Estimate of ULF electromagnetic noise caused by a fluid flow during seismic or volcano activity ANNALS OF GEOPHYSICS, 58, 6, 2015, S0655; doi:10.4401/ag-6767 S0655 Estimate of ULF electromagnetic noise caused by a fluid flow during seismic or volcano activity Vadim V. Surkov1,*, Vyacheslav A. Pilipenko2 1 National Research Nuclear University MEPhI, Moscow, Russia 2 Institute of Physics of the Earth, Russian Academy of Science, Moscow, Russia ABSTRACT The elaboration of theoretical models, even oversimplified, capable to es- timate an expected electromagnetic effect during earthquake preparation process is not less important than the advancement of observational tech- nique to detect seismic-related electromagnetic perturbations. Here pos- sible mechanisms of ULF electromagnetic noise associated with seismic or volcanic activity are discussed. The electrokinetic (EK) and magneto- hydrodynamic (MHD) effects due to an irregular flow of conducting rock fluid or magma flow are being revised. The conventional theory of EK ef- fect in a water-saturated rock has been advanced by consideration of el- liptic-shaped channels. A contribution of both mechanisms to observed ULF signal on the ground is shown to be dependent on the pore channel size/rock permeability. Estimates of magnetic and electrotelluric pertur- bations caused by magma motion along a volcano throat indicate on the important role of the surrounding rock conductivity. These estimates have proven that the mechanisms under consideration are able to generate ULF electromagnetic perturbations which could be detected by modern mag- netometers under favorable conditions. 1. Introduction At the time being it is clear that the tectonic plate dynamics can provide long-term (tens-hundred years) earthquake prediction, but not short-term (days-weeks) seismic warning. This situation demands the search for alternative techniques for the short-term prediction of impending earthquakes. A special credit has been paid in the last decades to the study of a variety of electro- magnetic and other non-seismic phenomena possibly associated with the earthquake preparation process. Considerable efforts have been devoted to the study of electromagnetic signals/noise in the Ultra-Low-Fre- quency (from few mHz to tens of Hz) band (extensive list of references can be found in papers collected by Hayakawa and Molchanov [2002], Molchanov and Hayakawa [2008], and Hayakawa [2013]). These stud- ies were stimulated by effective detection of electro- magnetic effects in a wide frequency band accompany- ing sample fracture in laboratory [e.g., Cress et al. 1987, Freund 2000, Vallianatos et al. 2012]. Easy availability of data from world-wide array (~200) of magnetome- ters favored an extensive search for seismic-related ULF anomalies. However, it was soon realized that ULF per- turbations possibly related to the seismic activity are weak as compared with typical magnetosphere/ionos- phere pulsations and industrial interference, so they can be directly recorded only under exceptionally favorable conditions: close proximity to an epicenter of impend- ing earthquake and geomagnetically quiet period [e.g., Molchanov et al. 1992]. Therefore, much effort has been concentrated in search of peculiar features of seis- mic-related ULF perturbations that would make possi- ble to reveal them even under low signal/noise ratio. There were numerous attempts to find anomalous ULF behavior with a simple measure of their spectral fea- tures - the slope of averaged power spectrum (“fractal properties”) [e.g., Gotoh et al. 2004]. Another approach uses the ratio between the ULF vertical Z and horizontal G components. It is expected that an underground source produces a signal on the ground with larger Z/G ratio than a magnetospheric/ionospheric source does [Hayakawa et al. 1996]. Attempts to discriminate seismic and magnetospheric ULF sources were made with the use of the gradient observations [Krylov and Nikiforova 1995, Kopytenko et al. 2006]. More advanced technique - the principal component analysis, seems promising to identify and suppress magnetospheric pul- sations and industrial interference [Gotoh et al. 2002]. However, many of seemingly successful results of seis- mic-related ULF perturbation discovery could not pass simple tests: lack of correlation with geomagnetic ac- tivity and absence of claimed features at distant stations [Campbell 2009, Thomas et al. 2009, Masci 2011]. Article history Received March 25, 2015; accepted July 31, 2015. Subject classification: Models and forecasts, Earthquake source and dynamics, Groundwater processes, Volcano seismology, Magmas. Development in a contentious field of earthquake prediction requires an advance not only in monitoring technique, but in a reliable estimate of physical mod- els plausibility. Electromagnetic disturbances in the ULF frequency band, with the skin-depth correspon- ding to crustal earthquake hypocentral depth, are still considered as one of the most promising monitors of earthquake precursors. Majority of modern theories predict that the amplitude of the seismic-related ULF signals can be of the order of or greater than back- ground ULF noise at the epicentral distances no more than one hundred km. The generation mechanisms of seismic-related ULF electromagnetic fields considered so far (see the book by Surkov and Hayakawa [2014] for a complete review) comprise: - the electric charge redistribution during micro- cracking [Molchanov and Hayakawa 1995]. However, the estimated amplitude of this effect seems to be much lower than the background noise level because of the random orientation of the dipole moments of individual microcracks [Surkov and Hayakawa 2014]; - inductive geomagnetic response to the tension crack openings in a conductive rock [Surkov 1997, Surkov and Hayakawa 2006]. An advantage of this mechanism is that the effective magnetic moments of all cracks are co-directed and anti-parallel to the Earth magnetic field; therefore they operate as a coherent am- plifier of ULF noise; - the stress-induced electric current in the rock caused by the changes in mobility of charged disloca- tions [Tzanis and Vallianatos 2002] and/or point defects [Freund 2000]. Some theories interpreted the occurrence of ULF electromagnetic noise as a result of the crust fluid dy- namics. The flow of high-pressure fluid in fault zones has an irregular character (“stop-and-start”) [Byerlee 1993]. Such non-steady filtration of conductive fluid is to be accompanied by electromagnetic disturbances due to magnetohydrodynamic (MHD) effect [Draganov et al. 1991]. However, the importance of this mechanism was overestimated by four orders of magnitude by Draganov et al. [1991] because of an unrealistic rock permeability used in this study [Surkov and Pilipenko 1997, 1999]. The electrokinetic effect (EK) is another promis- ing candidate which can give a plausible interpretation of anomalous ULF electromagnetic disturbances ob- served before strong earthquakes [e.g., Pride 1994]. The EK effect was applied to interpret both the occurrence of precursory ULF perturbation before earthquake [Ishido and Mizutani 1981, Surkov et al. 2002] and a co- seismic electric impulse caused by propagating seismic waves [Nagao et al. 2000]. In realistic geophysical media a combination of several mechano-electromagnetic mechanisms may occur: for example, a high level of geoacoustic impulses produced by microcracking can enhance the fluid filtration and EK processes [Pilipenko and Fedorov 2014]. Similar ULF electromagnetic effects may accom- pany volcano activity [Johnston 1989, Uyeda et al. 2002]. Numerous underground chambers in the rock surrounding a volcano are filled with underground fluid whose pressure varies from hydrostatic level up to lithostatic pressure depending on the chamber sizes, rock permeability, and other parameters. The magma movement along the volcano throat and variations of tectonic stresses may cause the destruction of cham- bers followed by changes in pore fluid pressure, which in turn results in generation of EK currents [Johnston 1997, Zlotnicki and Nishida 2003]. Indeed, several days before and after a volcano eruption electromagnetic noise in the band 0.01-0.6 Hz was observed by Fujinawa et al. [1992]. At the same time, an irregular movement of a highly-conductive magma along a volcano throat can produce magnetic ULF noise by the MHD effect [Kopytenko and Nikitina 2004a, 2004b]. To evaluate the significance of possible effects and their dependence on crust parameters and to identify favorable locations for electromagnetic monitoring one needs an approximate but handy model. Hopefully, on the basis of adequate theoretical models a special tech- nique, but not standard magnetometers, for a search of seismic-related ULF perturbations will be designed. Therefore, the development of analytical models, though sometimes oversimplified, is of primary importance for the progress in search of reliable ULF electromagnetic precursors. In this paper we revisit the conventional theory of the EK phenomenon by incorporating of the MHD effect in the description of pore fluid flow. Then we compare contribution of the EK and MHD mecha- nisms for various sizes and shapes of pores/channel cross sections. We model pores/cracks as ellipsoidal channels and apply this model for a qualitative estimate of ULF magnetic perturbations caused by seismic or volcano activity. 2. The electrokinetic effect in a medium with ellip- tic-shaped channels The EK effect in multiphase porous media builds up as a result of fluid filtration followed by appearance of a contact potential drop at the interfaces. It is usually the case that the groundwater contains the electrolyte solutions including ions and dissociated molecules. The surfaces of cracks and pores can adsorb ions of certain polarity from the solution that results in a charge sepa- ration between the crack walls and fluid followed by SURKOV AND PILIPENKO 2 3 the formation of electric double layer (EDL) at the solid- fluid interface. As a rule, the solid is negatively charged due to the adsorption of hydroxyl groups originating from acid dissociation [Parks 1965]. The EDL includes a diffuse mobile layer extending into the fluid phase. The moving fluid drags solvated cations thereby excit- ing the EK current. We introduce the model of a pore as a cylindrical channel with the elliptic cross-section x2/a2 + y2/b2 = 1, where a and b are the ellipse semi-axes. In this ap- proach, we can analyze the effect of the cross-section shape on the EK phenomenon since this model involves either circular channels (a = b) or plane cracks (a>>b). A viscous fluid is assumed to flow along z axis. The channel is surrounded by an incompressible solid ma- trix. The crust is immersed in the geomagnetic field B. We assume a laminar fluid flow because of small value of Reynolds number [Sparnaay 1972]. The fluid veloc- ity V is controlled by the fluid pressure gradient ∇P along a channel, so the velocity distribution over the channel cross-section V (x,y) is given by [Landau and Lifshitz 1959] (1) where h is the fluid viscosity. Due to the EK effect the fluid contains an excess of ions, more frequently cations, while the channel wall adsorbs the opposite electric charges. As a result, the EDL is formed in the fluid near the channel walls. The typical size of the EDL is of the order of cation Debye radius which is much smaller than the characteristic size of the channel [Sparnaay 1972]. The electric potential { in the pore fluid satisfies the Poisson equation (2) where q denotes the cation charge, Dn is the number density of the cation excess, f is the dielectric perme- ability of the fluid, and f0 is the dielectric permittivity of a free space. The total current density inside the channel is composed from the conduction and Hall currents, and the EK current with density jEK= qDnV, as follows: (3) Here vf is the fluid conductivity, and E = −∇{ is the electric field strength. It is generally accepted that the conduction current vf E is much larger than the Hall current vf (V×B). The mean density of the EK current 〈jEK〉, averaged over the channel cross-section, is determined from (2) through the following integral (4) where S =rab is the area of the cross-section and dS is the small element of this area. Further, for the sake of simplicity we shall omit the symbol 〈〉. Substituting Equation (1) for V into Equation (4) and taking into account the fact that { changes rapidly in the narrow EDL near the channel walls, one can sim- plify the integral in Equation (4). In the case of a circu- lar cross-section (a = b), Equation (4) is reduced to the known form [e.g., Surkov et al. 2002] (5) Here g is the potential drop across the EDL, or so- called zeta potential. In the case of an elliptic cross-section some math- ematical complications can arise due to the potential vari- ations on the surface of channel. This problem is studied in a greater detail in the Appendix. The analysis shows that if the potential is assumed to be constant on the channel surface then the EK current density is given by the same Equation (5). Thus, in the first approximation the EK currents through the circular and elliptic cross- sections are described by the same equation. Owing to a finite conductivity vr of the dry rock surrounding the channel the surface potential tends to be equal. The above approach holds true if the relaxation time ∝f0/vr is much smaller than the period of variations of pore fluid pressure and velocity, and this requirement is valid in the processes under consideration. In any homogeneous conducting medium with an arbitrary distribution of pore fluid pressure, the total magnetic effect due to EK effect vanishes [Fitterman 1979]. That is, on average the magnetic effect of the electric current resulted from the motion of the pore fluid is cancelled by the effect of the backward con- duction current. A non-zero magnetic effect occurs only in an inhomogeneous medium, and its magnitude depends on the degree of heterogeneity. 3. MHD effect and the Onsager reciprocal relations In this section we ignore the EK effect for a mo- ment and focus on the MHD effect only. The motion of the conducting underground fluid in the geomag- netic field B gives rise to the generation of Hall current jH=vf (V×B) pointed normal to the channel axis. Tak- ing into account Equation (1) for V we obtain ULF ELECTROMAGNETIC NOISE In the case of non-conductive rock the Hall cur- rent is closed by the conduction and EK currents in the fluid. In fact, the total current may flow out of the channel due to a finite rock conductivity. The closed system of longitudinal and transverse electric currents excited in the rock and fluid is shown in Figure 1. According to De Groot and Mazur [1962], the mean EK current density in rocks reads 〈jEK〉= −LEV∇P, where LEV stands for the streaming current coupling coefficient. This coefficient can be derived from (4) to yield LEV = −ff0gm/(hb 2), where m is the rock poros- ity, and b is the pore space tortuosity. Similarly, gen- eralizing (6) for the Hall current density yields, 〈jH〉= −LEB(∇P × B), where LEB~LEVvf S/(4rff0g) = vf mS/4rhb 2 is the Hall coefficient. In a more complete theory the relationship between LEB and LEV should de- pend on the rock permeability rather than on S. Thus the total mean current density in a porous rock can be written as follows: (7) where ∑= LEE stands for the mean rock conductivity. To summarize, we note that the electric current in porous rocks can result in electroosmotic and other ki- netic effects. According to the Onsager reciprocal rela- tions the mean flux density of the fluid flow, J, is given by (8) where LEV = LVE, and LEB= − LBE. The first term in the right-hand part of Equation (8) describes the elec- troosmotic effect, the second term describes Darcy law in a porous rock, while the last term arises from the magnetic force acting on a moving conductive fluid. The Equations (7) and (8) permit the extension of basic thermodynamic principles [e.g., De Groot and Mazur 1962] to the case of rock immersed in ambient mag- netic field. In order to compare the EK and Hall current den- sities, we return to the consideration of individual chan- nels. Combining Equations (5) and (6), assuming a ~ b and taking into account that the Hall current reaches its peak value at the center of the channel, yields (9) where a is the angle between vectors ∇P and B. Notice that if b< a): (14) where Bx is the geomagnetic field component along x-axis. The magnetic disturbance decays away from the cylinder axis as ∝r -1. If the magma conductivity is much greater than the rock conductivity, that is vm >>vr , then the relationship (14) can be simplified (15) Equation (15) differs from the relationship derived by Kopytenko and Nikitina [2004a, 2004b] by a small factor vr /vm << 1. This difference is due to the fact that they ignored the conductivity of the crust vr and thus ULF ELECTROMAGNETIC NOISE overestimated an expected magnitude of magnetic per- turbations. The rock conductivity determines the cur- rent leakage from a channel into the environment, and thus may greatly affect the magnitude of magnetic per- turbations. The transverse conduction current inside magma is directed opposite to the Hall current thereby reduc- ing it. As a result, the total current inside the cylinder is smaller than jH and is directed opposite to the electric field E: (16) It should be noted that both j and E are homoge- neous inside the cylinder (see Figure 1). The electric field induced in the surrounding rock due to the magma movement in the geomagnetic field is estimated to be (17) If vm >>vr , this field only weakly depends on the rock conductivity. The electric field disturbance decays away from the cylinder more rapidly ∝r -2 than the magnetic disturbance does. A typical amplitude of magnetic disturbance esti- mated from relationship (15) is as follows: dBmax~ n0a 2vr Vmax B/r, where Vmax is the amplitude of the magma flow velocity variations. For the same param- eters vr =10 -3−10-2 S/m, B = 5 · 10-5 T, Vmax = 5 m/s, a = 0,1−1 km as used by Kopytenko and Nikitina [2004a, 2004b] one gets the estimate of magnetic disturbance at distance r = 1 km of dBmax~ 3 · 10 -3− 3 nT. This esti- mate is compatible with observations of the magnetic perturbation, about several nT, during volcano activity [Johnston 1997]. The electric component of disturbance estimated from (17) is as follows: Emax~a 2Vmax B/r 2. For the same parameters Emax~ 2.5 − 250 nV/m. Tel- luric fields of such amplitude can be detected by mod- ern sensors. The apparent impedance of disturbance produced by the magma flow dynamics can be estimated as Z =n0dE/dB ~ (vrr) -1. This value differs considerably from the apparent impedance of magnetospheric waves, and this distinction could be used for their dis- crimination. The spectrum of the ULF electromagnetic noise observed on the ground is determined by a source spec- trum and by attenuation factor due to the skin-effect. The fluctuations of magma velocity along with oscilla- tions of the magma surface or seismic vibrations of the underground cavity can contribute to the source spec- trum. Fundamental frequency of such vibrations is f ~VS/l, where l = 0.1−10 km is the cavity scale, and VS = 2 − 2.5 km/s is the magma sound velocity. For these typical values, this frequency, f ~ 0.2 − 25 Hz, falls into ULF/ELF band which is consistent with observa- tions [Fujinawa et al. 1992, Johnston 1997]. The analytical relationships (14) and (15) show that magnetic perturbation depends mainly on the conduc- tivity of the surrounding rocks rather than on magma conductivity. Under low rock conductivity, the gener- ated system of Hall currents is nearly completely short- circuited by the conductivity currents within magma, and the magnetic effect on the ground is to be weak. Under high rock conductivity the conduction currents expand far into the rock, and the magnetic effect on the ground is more significant. 5. Discussion The fact that some published results on ULF “pre- cursors” were not supported upon a more detailed analy- sis [Thomas et al. 2009, Masci 2011] should not rule out the problem of seismo-electromagnetic phenomena entirely. For a search of seismic-related ULF signals just standard magnetic observations could be inappropriate because of a small value of signal-to-noise ratio. An elaboration of specialized detection methods of ULF seismic-related signals/noise, and their discrimination from the magnetospheric waves, are to be based on some models, even oversimplified. The elaboration of theoretical models capable to estimate an expected ef- fect under observational conditions is not less impor- tant than the advancement of observational technique. The proposed paper is a step in this direction. The increase of ULF electromagnetic noises asso- ciated with enhancement of seismic or volcano activity can be explained in terms of different physical mecha- nisms. The average current densities and fluid fluxes can be described in terms of Onsager reciprocal rela- tions. The rough estimate of the EK and Hall current amplitudes has shown that the EK effect plays a key role as the mean cross-section of channels is smaller than a certain critical value. This situation is typical for realis- tic water-saturated rocks with a weak permeability. The MHD effects dominate a macroscopic flow such as the groundwater migration through a broken rock with a high permeability or magma motion along a volcano throat. In the above consideration we have neglected the atmosphere-ground interface. The account of it may modify the estimates, but not significantly, less than by factor about 2 [Fedorov et al. 2001]. Our analysis has shown that the EK and Hall cur- rents in an individual channel have different structures. SURKOV AND PILIPENKO 6 7 The EK and back conduction currents are directed along the fluid flow; that is, parallel to the channel walls, whereas the Hall currents are predominantly concen- trated in the cross-section of the channels. Therefore, the resulted magnetic disturbances have different field polarization. The magnetic field perturbation due to the MHD effect is parallel to the axis of a channel (dBz component in Figure 1). By contrast, the magnetic per- turbation caused by the EK effect (dBr and dBi compo- nents) is perpendicular to the channel axis. The averaging of these effects over the rock volume cannot cancel this tendency since there is a predominant di- rection in ground fluid filtration or magma motion. However, in practice it seems very difficult to distin- guish between these two factors only on the basis of signal polarizations. Actually the fluid-filled cracks, pores and channels are randomly distributed in the rock. In order to interpret the observations adequately, the Hall and EK current densities given by Equations (5) and (6) should be averaged over the rock volume. This problem requires further consideration with a nu- merical modeling. It follows from our model that the EK current den- sities through the circular and elliptic cross-sections are described by the same equation. So, we may assume that the cross-section shape of pore channels has a min- imal effect on the EK phenomena except for the case of very narrow cracks when the distance between the crack surfaces becomes comparable with the EDL thickness. The latter case should be studied separately because of the overlap of the adjacent EDLs inside the crack space. It appears that the crack tortuosity may have a more significant effect on both the rock perme- ability and EK effect. Using a simplified model of steady flow of con- ducting magma along a cylindrical channel we have es- timated the amplitude of magnetic perturbations at small distances from a volcano. In contrast to [Kopy- tenko and Nikitina 2004a, 2004b], we have found that the rock conductivity reduces this estimate essentially. However, the upper limit of this estimate (~3 nT and ~250 µV/m) is close to the amplitudes of signals occa- sionally observed during volcanic eruption and the en- hanced seismic activity possibly associated with magma motion. Despite uncertainties with factual parameters of magma flows, volcano geometry, and crust parame- ters, the estimates prove that under favorable condi- tions ULF magnetic monitoring on the ground of the underground magma flow becomes feasible. The ULF electromagnetic effects possibly associ- ated with enhancement of seismic activity can be ex- plained in terms of different physical mechanisms. In this study we have reanalyzed only two such mecha- nisms - the EK and MHD effects. The ULF magnetic perturbation produced by acoustic noise in conducting layers of the ground is another promising mechanism [Surkov 1997, Surkov and Hayakawa 2006]. What mech- anism makes a major contribution to the observed seis- mic-related signals is the key question to be answered. A progress in observational studies of possible anom- alous seismic-related ULF electromagnetic fields would be impossible without elaboration of specialized de- tection methods, based on adequate models. Elabora- tion of such models may indicate what ULF signatures (e.g., polarization, impedance, gradients, waveforms, etc.) can be used as an indicator of an impending earth- quake or volcano eruption. 6. Conclusions We have considered the EK and MHD effects due to an irregular flow of the crust fluid or magma as a pos- sible mechanism of ULF electromagnetic noise associ- ated with seismic or volcanic activity. The conventional theory of the EK effect has been advanced by consid- ering elliptic-shaped channels. A contribution of both mechanisms to observed magnetic disturbance is shown to be different depending on the pore/channel perme- ability. Magnitudes of magnetic and electric field per- turbations depend on a contrast between fluid/magma and rock conductivities. The suggested model proves the possibility to estimate analytically by order of magnitude the expected electromagnetic effect of the fluid/magma flow under chosen geophysical parameters. Such esti- mates prove a feasibility of the ULF electromagnetic monitoring of magma dynamics in a volcano conduit, supplementary to the observations of volcano tremor. Acknowledgements. This study was supported by the grant No. 13-05-12091 from RFBR. We appreciate useful comments of all Reviewers. References Byerlee, J. (1993). Model for episodic flow of high-pres- sure water in fault zones before earthquakes, Geol- ogy, 21, 303-306. Campbell, W.H. (2009). Natural magnetic disturbance fields, not precursors, preceding the Loma Prieta earthquake, J. Geophys. Res., 114, A05307; doi:10.10 29/2008JA013932. Cress, G.O., B.T. Brady and G.A. Rowell (1987). Sources of electromagnetic radiation from fracture of rock samples in the laboratory, Geophys. Res. Lett., 14, 331-334. De Groot, S.R., and P. Mazur (1962). Non-Equilibrium Thermodynamics, North-Holland, Amsterdam; Wiley, New York. Draganov, A.B., U.S. Inan and Yu.N. Taranenko (1991). ULF ELECTROMAGNETIC NOISE ULF magnetic signature at the Earth surface due to ground water flow: a possible precursor to earth- quakes, Geophys. Res. Lett., 18, 1127-1130. Fedorov, E., V. Pilipenko and S. Uyeda (2001). Electric and magnetic fields generated by electrokinetic processes in a conductive crust, Phys. Chem. Earth, 26, 793-799. Fitterman, D.V. (1979). Theory of electrokinetic-mag- netic anomalies in a faulted half-space, J. Geophys. Res., 84, 6031-6040. Freund, F. (2000). Time-resolved study of charge gen- eration and propagation in igneous rocks, J. Geo- phys. Res., 105, 11001-11019. Fujinawa, Y., T. Kumagai and K. Takahashi (1992). A study of anomalous underground electric-field vari- ations associated with a volcanic eruption, Geophys. Res. Lett., 19, 9-12. Gaillard, F., and G.I. Marziano (2005). Electrical conduc- tivity of magma in the course of crystallization con- trolled by their residual liquid composition, J. Geophys. Res., 10, B06204; doi:10.1029/2004JB003282. Gotoh, K., Y. Akinaga, M. Hayakawa and M. Hattori (2002). Principal component analysis of ULF geo- magnetic data for Izu islands earthquakes in July 2000, J. Atmos. Electricity, 22, 1-12. Gotoh, K., M. Hayakawa, N.A. Smirnova and K. Hat- tori (2004), Fractal analysis of seismogenic ULF emissions, Phys. Chem. Earth, 29, 419-424. Hayakawa, M., R. Kawate, O.A. Molchanov and K. Yu- moto (1996). Results of ultra-low frequency magnetic field measurements during the Guam earthquake of 8 August 1993, Geophys. Res. Lett., 23, 241-244. Hayakawa, M., and O. Molchanov, eds. (2002). Seismo Electromagnetics, TERRAPUB, Tokyo, 477 p. Hayakawa, M., ed. (2013). Earthquake Prediction Stud- ies: Seismo Electromagnetics, TERRAPUB, Tokyo. Ishido, T., and H. Mizutani (1981). Experimental and theoretical basis of electrokinetic phenomena in rock- water systems and its applications to geophysics, J. Geophys. Res, 86B, 1763-1775. Johnston, M.J.S. (1989). Review of magnetic and elec- tric field effects near active faults and volcanoes in the USA, Phys. Earth Planet. In., 57, 47-63. Johnston, M.J.S. (1997). Review of electric and mag- netic fields accompanying seismic and volcanic ac- tivity, Surv. Geophys., 18, 441-475. Kopytenko, Yu.A., and L.V. Nikitina (2004a). ULF os- cillations in magma in the period of seismic event preparation, Phys. Chem. Earth, 29, 459-462. Kopytenko, Yu.A., and L.V. Nikitina (2004b). A possible model for initiation of ULF oscillation in magma, Annals of Geophysics, 47, 101-105. Kopytenko, Yu.A., V.S. Ismaguilov, K. Hattori and M. Hayakawa (2006). Determination of hearth position of a forthcoming strong EQ using gradients and phase velocities of ULF geomagnetic disturbances, Phys. Chem. Earth, 31, 292-298. Krylov, S.M., and N.N. Nikiforova, (1995). About ULF electromagnetic emission of active geological medium, Fizika Zemli, 6, 42-57. Landau, L.D., and E.M. Lifshitz (1959). Fluid Mechan- ics (vol. 6 of A Course on Theoretical Physics), Perg- amon Press, Oxford. Landau, L.D., and E.M. Lifshitz (1960). Electrodynam- ics of Continuous Media (vol. 8 of A Course on Theoretical Physics), Pergamon Press, Oxford. Masci, F. (2011). On the seismogenic increase of the ratio of the ULF geomagnetic field components, Phys. Earth Planet. In.; doi:10.1016/j.pepi.2011.05. 001. Molchanov, O.A., Yu.A. Kopytenko, P.M. Voronov, E.A. Kopytenko, T.G. Matiashvili, A.C. Fraser-Smith and A. Bernardi (1992). Results of ULF magnetic field measurements near the epicenters of the Spitak (Ms=6.9) and Loma Prieta (Ms=7.1) earthquakes: comparative analysis, Geophys. Res. Lett., 19, 1495- 1498. Molchanov, O.A., and M. Hayakawa (1995). Generation of ULF electromagnetic emissions by microfractur- ing, Geophys. Res. Lett., 22, 3091-3094. Molchanov, O.A., and M. Hayakawa (2008). Seismo- Electromagnetics and Related Phenomena: History and Latest Results, TERRAPUB, Tokyo. Nagao, T., Y. Orihara, T. Yamaguchi, I. Takahashi, K. Hattori, Y. Noda, K. Sayanagi and S. Uyeda (2000). Co-seismic geoelectric potential changes observed in Japan, Geophys. Res. Letters, 27, 1535-1538. Parks, G.A. (1965). The isoelectric points of solid ox- ides, solid hydroxides, and aqueous hydroxo com- plex systems, Chem. Rev., 65, 177-198. Pilipenko, V., and E. Fedorov (2014). Coupling mecha- nism between geoacoustic emission and electro- magnetic anomalies prior to earthquakes, Research in Geophysics, 4:5008; doi:10.4081/rg.2014.5008. Pride, S. (1994). Governing equations for the coupled electromagnetics and acoustics of porous media, Phys. Rev. B 50, 15678-15696. Sparnaay, M.J. (1972). The electrical double layer (vol. 4 of Properties of Interfaces; Topic 14 of The Inter- national Encyclopedia of Physical Chemistry and Chemical Physics), Pergamon Press, Oxford. Surkov, V.V. (1997). The nature of electromagnetic fore- runners of earthquakes, Transactions of the Russian Academy of Science, Earth Science Sections, 355, 945-947. Surkov, V.V., and V.A. Pilipenko (1997). Magnetic effects SURKOV AND PILIPENKO 8 9 due to earthquakes and explosions: a review, Annali di Geofisica, 40, 227-239. Surkov, V.V., and V.A. Pilipenko (1999). The physics of pre-seismic electromagnetic ULF signals, In: M. Hayakawa (ed.), Atmospheric and Ionospheric Phe- nomena Associated with Earthquakes, TERRAPUB, Tokyo, 357-370. Surkov, V.V., S. Uyeda, H. Tanaka and M. Hayakawa (2002). Fractal properties of medium and seismo- electric phenomena, J. Geodyn., 33, 477-487. Surkov, V.V., and M. Hayakawa (2006). ULF geomag- netic perturbations due to seismic noise produced by rock fracture and crack formation treated as a stochastic process, Phys. Chem. Earth, 31, 273-280. Surkov, V.V., and M. Hayakawa (2014). Ultra and Ex- tremely Low Frequency Electromagnetic Fields, Springer Geophysics. Thomas, J.N., J.J. Love and M.J.S. Johnston (2009). On the reported magnetic precursor of the 1989 Loma Prieta earthquake, Phys. Earth Planet. In., 173, 207- 215. Tzanis, A., and F. Vallianatos (2002). A physical model of electrical earthquake precursors due to crack propagation and the motion of charged edge dislo- cations, In: M. Hayakawa and O. Molchanov (eds.), Seismo Electromagnetics: Lithosphere - Atmos- phere - Ionosphere Coupling, TERRAPUB, Tokyo, 117-130. Uyeda, S., M. Hayakawa, T. Nagao, O.A. Molchanov, K. Hattori, Y. Orihara, K. Gotoh, Y. Akinaga and H. Tanaka (2002). Electric and magnetic phenomena observed before the volcano-seismic activity in 2000 in the Izu islands regions, Japan, Proc. Natl. Acad. Sci. USA, 99, 7352-7355. Vallianatos, F., A. Nardi, R. Carluccio and M. Chiappini (2012). Experimental evidence of a non-extensive statistical physics behavior of electromagnetic sig- nals emitted from rocks under stress up to fracture. Preliminary results, Acta Geophys., 60, 894-909. Zlotnicki, J. and Y. Nishida (2003). Review of morpho- logical insights of self-potential anomalies on vol- cano, Surv. Geophys., 24, 291-338. * Corresponding author: Vadim V. Surkov, National Research Nuclear University MEPhI, Moscow, Russia; email: surkovvadim@yandex.ru. © 2015 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved. Appendix A: EK current through a channel with el- liptic cross-section To perform integration in Equation (4) we first in- troduce the elliptic coordinates n and o according to x = c coshncoso, y = c sinhnsino, where n≥0, 0≤o<2r and c2 = a2 − b2 (a > b). The lines n(x,y) = C1 and o(x,y) = C2 (C1 and C2 are constants) determine the families of confocal ellipses and hyperboles which form an or- thogonal grid. Taking the notice of Lame coefficients hn= ho= c (sinh 2n+ sin2o)½, the unit cross-section is dS = h2ndndo. The Laplace equation for the potential { is given by (A1) Since inside the EDL the electric potential { varies most rapidly along the direction normal to the wall, the derivative with respect to o in Equation (A1) can be neglected. Taking into account this approximation and substituting Equations (1) and (A1) into Equation (4) we get: Integrating Equation (A2) by parts and taking into account that coshnmax= a/c, sin hnmax= b/c, and d{(0)/dn= 0, we come to (A3) Considering the fact that { changes rapidly in the narrow EDL near the walls and d{/dn tends to zero as n→ 0, we set n=nmax in the factor sin h 2n in the in- tegrand. We can thus perform the integration in Equa- tion (A3), arriving at (A4) Assuming that g={(nmax) −{(0) is a constant value and performing integration in Equation (A4), we arrive at Equation (5). ULF ELECTROMAGNETIC NOISE (A2) << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles false /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.3 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.1000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize false /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile (None) /AlwaysEmbed [ true /AndaleMono /Apple-Chancery /Arial-Black /Arial-BoldItalicMT /Arial-BoldMT /Arial-ItalicMT /ArialMT /CapitalsRegular /Charcoal /Chicago /ComicSansMS /ComicSansMS-Bold /Courier /Courier-Bold /CourierNewPS-BoldItalicMT /CourierNewPS-BoldMT /CourierNewPS-ItalicMT /CourierNewPSMT /GadgetRegular /Geneva /Georgia /Georgia-Bold /Georgia-BoldItalic /Georgia-Italic /Helvetica /Helvetica-Bold /HelveticaInserat-Roman /HoeflerText-Black /HoeflerText-BlackItalic /HoeflerText-Italic /HoeflerText-Ornaments /HoeflerText-Regular /Impact /Monaco /NewYork /Palatino-Bold /Palatino-BoldItalic /Palatino-Italic /Palatino-Roman /SandRegular /Skia-Regular /Symbol /TechnoRegular /TextileRegular /Times-Bold /Times-BoldItalic /Times-Italic /Times-Roman /TimesNewRomanPS-BoldItalicMT /TimesNewRomanPS-BoldMT /TimesNewRomanPS-ItalicMT /TimesNewRomanPSMT /Trebuchet-BoldItalic /TrebuchetMS /TrebuchetMS-Bold /TrebuchetMS-Italic /Verdana /Verdana-Bold /Verdana-BoldItalic /Verdana-Italic /Webdings ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.10000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.10000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.08250 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org) /PDFXTrapped /Unknown /CreateJDFFile false /SyntheticBoldness 1.000000 /Description << /ENU (Use these settings to create PDF documents with higher image resolution for high quality pre-press printing. The PDF documents can be opened with Acrobat and Reader 5.0 and later. These settings require font embedding.) /JPN /FRA /DEU /PTB /DAN /NLD /ESP /SUO /NOR /SVE /KOR /CHS /CHT /ITA >> >> setdistillerparams << /HWResolution [2400 2400] /PageSize [595.000 842.000] >> setpagedevice