downgoing Alfven wave. Let us consider influence a moving density variation in the ionosphere (e.g., gravity waves). Alperovich et al. (2002) showed that such a variation leads to mainly perturbation of Pedersen conductivity. So in (3.4) we leave only the first term in the integrand and present the perturbation as following: kg x - { x2 F exp b- 2l 2 4L P (k) = 2 r L P0&e - k L + 1 $ 2 - (k - k) L - { - (k + k) L + { (3.5) $ 7e +e A0 P (x) = 2 P0 2 2 g 2 2 g 2 2

In (3.7) we denote undisturbed integrated Pedersen and Hall conductivities P0, H0 respectively. In a case of the large perturbation zone, >> 1 after simple calculations we have
p2 b ` , p j = 1 - f exp e o Re $ 4a 2 Z _ ] w 0 sinh _ w x i9 a1 + 2 - w 2 + iw x coth _ w x i C b x ` $[ 2 2 ] w x sinh _ w 0 i9 a1 + - w 0 + iw 0 coth _ w 0 i C b \ a p w0 = w x + i (3.8) 2 2a

2

where P0 is averaged amplitude of the perturbation induced by gravity wave, is random phase of the gravity wave, L is spatial scale of the seismic region. Substituting (3.5) in (3.4) we obtain the relative change of ULF magnetic field at the ground bx b - bx1 = x0 =1 - f L A (k x ) r bx0 bx0

In the center of the zone, = 0 relation (3.8) reduced to the following:
b () = 1 - f f
1, 2

f 1 f 2 + f 32 f 22 + f 32 = a1, 2 + 2 - w 2 h _ - w x i x 2 - w 2 h _ w x - i + w x coth w x
x

#
-3

3

dkB (k) $ 194

f3 =

(3.9)

where (x 0) = 1, (x < 0) = 0.


Depression of the ULF geomagnetic pulsation related to occurrence of the ionospheric irregularities

Fig. 2. Dependence of the relative magnetic field at the ground on frequency for night and day hours. Thin lines show the results of calculations in the thin film ionospheric model, bold lines correspond to full-wave calculations in the IRI-90 model. kx = 0.01 km-1 and other parameters are shown on the picture.

Fig. 3. Spatial distribution of the relative magnetic field dependence on distance from projection of the perturbation center in the ionosphere, h is height of lower boundary of the ionosphere (here h = 100 km).

195


Valery M. Sorokin, Evgeny N. Fedorov, Alexander Yu. Schekotov, Oleg A. Molchanov and Masashi Hayakawa

It is evident that ( = 0) = 1 - , ( ) = 1 - (a1 + 1) / (a2 + 1) and () decreases on frequency. At night-time ionosphere when P0 << A we have P0 /A, a1 1, and a2 << 1. At day-time ionosphere when P 0 >> A we have P0 /A, a1 a2 >> 1. Dependence of on frequency under the center of inhomogeneity is shown in fig. 2 for the night and day hours. The values of integrated Pedersen and Hall conductivities are given in the figure. For comparison, these dependences calculated for laterally homogeneous ionosphere of the finite thickness are also shown in fig. 2 for the same values of integrated ionospheric conductivities. The values of () at relatively low frequencies (f < 0.05 Hz) are about 0.6-0.7 for nighttime and 0.90.95 at daytime for both models. At higher frequencies (0.2-0.3 Hz) () calculated with the use of IRI model grows almost up to unity. Several extrema seen at the curve are caused by the ionospheric Alfven resonance and ionospheric MHD waveguide. This effect is not obtained in the thin ionosphere model that gives strong monotonous decrease of with frequency at f > 0.3 Hz. At daytime weakly depends on frequency and is about unity in all the frequency range considered. Spatial distribution of value at the ground found with the relation (3.7) is presented in fig. 3. Note that the size of the depression area is larger than the perturbation scale in the ionosphere.

4. Discussion and conclusions It seems that theoretical results here coincide with observational data reported by Molchanov et al. (2003). Recently Sorokin et al. (2002, 2003) investigated the possibility of generating seismoinduced geomagnetic pulsations due to preseismic changes in the background electric field. Here we try to estimate another possibility in connection with intensification of the atmospheric gravity waves before earthquakes and following the appearance of the ionospheric inhomogeneities. While influence of the horizontal ionospheric irregularities on propagation of the VLF waves is known (e.g., Shklyar and Nagano, 1998), the same influence on the Alfven waves is a rather original problem and we are going to continue this research for a more complicated model taking into consideration both vertical and horizontal stratifications of the ionosphere. Acknowledgements This research was partially supported by ISTC under grant 1121, by Commision of the EU (grant No. INTAS-01-0456) and by RFBR (grant No. 03-05-64553). Two authors (O.A.M. and M.H.) are thankful for support from International Space Science Institute (ISSI) at Bern, Switzerland within the project «Earthquake influence of the ionosphere as evident from satellite densityelectric field data».

Appendix Let us represent the solution of (2.3) as the sum of downgoing and reflecting waves E x (k, z, ~) = E ) (k) 7 e
3 ik A z

+ R a (k, ~) e
ik A z a

- ik A z

A
- ik A z

b y (k, z, ~) = E ) (k) ` c C A j7 e E ) (k) =

- R (k, ~) e
A

A

#
-3

dxe

- ikx

E ) (x),

kA = ~ C

(A.1)

where E* (x, ) is amplitude distribution on the wave front and Ra is reflection coefficient. 196


Depression of the ULF geomagnetic pulsation related to occurrence of the ionospheric irregularities

The similar relationship for isotropic wave as follows: E y (k, z, ~) = E ) (k) R i (k, ~) e - ik ki b x (k, z, ~) = ~ E ) (k) R i (k, ~) e 2 ki = k A - k 2
i

z

- ik i z

ki = ~ E y (k, z, ~) (A.2)

where Ri is reflection coefficient for isotropic waves. As concerned solution of (2.5) we need to take into consideration that Ex,y (z = h) = 0, and to match with above-mentioned solutions at the lower boundary of the ionosphere, hence E x (k, z, ~) = E ) (k) T a (k, ~) sinh 8 k ^ z - h h B b y _ k, z, ~ i =- i ~ E ) (k) T a (k, ~) cosh 8 k ^ z - h h B = - i ~ coth 8 k ^ z - h h B E x (k, z, ~) k k i E y (k, z, ~) = E ) (k) T (k, ~) sinh 8 k ^ z - h h B k k b x _ k, z, ~ i = i ~ E ) (k) T i (k, ~) cosh 8 k ^ z - h h B = i ~ coth 8 k ^ z - h h B E y (k, z, ~) (A.3)

where Ta is transmission coefficient for Alfven wave and T i is coefficient of transformation the Alfven wave into isotropic wave in the ionosphere. It is evident that by / bx = (/ c)2T a/ (k 2T i) << 1, if the transformation is essential. It means that geomagnetic pulsations observed at the ground surface are mainly related to isotropic wave, which is originated from Alfven wave inside ionosphere. The electric fields at the upper boundary of the ionosphere are continuous, hence 1 + R a = - T a sinh (kh), R i = - T i sinh (kh). (A.4)

However discontinuity of the magnetic fields equals to surface currents at the boundary dte i~t # dxe - ikx bx (x, z =+ 0, t) - # dte i~t # dxe - ikx bx (x, z = - 0, t) = -3 -3 -3 R -3 V 3 3 3 3 4r S dte i~t dxe - ikx (x, t) E (x, 0, t) + =cS# # # dte i~t # dxe - ikx H (x, t) E x (x, 0, t)W P y W S- 3 W -3 -3 -3 T X

#

3

3

3

3

#
-3

3

dte

i~t

#
-3

3

dxe

- ikx

b y (x, z =+ 0, t) -

#
-3

3

dte

i~t

#
-3

3

dxe

- ikx

b y (x, z = - 0, t) =

R3 V 3 3 3 W rS (A.5) =- 4c S # dte i~t # dxe - ikx P (x, t) E x (x, 0, t) - # dte i~t # dxe - ikx H (x, t) E y (x, 0, t) W S-3 W -3 -3 -3 T X Suppose now that time variation of the ionospheric conductivity is slow in comparison with geomagnetic pulsations. For example characteristic frequencies of the atmospheric gravity waves are 0 (10-3 - 10-4)c-1 << . If so, we can simplify time integration in (A.5). Using now (2.1), (A.1A.4) and obvious relation

#
-3

3

dte

i~t

#

3

dxe

- ikx



P, H

(x, t) E x, y (x, 0, t) =

#
-3

3

dxe

- ikx



P, H

(x, t) E x, y (x, 0, ~) =

-3

197


Valery M. Sorokin, Evgeny N. Fedorov, Alexander Yu. Schekotov, Oleg A. Molchanov and Masashi Hayakawa

=

P, H0

E

x, y

(x, 0, ~) +

#
-3

3

dk l 2r

P, H

(k - k l, t) E

x, y

(k l, 0, ~)

(A.6)

we finally find for electric field in the ionosphere " K (k, ~) E (k, 0, ~) = 2k A E ) (k) - 4r~ c2

#
-3

3

! dk l (k - k l, t) E (k l, 0, ~) . 2r

(A.7)

Here time t is parameter and definitions are as follows: RE V RE x ) E = S W, E ) = S S0 SEy W S SW TX T k1 = k P + k i + ik coth V R W, " = S k1 - k H KS W k2 W SkH X T (kh), k 2 = k P + k A
2

V ! W, = W W X , k P, H =

R - H SP S H P S T 4r P, H ~ c 2

V W W W X

k A = 4r A ~ c 2 , A = c

4rC A .

REFERENCES CHAIKOVSKY,YU. GURVICH and A. MELLaboratory modeling of the disturbed D- and E-layers: DC and AC fields, in Seismo Electromagnetics: Lithosphere-Atmosphere-Ionosphere Coupling, edited by M. HAYAKAWA and O.A. MOLCHANOV (Terra Scientific Publishing Co., Tokyo), 343-348. LYATSKY, W.B. and YU. P. MALTSEV (1983): The Magnetosphere-Ionosphere Interaction (Nauka, Moscow), pp. 192. MAREEV, E.A., D.I. IUDIN and O.A. MOLCHANOV (2002): Mosaic source of internal gravity waves associated with seismic activity, in Seismo Electromagnetics: Lithosphere-Atmosphere-Ionosphere Coupling, edited by M. HAYAKAWA and O.A. MOLCHANOV (Terra Scientific Publishing Co., Tokyo), 335-342. MOLCHANOV, O.A., A.YU. SCHEKOTOV, E. FEDOROV, G.G. A
LPEROVICH, L., I. NIKOV (2002):

BELYAEV, M. SOLOVIEVA and M. HAYAKAWA (2004): Preseismic ULF effect and possible interpretation, Ann. Geophysics, 47 (1), 119-131 (this volume) SHKLYAR, D.R. and I. NAGANO (1998): On VLF wave scattering in plasma with density irregularities, J. Geophys. Res., 103 (A12), 29515-29526. SOROKIN, V.M., V.M. CHMYREV and A.K. YASCHENKO (2002): Ionospheric generation mechanism of seismic related ULF magnetic pulsations observed on the Earth surface, in Seismo Electromagnetics: Lithosphere-Atmosphere-Ionosphere Coupling, edited by M. HAYAKAWA and O.A. MOLCHANOV (Terra Scientific Publishing Co., Tokyo), 209-214. SOROKIN, V.M., V.M. CHMYREV and A.K. YASCHENKO (2003): Ionospheric generation mechanism of geomagnetic pulsations observed on the Earth surface before earthquake, J. Atmos. Solar Terr. Phys., 64, 21-29.

198