Annals 47, 1, 2004, 01/07def 171 ANNALS OF GEOPHYSICS, VOL. 47, N. 1, February 2004 Key words Earth crust – Tolman-Stewart effect 1. Introduction The excitation of magnetic oscillations by seismic waves has attracted considerable atten- tion for a long time (e.g., Breiner, 1964; Ele- man, 1966; Belov et al., 1974; Iyemory et al., 1996; Tsegmed et al., 2000). The interest in seismomagnetic phenomena is motivated by the hope for advances in understanding me- chano-magnetic transformations in the Earth’s crust. The challenging task on this way is the detection of the rather small seismomagnetic signals against a noise background. Strong in- terferences hamper the collection of experi- mental data. Recently Tsegmed et al. (2000) proposed the polarization method for recogni- tion of signals. The method is based on the fact that the magnetic signal has circular polariza- tion in the vertical plane regardless of the par- ticular mechanism of magnetic field excitation by the seismic wave. The polarization plane is perpendicular to the seismic wave front, and the rotation direction of the magnetic vector is controlled by the direction of seismic wave propagation. In the present paper we describe the polar- ization method and apply it to the detection of the magnetic oscillations accompanying the propagation of surface Love wave after a strong earthquake. The selection of this type of seis- mic waves is not accidental. It is motivated by some special physical reasons. The Love wave is of immediate interest to the experimentalist because theoretically this wave induces the Tol- man-Stewart effect in the Earth’s crust, which is responsible for the magnetic field that is ob- servable over the Earth’s surface (Guglielmi, 1992, 1999). On the excitation of magnetic signals by Love waves Anatol V. Guglielmi (1), Alexander S. Potapov (2) and Battuulai Tsegmed (2) (3) (1) Schmidt United Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia (2) Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia (3) Astronomy and Geophysics Research Center, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia Abstract The polarization method for recognition of seismomagnetic waves against a noise background is presented. The method is applied to detection of magnetic oscillations accompanying the propagation of surface Love wave after a strong earthquake. A specific property of the Love waves is that theoretically the Tolman-Stew- art effect is alone responsible for the magnetic field that penetrates into the Earth’s surface. Data from the Mondy Magnetic Observatory and the Talaya Seismic Station suggest that the arrival time, duration, period, and polarization of magnetic signals conform with the idea of generation of alternating electric currents due to fluid vibrations in pores and fractures of rocks under the action of the inertial force associated with the Love wave propagation. Mailing address: Dr. Alexander S. Potapov, Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, P.O. Box 4026, 664033 Irkutsk, Rus- sia; e-mail: potapov@iszf.irk.ru 172 Anatol V. Guglielmi, Alexander S. Potapov and Battuulai Tsegmed 2. Mechano-magnetic transformations The equation of the mechano-magnetic trans- formations in the Earth’s crust makes it easy to understand our interest into the Love waves. In- deed, let us put B = ∇ × A. The equation for the vector-potential A has the form DA S=t (2.1) where D t 2 2 2 d= - at (2.2) is the evolution operator, and the term S M E u B v a0 0# $ #d d= + + -a b c (2.3) describes the underground sources of the mag- netic field B (x, t) (Guglielmi, 1999; Tsegmed et al., 2000). We have used the following desig- nations: c2 , , , ., lnc m e M p p p c u c u u x u x t t B u v u a v 2 2 i ll ij ij j ij t ij l t ij ij i j j i ef 2 0 1 2 0 2 2 2 $ 2 2 2 2 2 2 d 2 2 2 2 = = = = + = + - = + = = = a f v b v i c m d m t t id i _ ^ _ i h i Here the mechanical values a, v, and u are the acceleration, velocity and displacement of the rocks, pij and uij are the stress and strain tensors, E 0 is the electric field associated with the ter- restrial currents, B0 is the geomagnetic field, ct and cl are the velocities of transverse and longi- tudinal elastic waves, c is the light velocity, ε 0 is the permeability of free space, ρ and σ are the density and conductivity of rocks, e and mef are the charge and effective mass of the conduction ion in the porous fluid. The four terms in the right-hand side of eq. (2.3) have the following interpretation: the first accounts for the piezo- magnetic effect, the second describes the mod- ulation of the terrestrial currents by the seismic vibrations, and the two last terms describe the induction and inertial effects. The five phenom- enological parameters of the model have the following interpretation: α is the diffusion co- efficient, and β, γ, λ1, λ2 are the coefficients de- scribing the conversion of mechanical energy into the energy of magnetic field. We see that generally at least four mecha- nisms operate in the Earth’s crust simultaneous- ly and independently of each other. So we have a rather cumbersome superposition of fields. However, it is always interesting to select and clarify the limiting case when only one genera- tion mechanism concerned prevails. And in this respect, the Love wave is especially interesting. A specific property of this wave is that, theoret- ically, the inertial mechanism alone is responsi- ble for the magnetic field which penetrates into the Earth surface (Guglielmi et al., 1996). Moreover, the Love wave makes it possible to switch on the least understood generation mechanism. The most striking feature of it is its universality. It operates in any conductive body and, therefore, it operates in the Earth’s crust too. This simple and universal mechanism was brought into classical physics in 1936 by Dar- win in his attempt to explain the Tolman-Stew- art effect. Darwin’s theory predicts that the co- efficient of mechano-magnetic transformation γ is proportional to the mass of electron (e.g., Landau and Lifshitz, 1984). This is true in the case of a metal. But in the case of the porous moist body, we expect that γ is proportional to some effective mass mef, which is many orders above the mass of electron (Guglielmi, 1992). It should be noted that the Tolman-Stewart effect was never observed in the laboratory using rock samples and we assume that it is practically im- possible because the typical skin-length is many orders higher than the feasible size of a rock sample. Below we present our attempt to crack a problem by the full-scale observations. 3. Polarization method It is common knowledge that observations of the seismomagnetic signals are impeded by the noise of magnetospheric origin. To suppress the magnetospheric interference, we have elab- orated a special method based on the tapping of a priori information on the polarization state of seismomagnetic field (Tsegmed et al., 2000). In this section, we present a general idea. The ap- plication of the polarization method to record 173 On the excitation of magnetic signals by Love waves magnetic wave that accompany the Love wave will be described in the next section. We introduce the Cartesian coordinate sys- tem (x, y, z) such that the Earth’s surface coin- cides with the (x, y) plane and the z-axis is di- rected upward (fig. 1). Let a plane (∂ / ∂y = 0) monochromatic elastic wave travel in the posi- tive direction of the x-axis in the lower half- space (z < 0) supposed to be horizontally ho- mogeneous. We are interested in the magnetic field B (x, z, t) in the upper half-space (z ≥ 0), where it obeys the Laplace Law ∇2B = 0 and the solenoidality condition ∇∴ B = 0. We sup- pose that the field B is excited by the elastic wave, and it is linearly related to the mechani- cal variables. Then B ∝ exp (ikx − iωt), the so- lenoidality condition takes the form B k i z B x z 2 2 = (3.1) and the Laplace equation yields z B k B 0 z z2 2 2 2 2 - = (3.2) where k = ω /cL, ω is the frequency and cL is the horizontal velocity of elastic wave (in the next sections cL will be considered the velocity of Love wave). The magnetic field tends to zero with in- creasing the height above the Earth’s surface because the field sources are located beneath the surface. Hence, the eq. (3.2) gives Bz ∝ exp ⋅ ⋅ (− kz). Substitution of this expression in (3.1) yields Bz = iBx. As regards By component, it is negligible in comparison with Bx and Bz (in the particular case of the Love wave By = 0) There- fore we have , , .exp B i k ix z i tB 2 1 0= - - ~^ ]h g6 @ (3.3) This means that on the Earth’s surface and above it the modulus Bremains constant. The magnetic wave has circular polarization with counterclockwise rotation. The vector B rotates with the frequency ω in the vertical plane par- allel to the direction of seismic wave propaga- tion. These polarization properties are quite general. Besides, these properties are so specif- ic, that one can try to use them for the detection of seismomagnetic signals. 4. Observations An earthquake with magnitude M = 7.9 oc- curred on June 18, 2000, at a depth of 10 km with epicenter in the Indian Ocean (see the site of the IRIS Consortium at www.iris.washing- ton.edu). To search for a seismomagnetic sig- nal, we used data from the Mondy Magnetic Observatory (51.6ºN, 100.8ºE) and the Talaya Seismic Station (51.7ºN, 103.6ºE). The Mondy Observatory is equipped with a high-frequency digital three-component induction magnetome- ter developed at the University of Tokyo and kindly provided by Prof. K. Hayashi. The main parameters of the magnetometer are as follows: frequency range, 0.001-3.0 Hz; sampling rate, 10 Hz; GPS time synchronization; data storage on magneto-optical disks. The Talaya seismic station 200 km east of Mondy is equipped with a highly sensitive digital seismometer with a sampling rate of 1 Hz. Talaya seismic wave records were taken from the Internet (www.fd- sn.org/station_book/II/TLY/tly_3.html). The epicentral distances to the Mondy Observatory Fig. 1. Polarization of seismomagnetic oscillations (see the text). 174 Anatol V. Guglielmi, Alexander S. Potapov and Battuulai Tsegmed and Talaya Station are, respectively, 7280 and 7269 km. The azimuthal aperture between these two points is 4.2º. First, the seismogram was used to visually assess the arrival time (15:17:45 UT), charac- teristic period (T = 23 s), and amplitude (about 300 µm/s) of surface Love waves. The onset of waves corresponds to an average velocity of 3.6 km/s. Thus, the Love wave delay at Mondy is 3 s, i.e. it is small compared to the period of seismic waves. The distance between the obser- vation points of magnetic and seismic waves is also small compared to the epicentral distance. Therefore, for simplicity, we will ignore the ef- fects due to the difference between locations of the observation points. For subsequent analysis, we transformed the initial numerical dataset to a coordinate system rotated about the vertical axis z in such a way as to bring the x-axis into coincidence with the tan- gent to the arc of the great circle passing through the epicenter and to direct it away from the epi- center. Moreover, the initial data were subjected to broadband filtering with a passband of 5-200 mHz in order to eliminate high-frequency noise and long-period trends. Finally, using the results of the preliminary visual analysis, we chose a frequency-time window containing Love waves and constructed the wave amplitude spectrum, after which we determined more accurately the carrier frequency (f = 43 mHz) and the time in- terval (15:13:20-15:25:00 UT) suitable for de- tecting seismomagnetic oscillations. Figure 2 shows oscillograms of mechanical and magnetic oscillations after the rotation of the coordinate axes and broadband filtering. Here, Vy is the transverse component of the ve- locity, and Bx : and By : are time derivatives of the horizontal and vertical components of the mag- netic field, respectively. The seismogram dis- . B x, n T /s V y, n m /s -0.025 0 0.025 15:13:20 15:20:00 15:26:40 UT -0.025 0 0.025 -300 300 . B z, n T /s Fig. 2. Seismic waves and magnetic oscillations recorded at the Talaya Station and the Mondy Observatory, re- spectively, on June 18, 2000. Here, Vy is the transverse component of the displacement velocity, and Bx : and By : are the horizontal and vertical components of the magnetic field, where dots mean the differentiation with re- spect to time. The coordinate system is oriented in such a way as to make the x-axis parallel to the arc of the great circle that passes through the earthquake epicenter (see text). 175 On the excitation of magnetic signals by Love waves plays quasi-harmonic oscillations typical of Love waves in the far-field zone. The record of the magnetic field is severely complicated by noise. Against the background of this noise, the seismomagnetic signal cannot be detected by simple comparison of the oscillograms. We at- tempted to identify the seismomagnetic signal by the spectral method. Figure 3 presents the spectra of mechanical and magnetic oscillations in the time interval 15:16:40-15:25:00 UT. The mechanical spectrum exhibits a distinct peak at a frequency of 43 mHz. However, this effect is not observed in the spectra of magnetic field components. Therefore, we applied the method of spec- tral polarization filtering based on the theoreti- cal idea that the electromagnetic field of har- monic Love wave has the structure of an H- wave with a left-hand circular polarization in the vertical plane. The state of polarization can be conveniently described by the ellipticity pa- rameter varying from − 1 to + 1 and chosen such that its value − 1 corresponds to the left- hand polarization. The variation in the elliptici- ty of magnetic oscillations in the vertical plane at the frequency of 43 mHz is shown in the mid- dle part of fig. 4. The lower plot shows the vari- ation in the amplitude B of the circular compo- nent of oscillations with a left-hand rotation of the magnetic vector at the same frequency. As expected, the lowest values of the ellipticity and the highest amplitudes of magnetic oscillations with the left-hand circular polarization are ob- served during the passage of the 43 mHz Love wavetrain. This leads to the assumption that we have detected seismomagnetic oscillations with the amplitude B = 0.02 nT. 5. Discussion The period, polarization, onset time, and du- ration of the detected magnetic oscillations are consistent with the concept according to which these oscillations are excited by Love wave. It is quite clear that the seismic waves are no more than a causa instrumentalis; i.e. they are only an external cause of the field generation, where- as the immediate cause is the current, and our task is to identify the current-generating mech- anism. In the general case, this is a difficult problem because several mechanisms operate in the crust concurrently and independently of each other during seismic wave propagation. We chose the Love waves because the theory (Guglielmi et al., 1996) leaves no other alterna- tive and unambiguously indicates an inertial generation mechanism in this particular case. This universal mechanism, describing by the equation t B B 2 2 2 d+ =c aΩ_ i (5.1) operates in the terrestrial and celestial conduc- tive bodies which are in motion with time-de- pendent vorticity Ω = ∇ × v. (The values v, α, u . B z( f) u, n T 0 0.4 0.8 1.2 1.6 0 0.2 0.4 0.6 0.8 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 f, mHz u . B x ( f) u, n T u V y( f) u, n T Fig. 3. Spectra of oscillations shown in fig. 2. 176 Anatol V. Guglielmi, Alexander S. Potapov and Battuulai Tsegmed and γ are defined above in the Section 2). For example, Sedrakian (1974) proposed that the magnetic fields of the neutron stars could be ex- plained in part by the inertia effect. In his mod- el the pulsar consists of the rotating superfluid of neutrons and protons, and the normal fluid of electrons. Because the angular velocity of neu- tron star is not constant, the protons move rela- tive to the electrons creating the toroidal elec- tric currents that produce extremely strong magnetic field. This is a sort of Tolman-Stewart effect. We must realize that the Tolman-Stewart ef- fect provides the generation of magnetic field in any conductive body, which moves with nonze- ro vorticity Ω. In this regard there is no ques- tion that the Love wave generates the magnetic field oscillations because Ω ≠ 0 during the pas- sage of this wave. The real problem is the am- plitude of magnetic oscillations, which is deter- mined by the coefficient of mechano-magnetic transformation γ = me f /e. In a metallic conduc- tor mef = me, where me is the mass of electron. Then γ = − 5.68⋅10− 12 kg/s⋅A, and it is likely that Eleman (1966) expected just this case when he rejected a priori the inertial mechanism as a possible cause of seismomagnetic signals. The electronic mechanism of conductivity operates in the Earth’s core and lower mantle, and here the Tolman-Stewart effect is truly negligible. In the upper mantle the ionic conductivity takes place, i.e. mef ≈ mi. However, the Tolman-Stew- art effect is also negligible in the upper mantle. The Earth’s crust may be considered as an ionic conductor too, but mef > > mi because the inertial force sets in motion the porous fluid, and not just the conduction ion (Guglielmi, 1992). A rough estimate gives γ ≈ ρ f K, where K is the electrokinetic coefficient, and ρ f ≈103 kg/m3 is the density of porous fluid. Laboratory experi- ments with the rock samples indicate that K varies from 10 mV/MPa to 10 V/MPa depend- V y, n m /s 15:13:20 15:20:00 15:26:40 UT 0 0.01 0.02 -1 -0.5 0 0.5 1 -300 0 300 el li pt ic it y B , n T Fig. 4. Comparison of seismic oscillations Vy (top panel) with variations in the ellipticity of magnetic oscilla- tions (middle panel) and the amplitude of magnetic oscillations with a left-hand circular polarization in the tan- gent plane (bottom panel). 177 On the excitation of magnetic signals by Love waves ing on the temperature and salinity of water and on the structure and saturation of the porous space. The coefficient of mechano-magnetic transformations γ varies correspondingly from 10−5 to 10−2 kg/s. Let us show that our observa- tions do not contradict these estimates. One can see from eq. (5.1) that γ ∼ Β / kV, where k = ω / cL. According to our measurements B ∼ 2⋅10− 2 nT, V∼ ∼ 3⋅10− 4 m/s, cL ∼ 3.6 km/s, so that γ =10−3 kg/s⋅A. 6. Summary We have presented the polarization method for recognition of seismomagnetic waves against a noise background. The method is applied to detection of magnetic oscillations accompany- ing the propagation of surface Love wave after the strong earthquake. We have focused our at- tention on the Love wave because theoretically the Tolman-Stewart effect in the Earth’s crust is responsible for the magnetic field that pene- trates to the Earth’s surface. Data from the Mondy Magnetic Observatory and the Talaya Seismic Station suggest that the arrival time, duration, period, and polarization of magnetic signal conform with the idea of generation of alternating electric currents due to fluid vibra- tions in pores and fractures of rocks under the action of the inertial force associated with the Love wave propagation. The estimated ratio of the amplitude of magnetic oscillations to the amplitude of Love waves is indirect evidence that the inertial mechanism of converting the seismic wave energy into the electromagnetic field energy is reasonably effective. We believe that the inferred result provides an additional basis for the interpretation of seismoelectro- magnetic phenomena. Our conclusion is as follows. In his ‘Fore- word’ to the recent monograph Seismo-Electro- magnetics, Prof. Uyeda (2002) said that «the earthquakes are nothing but physical phenome- na». These are remarkable and optimistic words in the context of the earthquake prediction re- search. The specifics of such research is that the laboratory modeling of the pre-seismic evolu- tion of the geophysical fields is practically im- possible. This resembles in some respects the situation with the inertial mechanism of mag- netic field generation. 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