Annals 47, 1, 2004, 01/07def 101 ANNALS OF GEOPHYSICS, VOL. 47, N. 1, February 2004 Key words ULF oscillations – magma – volcano – electromagnetic emission 1. Introduction Seimoelectric and seisomomagnetic effects in rock were first measured and described in the late 1930’s, and since that time have been the subject of various analytical investigations. The electromagnetic effects are explained by tectonic processes that occur in rock prior to an earth- quake (see, e.g., Stacey, 1964; Mogi, 1985). In this article, another possible model of electro- magnetic excitation over an active volcanic zone is proposed. Consider magma as a two-phase liquid (liquid and gas) with viscosity of approximately ν = 5 m2/s and a density ρ ≈ 2500 kg/m3 (Marchinin, 1985). Initially, magma is found at a depth of ap- proximately 100 km. When volcanic activity in- creases, magma moves upward toward the Earth’s surface through volcanic channels, filling inter- mediate volcano capacities whose depth can vary from 2 to 20 km and whose radii vary. For exam- ple, the capacity under the Kluchevskii volcano is estimated to be 4 km deep with a radius of 3600 m (Fedotov et al., 2000) and the capacity under the Shiveluch volcano is 20 km deep with a radius of 6000 m. Just prior to an earthquake, the move- ment of magma becomes more intense, and waves and vortices develop. In the presence of the Earth’s constant magnetic field, these movements induce the formation of variable magnetic fields with different periods which then contribute to the common electromagnetic emission that is present before the earthquake starts (Ismaguilov et al., 2001.) We will now discuss the possible mecha- nisms of excitation of magnetic fields in magma and estimate their magnitude. 2. Hydrodynamic processes in magma Consider three kinds of hydrodynamic pro- cesses in magma that can lead to electromag- netic emission. A possible model for initiation of ULF oscillation in magma Yuri A. Kopytenko and Lidia V. Nikitina St. Petersburg Department of Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (SPbFIZMIRAN), Russian Adademy of Science, St. Petersburg, Russia Abstract During the period just prior to an earthquake, an electomagnetic emission develops over seismic zones. In this paper, a model of excitation of magnetic fields over zones of volcanic activity is proposed. Movement of mag- ma along volcanic channels precedes an earthquake, hydrodynamic processes in the moving magma can lead to formation of waves and vortices in the flow which, in turn, can cause development of magnetic fields in con- ducting magma. During this period, the movement of the magma intensifies leading to a corresponding intensi- fication of the magnetic fields. In this paper, different possible sources of ULF pulsation in magma are exam- ined, and the variable geomagnetic fields induced by this pulsation are estimated. Mailing address: Dr. Lidia V. Nikitina, St. Petersburg Department of Institute of Terrestrial Magnetism, Iono- sphere and Radiowave Propagation (SPbFIZMIRAN), Rus- sian Adademy of Science, p/b 188, Muchnoi 2, 191023 St. Petersburg, Russia; e-mail: lida@mail.spbnit.ru 102 Yuri A. Kopytenko and Lidia V. Nikitina 2.1. Lifting of magma in magma channels Prior to the seismic event, magma moves in volcanic channels toward the ground’s surface. Magma velocity is approximately 1-5 m/s (Mar- chinin, 1985; Slezin, 1999). The electromagnet- ic fields can be induced by magma flow in the presence of the Earth’s constant magnetic field. These fields are quasi-constant, and their values depend on the velocity of rising magma and the radius of the volcanic channel. 2.2. Oscillations at the magma surface The possible sources of the ULF electro- magnetic pulsations are the oscillations that can appear at the magma surface (fig. 1). Inertial waves appear on the surface of liquid between two media with different densities. The frequen- cy of waves on the magma surface depends on the relative change of density between the gas and the magma and on the diameter of the chan- nel. f gk 2 2 1 2 1= - +t t t t_ _` i ij (2.1) where k is the wave number, ρ1 is the gas den- sity, ρ2 is the magma density. Relative changes in the density can be estimated as (ρ2 − ρ1)/ (ρ2 + + ρ1) ≈ 0.5. If the magma surface is in the intermediate volcanic capacity with diameter d ≈ 103 m (k = = 10−3 m−1) then according to (2.1) oscillations exciting in magma have frequencies of approx- imately f = 10−2 Hz (T = 100 s). If magma is in a channel with a diameter of approximately 100 m then oscillations with period ranging 10-30 s are excited in the magma. Bubbles of gas dis- turb the magma surface constantly and support the oscillations on this surface. Increasing volcanic activity leads to the ap- pearance of new gas bubbles. Gas moves in a channel with a velocity greater than the up- welling velocity of the magma (Proussevitch et al., 1993; Slezin, 1999). Step by step, a large volume of bubbles accumulates at the magma surface where they create a foam structure. This leads to a smaller difference in density between the magma and the gas, and inertial waves be- come weaker. The decrease in wave intensity must be typical for the duration of the pre- earthquake period when a large amount of gas accumulates in the magma. After the magma becomes free of the «foam cap» (for example, when new cracks appear), the density difference between the gas and the magma is restored, and inertial waves are initi- ated at the magma surface again. So, at the fre- quency of inertial waves we can observe that an increase in ULF magnetic pulsation is replaced by a decrease in oscillation corresponding to increased volcanic activity. 2.3. Influence of Coriolis force to the magma movement Another cause of the ULF movements in magma is related to vortex structures that appear in magma flow (see fig. 1). When magma is fill- ing a large intermediate volcano capacity, vortex flow appears in magma according to Coriolis force v2= ΩRv r 2 { where R is the vortex radius, Ω is the angle ve- locity of the Earth’s rotation, Ω ≈ 7⋅10−5c−1, vϕ is the rotation velocity of liquid, vr is the radial ve- locity. If we assume that vr is approximately Fig. 1. Oscillations and waves in a volcano capaci- ty. The magnetic field bz induced by the vortex in the volcano capacity. 103 A possible model for initiation of ULF oscillation in magma equal to the upwelling velocity of magma in the channel and the radius of the volcanic center is approximately R = 1000 m, then the liquid rotates with angle velocity 5.10− 3 rad/s and rotation ve- locity vϕ = 5 m/s. 3. Electromagnetic emission induced by hydrodynamic processes in magma Let us estimate the magnetic fields induced by the processes in magma described above. The most difficult problem connected with the esti- mation of electromagnetic fields is estimating the conductivity of magma. Conductivity of basalts is estimated to be 10− 3 Sm/m at the Earth’s surface, but their conductivity depends strongly on tem- perature. Magma temperature in volcano chan- nels reaches 1000-1300°C. If temperature in- creases to the values 500-1000° then conductivi- ty increases on 2-3 fold (Van’yan, 1983). Accord- ing to these data we assume that conductivity of hot magma is approximately σ = 10− 1 Sm⋅m−1. 3.1. Magnetic fields induced by rising magma flow Assume lifting magma in a channel is similar to the cylindrical flow of a conducting liquid. The magnetic field induced by the cylindrical flow can be estimated as (Parker, 1979) B B RvZ x Z0. nv where B0x is the horizontal component of the Earth’s magnetic field, R is the radius of the cylinder. If we assume that σ = 10−1 Sm⋅m−1, B0x = = 2⋅104 nT, vz = 1-5 m/s and the capacity radius is R = 1000 m then Bz ≈ 2-10 nT (fig. 2). The in- crease in the magnetic field during early seismic activity can be initiated by the acceleration of the flow. 3.2. Electromagnetic emission induced by inertial oscillations The vertical component of the magnetic field bz induced by inertial oscillations can be estimated from the induction equation nvrot v B0# = b∆^ h where σ is the media conductivity, v is the os- cillations velocity, B0 is the Earth’s magnetic field. The magnetic field induced by the wave is approximately b B k v kz z x x z0 2 = nv (3.1) where kx and kz are horizontal and vertical com- ponents of the wave vector. For inertial oscillations with T = 100 s ac- cording to (3.1) the induced magnetic field is bz ≈ 0.1 nT, if kx = 10−3 m−1, vx = f / kx = 10 m/s, kz = 10−2 m−1. For inertial oscillations with T = = 10-30 s the induced magnetic field is ap- proximately bz ≈ 0.01 nT if kx = 10−2 m−1, vx = = 1/( f⋅kx) = 6 m/s, kz = 10−1 m−1. As the period of oscillation increases, the magnitude of the induced magnetic fields increases too. 3.3. The magnetic fields induced by the vortex in intermediate volcano capacities A vortex in a conducting liquid in the pres- ence of a constant magnetic field induces a Fig. 2. The magnetic field Bz induced by the lifting flow of magma. R is the radius of the channel or magma capacity. 104 Yuri A. Kopytenko and Lidia V. Nikitina constant azimuthal magnetic field (Parker, 1979) B V B D 2z0= nv{ { where Vϕ is the rotation velocity, D is the depth of rotating liquid. The value of the magnetic field induced by magma movements in intermediate volcanic capacity is approximately Bϕ = 2.5 nT for D = = 1000 m, vϕ = 5 m/s, s = 10−1Sm⋅m−1. The vertical magnetic field bz over the vortex is calculated as a field of circular current jϕ = = σ (vr × B0 z) b j r dS2z S = n ## _ i where S is the magma surface. Then the in- duced magnetic field is approximately bz = µσπ⋅ · B0z R0vz. The qualitative estimation gives a val- ue bz ≈ 10 nT (see fig. 1). The value of the magnetic field that can be measured on the Earth’s surface, at distance r from the magnetic field source is approximately .b r B R v r2z z z0 0 3 2 = nvr] g At distance r = 100 km from the volcanic cen- ter the measured magnetic field must be ap- proximately 0.05-0.1 nT. The corresponding gradient of the magnetic field is approximately ∇bz ≈ 1 pT/km. These theoretical results are in accordance with the measurements. In practice, the verti- cal component of the magnetic fields decreas- es as r−n where n ≈ 1.2 (Ismaguilov et al., 2001) and the gradient of the magnetic field is 1-5 pT/km. 4. Comparison with observed data Let us compare the described mechanism of magnetic field excitation with the results of ac- tual measurements. Measurements of ULF electromagnetic disturbances were carried out in Japan before and during a period of seismic activity. (Ismaguilov et al., 2001). Behavior of the magnetic field prior to the earthquake has the following stages: 1) The magnitude of the magnetic field starts to increase ≈ 1.5 months before the seis- mic activity in the frequency band 0.001-0.01 Hz. 2) On the background of the common in- crease oscillations of the magnetic field value are observed with the period of approximately some days. 3) The magnetic field decreases sharply (1.5-2 days) prior to the earthquake. According to the mechanism described above, the increase in the magnetic field just prior to an earthquake is related to the lifting of magma to the Earth’s surface. Oscillations of the magnetic field can be related to changes in magma levels in volcanic channels and capaci- ties and with inertial waves at the surface of magma. Sharp decrease of the magnetic field 1.5-2 days before the earthquake can be explained by slowing of all movements in magma before the beginning of the earthquake, by the great amount of gas bubbles and/or hard particles that accumulate at the magma surface and dif- ficulties in upwelling of magma and also vor- tex and wave movements in it. The observed values of the magnetic fields are about 0.01-0.4 nT, that corresponds to the estimations made. 5. Conclusions We can assume that hydrodynamic process- es in magma are one of the possible causes of electromagnetic emission. In this work, three different possible mechanisms for excitation of magnetic fields were examined. These are: i) magma flow in volcano channels; ii) inertial waves at the magma surface that contribute to the magnetic field at the frequen- cies 0.01-0.1 Hz; iii) vortex flows that appear in magma when magma fills intermediate capacities. A general increase in seismic activity leads to an intensification of the hydrodynamic pro- cesses in magma and to changes in electromag- netic emission. 105 A possible model for initiation of ULF oscillation in magma Acknowledgements The authors are very grateful to Dr. Richert- Boe for her help and useful discussions. REFERENCES FEDOTOV, S.A., I.S. UTKIN and L.I. UTKINA (2000): The es- timation of scales of core volcano centers, Volcanol. Seismol., 3, 3-14. ISMAGUILOV, V.S., YU. A. KOPYTENKO, K. HATTORY, P.M. VORONOV, O.A. MOLCHANOV and M. HAYAKAWA (2001): ULF magnetic emissions connected with under sea bottom earthquakes, Natural Hazards Earth Sys. Sci., 1, 23-31. MARCHININ, J.K. (1985): Volcanism (Nedra, Moscow), pp. 285 (in Russian). MOGI, K. (1985): Earthquake Prediction (Academic Press. Tokyo), pp. 355. PARKER, E.N. (1979): Cosmical Magnetic Fields. Their Ori- gin and Their Activity (Claredon Press, Oxford), pp. 858. PROUSSEVITCH, A.A., D.L. SAHAGIAN and V.A. 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