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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 Vol. 1 No. 6 2007 646 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 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 1 No. 6 2007 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- Vol. 1 No. 6 2007 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. 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