Download Electric Field Perturbation Caused by an Increase in

ISSN 1990-7931, Russian Journal of Physical Chemistry B, 2007, Vol. 1, No. 6, pp. 644–648. © Pleiades Publishing, Ltd., 2007.
Published in Khimicheskaya Fizika, 2007, Vol. 26, No. 4, pp. 39–44.
CHEMISTRY
OF THE ATMOSPHERE
Electric Field Perturbation Caused by an Increase
in Conductivity Related to Seismicity-Induced Atmospheric
Radioactivity Growth
V. M. Sorokina, A. K. Yashchenkoa, and M. Hayakawab
a
Pushkov Institute of Terrestrial Magnetism, the Ionosphere, and Radio Wave Propagation (IZMIRAN),
Russian Academy of Sciences, Troitsk, Moscow Region, Russia
b The University of Electrocommunications, Department of Electronic Engineering, Tokyo, Japan
Received June 8, 2006
Abstract—The influence of conductivity perturbation in the lower atmosphere on the DC electric field over a
seismic region is investigated. This perturbation is related to the emanation of radon and other radioactive elements into the lower atmosphere as the seismic activity increases. An increase in the level of atmospheric radioactivity results in the appearance of additional ionization sources. The altitude dependence of the ion formation
rate is calculated. An ionization source changes the atmospheric conductivity because of the appearance of ions
with an equilibrium number density. The perturbation of the atmospheric conductivity is calculated as a function of the altitude. Lower atmosphere conductivity changes disturb the electric current that flows in the global
atmosphere–ionosphere circuit. This disturbance is caused by an external current over a seismic region. DC
electric field perturbations on the Earth’s surface and in the ionosphere are estimated.
DOI: 10.1134/S1990793107020200
1. INTRODUCTION
Starting with works [1, 2], attempts have been made
to use DC electric field perturbations observed above
seismic regions for predicting earthquakes [3–8].
According to [1, 2], DC electric field variations can be
caused by an increase in the conductivity of the lower
atmosphere resulting from the increased injection of
radioactive elements, including radon and aerosols, at
the preparative stage of an earthquake. Such injections
precede earthquakes by several days or several weeks
(e.g., see [9–13]). The time dependences of the concentration of radon in soil gases and in spring water were
studied in [10]. According to [10], the concentration of
radon suddenly increased by a factor of 2.5 or 1.5 about
a week before an earthquake within 300 km around the
epicenter. A fourfold increase in the concentration of
radon five days before an earthquake was reported in
[13]. According to the statistical data on 300 micro
earthquakes (M < 4), a significant growth of the radon
number density was observed in 75% of the events.
instance, before an earthquake, causes an increase in
the ion formation rate and, accordingly, conductivity.
A scheme of processes that perturb the electric field is
shown in Fig. 1. The conductivity of the near-earth
atmospheric layer is low, and its increase causes electric current variations between the Earth’s surface and
the ionosphere. This current appears because of an
The main ionizing factor that determines the level of
conductivity in the near-surface layer is atmospheric
radioactivity. The natural radioactivity of the lower
atmosphere is largely related to such elements as radon,
radium, thorium, and actinium and their decay products. Radioactive elements get into the atmosphere with
soil gases. They are then transferred upward by several
km by air streams. As a result, the ion formation rate
reaches several tens of ion pairs in 1 cm3 per second. An
increase in the level of atmospheric radioactivity, for
644
z
B
4
2
z1
3
5
x
6
7
8
1
Fig. 1. Scheme of the model used to calculate the influence of
radon on the electric field in the atmosphere–ionosphere circuit: (1) the Earth’s surface, (2) ionosphere, (3) conduction
current in the atmosphere and ionosphere, (4) field aligned
current, (5) region of vertical convection of charged aerosols
and formation of extraneous electric current, (6) region of
atmospheric conductivity perturbation caused by the injection of radioactive elements, (7) charged aerosols and soil
gases moving upward, and (8) the injection of radon.
ELECTRIC FIELD PERTURBATION CAUSED BY AN INCREASE
external current related to the preparation of an earthquake [14, 15]. It follows that this effect is responsible
for DC electric field perturbations both on the Earth’s
surface and in the ionosphere.
2. SOURCE OF IONIZATION
We obtained the vertical distribution of the ion production rate determined by the absorption of gamma
quanta and alpha particles formed in the decay of radioactive elements by the atmosphere. These are atmospheric radioactivity constituents. Let us introduce Cartesian coordinates (x, y, z) with the z axis directed
upward. Let the Earth’s surface coincide with the z = 0
plane. We assume that the vertical distribution of the
concentration of radioactive elements in the atmosphere is described by the NR(z) function and the ion
production rate under the action of atmospheric gamma
quanta, by the qγ(z) function. Because the initial angular distribution of gamma radiation is isotropic, the
number of quanta Nγ generated in unit volume per unit
time and unit solid angle is Nγ = ˚NR/4π, where ˚ =
ln 2/T and T is the effective half-life. Gamma radiation
is absorbed by electrons of air molecules as a result of
the Compton effect. The distribution function f(r, t, θ)
of quanta satisfies the transfer equation [16]
∂f
f
∂f
----- + v ----- = – ---- + N γ ,
∂r
τγ
∂t
τ γ = -----γ ,
c
(1)
where e(z) = e0 exp(z/H) is the mean free path of electrons depending on the altitude z. During their movement in air, fast electrons lose energy in collisions with
molecules. As a result, low-energy secondary electrons
appear. Let ε be the energy of a fast electron. The
absorbed energy of fast electrons in air in the unit volume is then nε. The formation of an electron–ion pair in
air requires ε0 = 33 eV absorbed energy [18]. The number of secondary low-energy electrons per 1 cm3 produced during the lifetime of fast electrons is therefore
nλ, where λ = ε/ε0. It follows that the mean rate of secondary electron formation qγ is determined by the
equality
λc
λc
q γ ( z ) = ------------n ( z ) = ------------n γ ( z ).
e ( z )
γ ( z )
The vertical distribution of the concentration of
radioactive elements in the atmosphere is determined
by many factors, such as meteorological conditions,
turbulent diffusion, gravity, etc. To estimate the influence of increasing atmospheric radioactivity near the
Earth’s surface on the conductivity and electric field of
the atmosphere, let us select the altitude dependence of
the concentration of radioactive substances in the form
NR = NR0 exp(–z/HR). Substituting (2) into (3) and integrating over the solid angle yields the altitude dependence of the ion formation rate under the action of
gamma quanta of atmospheric radioactivity,
where v is the quantum propagation velocity (|v| = c),
c is the velocity of light, γ is the mean free path of
quanta, and θ is the angle between the quantum velocity
vector and z axis. For an exponentially inhomogeneous
atmosphere with the scale H, the mean free path of
quanta depends on the altitude as
q γ = q γ 0 F [ exp ( – z/H R ) ]/F ( 1 ),
1
∫
F( y) = y x
∞
where γ0 denotes the mean free path on the Earth’s surface. In the one-dimensional and stationary approximation, we obtain
(2)
The number of quanta per unit volume nγ(z) is found by
integrating the f(z, θ) distribution function over the
solid angle,
π
∫
n γ ( z ) = 2π f ( z, θ ) sin θ dθ.
(3)
0
Because of the Compton effect, gamma radiation generates a flux of fast electrons in air whose number density n(z) is found by the equation [17]
e ( z )
e0
n ( z ) = ------------n
γ ( z ) = ------- n γ ( z ),
γ ( z )
γ 0
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
H/ H R – 1
0
γ ( z ) = γ 0 exp ( z/H ),
˚
df ( z, θ )
f ( z, θ )
------------------- + ------------------------- = ---------------------- N R ( z ).
dz
γ ( z ) cos θ 4πc cos θ
645
E1 ( u ) =
exp ( – ux )
- d x,
∫ ---------------------x
1
H
E 1  ------- x – y  d x,
 γ 0

λ˚H N R0 F ( 1 )
(4)
q 0 = ---------------------------------,
2 γ 0
where E1(u) is the integral exponential function. The qγ0
value is the ion production rate on the Earth’s surface,
and HR is the spatial scale of the altitude distribution of
the concentration of radioactive elements. Because the
mean free path of alpha particles in air is very small, the
altitude dependence of the ion formation rate qα under
the action of these particles coincides with the altitude
dependence of the concentration of radioactive substances in the atmosphere, qα = qα0 exp(–z/HR). In addition to atmospheric radioactivity, the lower atmosphere
is ionized by cosmic rays. The vertical distribution of
the rate of ion formation under the action of cosmic
rays can be approximated by the Chapman function
Ch(z – zm), where zm is the altitude corresponding to the
ionization rate maximum and the qm rate value at this
altitude [19]. The total ion production rate in the lower
atmosphere is the sum of the rates of ion formation
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SOROKIN et al.
z, km
z, km
4
8
3
6
2
4
1
1
2
3
2
0
0
50
100
3
2
1
10–3
150
qr(0, z), cm–3 s–1
10–2
σ, s–1
Fig. 2. Altitude dependences of the rate of formation of
ions at r = 0; the parameters used in the calculations: q0 =
10 cm–3 s–1, HR = 2 km, and B = 1; A = (1) 0, (2) 4, and
(3) 9.
Fig. 3. Altitude dependences of the atmospheric conductivity at r = 0; the parameters used in the calculations: q0 =
10 cm–3 s–1, HR = 2 km, Ha = 5 km, and B = 1. See Fig. 2
for the notation.
under the action of cosmic rays and atmospheric radioactivity,
where n+ and n– are the number densities of positive and
negative light ions and µ = µ0 exp(z/H) is the mobility of
light ions in the atmosphere [20]. To calculate the conductivity, we must find the dependence of the equilibrium ion number density on the ion formation rate. The
equilibrium concentrations of electrons and ions are
determined by their recombination in air. To estimate
the stationary ion–molecular composition of the atmosphere, we use a simplified system of ionization-recombination processes [21]. The lower atmosphere contains
not only light singly charged but also heavy ions
formed when light ions adhere to aerosols. The number
densities of light positive and negative ions n responsible for lower atmosphere conductivity are largely determined by their recombination and adhesion to aerosols
[20],
 r 2
q0
- 1 + A exp  – ----2
q ( r, z ) = q m Ch ( z – z m ) + -----------1+B
 r 0
(5)
 F [ exp ( – z/H R ) ]
z 
- + B exp  – ------- ,
×  ------------------------------------
F(1)
H R 

where A is the index of radioactivity growth in the nearEarth layer and B is the index of the relative efficiency
of gamma radiation and alpha particle ionization
sources. This index is within the range 0 < B < ∞. If
B = 0, ionization occurs under the action of gamma
radiation only, and, if B
∞, the source of ionization
is alpha particles. In the second term on the right-hand
side of (5), the horizontal dependence of the radioactiv2
ity source is selected in the form exp(–r2/ r 0 ). The altitude dependences q = q(r = 0, z) calculated by Eq. (5)
are shown in Fig. 2. It follows from these plots that the
vertical distribution of the ion formation rate differs
from the exponential altitude dependence of the atmospheric radioactivity. We see a significant increase in
the ion production rate at the function maximum.
3. CHANGES IN ATMOSPHERIC
CONDUCTIVITY
(7)
where N is the concentration of aerosols, α is the
recombination coefficient of light ions, and β is the
attachment coefficient of light ions to aerosols. The vertical distribution of the mean concentration of soil aerosols is described by the exponential function N(z) =
N0exp(–z/Ha) [22], where Ha is the spatial scale of this
distribution. The altitude dependence of the effective
recombination coefficient α satisfies the equation [12]
–8
–6
3
–1
α ( z ) = [ 5 × 10 + 2.5 × 10 exp ( – z/H ) ], cm s ,
The conductivity of the atmosphere σ(z) is determined by the concentration of light ions,
σ = e ( µ + n + + µ – n – ) ≈ 2eµn,
βN
αq  1/2
–1 ,
n = -------  1 + ----------2 2
α 
β N
(6)
where H is the spatial scale of the exponentially
inhomogeneous atmosphere. Induced conductivity
calculations are illustrated by Fig. 3. The following
parameters were used: the aerosol number density on
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ELECTRIC FIELD PERTURBATION CAUSED BY AN INCREASE
|Ez|, V/m
120
3
100
2
80
1
Er, mV/m
10
1
2
8
3
647
6
60
4
40
2
20
0
100
200
300
r, km
0
100
200
300
r, km
Fig. 4. Radial dependences of the vertical electric field component on the Earth’s surface at B = 1. See Fig. 2 for the
notation.
Fig. 5. Radial dependences of the horizontal electric field
component in the ionosphere at B = 1. See Fig. 2 for the
notation.
the Earth’s surface N0 = 2 × 103 cm–3, the spatial
scale of their vertical distribution Ha = 5 km, the
attachment coefficient of light ions to aerosols β =
4.3 × 10–6 cm3 s–1, qm = 40 cm–3 s–1, zm = 14 km, HR =
2 km, µ0 = 2.3 cm2 s–1 V–1, and q0 = 10 cm–3 s–1 [20]. It
follows from the plots that a rapid growth of conductivity is observed in the surface layer. Over the altitude
range 6–8 km, we observe an increase in conductivity
as the radioactivity level rises.
seismic region depends on the atmospheric conductivity as
E z ( r ) 1/2
1 
E z ( r ) = -----------------  [ J p ( r ) – j p ( r, 0 ) ]  1 + -----------
σ ( r, 0 ) 
Ec 
E z ( r )
– [ J n ( r ) – j n ( r, 0 ) ]  1 – -----------
Ec 
2
2
2
2
j p ( r, z ) = j p0 exp ( – r /r 0 – z/h p ),
j n ( r, z ) = j n0 exp ( – r /r 0 – z/h n ),
where jp and jn are the currents of the positively and
negatively charged aerosols, hp and hn are the vertical
scales of their distributions, and r0 is the scale length in
the horizontal direction. According to [14], the vertical
DC electric field component on the Earth’s surface in a
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
z1
∫
∫

,

(8)
–1
j p, n ( r, z ) 
dz 
-  ---------------- .
J p, n ( r ) = dz -------------------σ ( r, z )  σ ( r, z )
0
0
4. ELECTRIC FIELD PERTURBATION
Let us consider the influence of conductivity perturbations on DC electric fields on the Earth’s surface and
in the ionosphere. This field is related to the conduction
current flowing in the atmosphere–ionosphere circuit
whose source is an external current [14, 15]. The formation of an external electric current in the atmosphere
over a seismic region is caused by turbulent transport of
charged aerosols upward, their gravitational sedimentation, and charge neutralization. These aerosols are
injected from soil together with radon. Growth of seismic activity intensifies aerosol injection with soil gases.
This injection intensification covers areas of from tens
to hundreds of km in diameter. Let us consider a largescale external electric current with an axially symmetrical amplitude distribution in the horizontal plane and
a geomagnetic field directed vertically upward,
z1
1/2
The horizontal DC electric field component in the ionosphere is determined by the equality
r
1
E r ( r ) = ------------ dr'r'
2Σ P r
∫
(9)
0
E z ( r' )
× J p ( r' )  1 + ------------
Ec 
1/2
E z ( r' )
– J n ( r' )  1 – ------------
Ec 
1/2
.
The Ez(r) dependences for undisturbed conductivity
and conductivity disturbed by a five- and tenfold
increase in the radon concentration are shown in Fig. 4.
The dependences were calculated using (5)–(8). The
calculation parameters were selected the same as in
[14]: Ec = 0.015 CGSE = 450 V m–1, jp0 = 2.41 CGSE =
8 × 10–6 A m–2, jn0 =1.54 CGSE = 5.12 × 10–6 A m–2, hp =
7 km, hn = 5 km, r0 = 100 km, and ΣP = 2 × 1012 cm s–1.
The Er(r) dependence for the ionosphere calculated by
(9) is shown in Fig. 5. It follows from the calculation
results that the DC electric field on the Earth’s surface
increases by 10–20%. This field weakly depends on the
conductivity because of the electric field limitation
effect on the Earth’s surface. The Jp, n current deter-
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648
SOROKIN et al.
mined by (8) weakly depends on the conductivity
because both the numerator and denominator in (8)
depend on the conductivity. The relative electric field
changes in the ionosphere are of 10–20% and reach
2 mV/m in magnitude.
5. CONCLUSIONS
In this paper, we considered slow (from one to ten
days) and large-scale (from tens to hundreds of km)
changes in the conductivity over a seismic region and
their influence on DC electric fields in the atmosphere
and ionosphere. Such a scale of conductivity changes is
determined by the emanation of radioactive elements,
including radon, into the atmosphere over a seismic
region and their mixing by winds. As a result, the atmospheric radioactivity level increases. The injection of
radon, other radioactive elements, soil gases, and
charged aerosols is responsible for the formation of
atmospheric radioactivity and external electric current
in the lower atmosphere. The appearance of external
current in the lower atmosphere changes the conduction
current and electric field in the atmosphere–ionosphere
circuit. The injection of radon into the region of external current formation was shown to perturb conductivity in this circuit region and therefore the DC electric
field both on the Earth’s surface and in the ionosphere
over a seismic region. Calculations show that, because
of this mechanism, an increase in radioactivity by a factor of five or ten causes electric field changes on the
order of 10–20%. These changes are fairly substantial
for the ionosphere, whose electric field is higher than
2 mV/m. According to [7], an increase in the conductivity of the pure lower atmosphere without aerosols
changes the electric field by 10–30% near the Earth’s
surface and by a factor of two in the ionosphere. However, this field virtually does not penetrate into the ionosphere, because its value is only 10–3 mV/m. A twofold change in the field in the ionosphere is then insignificant.
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