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Geophys. 1. Int. (1991) 104,381-385 Electric currents in the ocean induced by the geomagnetic Sq field and their effects on the estimation of mantle conductivity Masahiko Takeda Data Analysis Center for Geomagnetism and Space Magnetism, Kyoto University, Kyoto 606,Japan Accepted 1990 September 17. Received 1990 September 17; in original form 1990 May 9 SUMMARY Electric currents induced in the ocean by the geomagnetic Sq field are simulated for a system which consists of a uniform geocentric sphere of finite conductivity and a non-uniformly conductive thin-shell sphere representing the sea-land distribution. The simulation results show that the induced currents have maximum intensity in the northern Pacific Ocean at 22 hr UT and enhance the total induced fields by about 60 per cent. Even when the external current vortex is located above the Eurasian continent, the internal current vortex is enhanced by about 10 per cent by the existence of the ocean. Next we have checked the effects of the electric currents in the ocean on the estimation of the mantle conductivity and found that ignoring the currents induced in the shell gives a less conductive and shallower estimation of the mantle conductor. Furthermore, an apparent dependence of the conductivity on the depth appears because of the effects of the currents induced in the shell even if the mantle is a uniform conductor. The conductivity and depth are estimated to be 0.1 S m-' and 500 km respectively from the data analysis for the 1 day period variation field of the Pi mode if the effects of the currents in the shell are ignored, but it should be 1S m-' and 780 km if the effects are considered. Key words: mantle conductivity, oceanic currents, Sq. 1 INTRODUCTION Since the decay time constant of the induced currents in the Oceans is about 10 hr, it is expected that fairly large electric currents are induced in the Oceans by the geomagnetic solar quiet daily variation (Sq), with a the period of one or a few cycles per day. However, currents are also induced in the mantle at the same time and couple with those flowing in the Oceans. Therefore, in order to examine the internal Sq field, it is necessary to examine the response of the mantle-ocean coupled system to the external field. Simulations for the induced currents in the Oceans have been made using the mantle model of the infinitely conductive sphere. For example, Beamish et af. (1980a, b, 1983) simulated the induction in realistically shaped oceans and examined the contribution in each harmonic term due to the currents in the oceans and in the mantle by the ocean currents. They concluded that the effect on the 8 hr period p', mode Sq field is the largest and that about 30 per cent of the internal variation fields result from currents in the oceans. Simulations by Hobbs & Dawes (1979) and Hobbs (1981) showed that total induced currents are enhanced by about 50 per cent at its maximum by the presence of the oceans. Takeda (1985) analysed the Sq field and found oceanic effects on the internal Sq field. Some researchers used the response of the internal to the external Sq field for studying the mantle conductivity assuming that the induced currents flow only in the mantle. For example, Campbell (1987) and Campbell & Schiffinacher (1988) estimated the mantle conductivity from the amplitude ratio and the phase difference between the internal and external parts of Sq. In these estimations the phase difference is regarded to be caused purely by the finiteness of the conductivity of the mantle. On the other hand, Winch (1984) used a model which consists of a uniform finite-conductivityshell representing the oceans and a perfectly conductive core and estimated the conductivity of the shell from the phase difference between the internal and external parts of the Sq field. The results are reasonable, which suggests that the phase difference may be considered as the result of the finite electric conductivity not of the mantle but of the oceans. These two treatments contradict each other in that one ignored the effect of the induced currents in the Oceans and the other assumed that the phase difference is due to the oceanic current. To examine the effects of the oceanic 381 M. Takeda 382 currents on the phase difference between the internal and external Sq fields, it is necessary to simulate the electric currents induced in the Oceans above the finitely conductive mantle. In this study, we first simulate the induced currents in a shell of which the conductivity distribution is determined by the sea-land distribution. Effects of the electromagnetic mutual coupling of the shell with the finite-conducting mantle are considered. Next we examine the effects of the electric currents in the shell on the estimation of the mantle conductivity and discuss the real mantle conductivity excluding the effects of the oceanic currents . 2 Table 1. Complex values of I and J for N, n S 2. N M n m 1 1 1 1 1 1 1 1 1 1 2 0 0 0 0 0 1 1 1 0 2 2 0 1 2 2 2 2 2 2 2 2 1 1 2 2 1 1 1 2 1 0 0 0 1 2 2 2 2 2 2 2 1 1 o 1 0 1 2 0 1 2 0 1 2 2 1 2 2 2 1 2 2 2 2 o J I 3.660E-03, 0.000E+00) (-2.057E-04, 1.194E-04) (-8.343E-05, 0.000E+00) (-6.599E-05, 9.386E-05) 2.939E-05.-2.571E-041 i-z.o57~-oa;-i.i94E-o4j ( 2.3258-03, O.OOOE+OO) ( 8.224E-05, 2.822E-04) ( 8.897E-04, 0.000E+00) (-2.0848-04. 5.827E-04) ( 2.824E-03, O.OOOE+OO) (-6.902E-05,-1.419E-04) (-1.315E-05,-2.821E-O5) (-6.9021-05. 1.419E-041 ( 1.889E-03. 0.000E+001 f-l.658E-04: 2.014E-041 i-i.315~-05; 2 . ~ 2 1 ~ - 0 5 j (-1.658E-04,-2.014E-O4) ( 1.2718-03. 0.000E+00) ( 9.2558-03, 0.000E+00) -2.645E-04, 1.001E-04) 6.1218-04, 0.000E+00) -5.934E-04. 1.5778-031 1.311E-04; -1.161E-03) -2.645E-04,-1.001E-04) 8.9661-03, O.OOOE+OO) 7.438E-04. 1.867E-03) 6.512E-03, 0.000E*00) -1.8828-03. 4.810E-031 2.062E-02; O.OOOE+OO j -5.631E-04,-3.050E-04) -4.0948-04, 1.715E-04) -5.6318-04. 3.050E-041 1.938E-02, 0.000E+00) -1.35OE-03. 1.309E-031 -4.094~-04;-1.715~-04j -1.350E-03,-1.309E-03) 1.4668-02. 0.000E+00) METHOD OF SIMULATION Winch (1989) showed the formulation of the electric currents induced in the oceans above the finitely conductive mantle, using the spherical harmonic expansion. He represented the sea-land system as a infinitely thin spherical shell and gave the following formula (his equations 28, 30, 31 and 32) for the spherical harmonic coefficients of the currents in the oceans: where J(P, n, N', m,M ' ) 4n ae ae sin2 e a+ a+ x P;,'(e, 4) sin 8 do d+, (32) a is the radius of the Earth (m), po is the magnetic permeability (4n x lo-' H m-'), w is the angular frequency of the harmonics (rad), Eo is the external magnetic potential (A m-'), p is the surface resistivity of the shell (a),8 is the colatitude, is the longitude, Yy are spherical functions, W: are expanded coefficients of the current function in the shell (A m-'), q is the radius of the mantle as a proportion of radius of the Earth, a, j, is a spherical Bessel function, and Aqa are the dimensionless arguments of the spherical Bessel function. Also + given by Takeda (1985, 1989). The spherical harmonic coefficients which represent the Sq field were obtained at every universal time on each day. Then they were averaged at every universal time through all the days and expanded as Fourier series. The Fourier coefficients of the external spherical harmonic coefficients field from one to four cpd (cycles day-') are used as the inducing field. As for the resistivity distribution at the Earth's surface, the ETOPO-5 of NOAA model of the global bathmetry is used to calculate the distribution. Bathmetry in the geomagnetic coordinates obtained by the average at every 1"x 1" mesh is shown in Fig. 1. Conductivities of sea and land are assumed to be 4 and 0.01 S m-', respectively, and surface resistivities on the 1" x 1" mesh in geomagnetic coordinate are calculated by integrating the conductivities from the Earth's surface to 10 km depth. Maximum degrees and orders of the spherical harmonics are both taken to be the 25th by the restriction of computer capacity and accuracy in the estimation of the spherical function. We have checked the effects of the truncation by limiting the degrees and orders to the 20th, but the results are almost identical. Thus the numbers of the highest orders and degrees seem to be large enough. The mantle is regarded as a uniform geocentric sphere of finite conductivity of radius qa m. We first show the result by assuming that the mantle conductivity is 0.1 S m-' and the depth is 500 km. These values are based on those obtained from the observed results assuming a uniform geocentric sphere of finite conductivity of radius qa m without the surface conductor. Once we have obtained the induced currents in the ocean, the effects of the currents on the estimation of the w 0 3 + 60 H tQ 30 _I 0 w 0 t- w -30 Z 0 Q t where a, is the conductivity of the mantle (S). Complex values of I and J for N, n S 2 are shown in Table 1. We have adopted this formulation for the simulation of the induced currents. Inducing external fields used in this study are the result of the Sq analysis from 1980 March 1-22 90 -60 0 w-3UL 0 0 I , 60 I I 120 . , . 180 240 GEOMAGNETIC L d 3CO 360 LONGITUDE Fiyre 1. Bathmetry in the geomagnetic coordinate obtained by the average at every 1" X 1" mesh from ETOPOJ of NOAA. Contours are drawn at every 2000 m. Induced oceanic currents and mantle Conductivity conductivity and depth of the mantle are discussed and other values of the conductivity and depth are considered to fit the observational result. 3 CURRENTS IN THE OCEANS A N D RESULTANT EQUIVALENT INTERNAL CURRENTS 383 90 3 I- H 60 I- 4 0 H 0 30 0 0 -30 0 F $ 0 Figures 2 and 3 give the electric currents induced in the spherical shell at 10 hr UT when the centre of the external current external dayside vortex is above the Eurasian continent and at 2 2 h r u ~when maximum currents flow in the northern hemisphere, respectively. Practically no currents flow in the dayside northern hemisphere at 10 hr UT. On the other hand strong currents flow at 22 hr UT; the intensities of the current vortices located in the northern and southern Pacific Ocean are 46 and 54 kA, respectively. These values are fairly large compared with those of the internal part of the Sq currents (-100kA), and it is expected that the induced currents in the shell have a significant effect on the total induced field. Figure 4 shows the UT variation of the intensity of the internal current vortex in the northern hemisphere in the daytime. Thin solid and dashed lines show the UT variation simulated for the case with and without the shell above the mantle, respectively. For comparison, bars represent the observational result. The thick line will be discussed later. There is a clear effect of the currents flowing in the shell in the UT variation. Comparing the simulated UT variation with the observed one, it is found that the enhancement at about 18 hr UT is fairly well reproduced although the depression at about 10hrwr found in the observational result does not clearly appear in the simulated one. The maximum effect of the shell is about 60 per cent enhancement at 22 hr UT when the external current vortex is in the Pacific Ocean. A striking feature is that the simulated current vortex is enhanced about 10per cent by the existence of the shell even when the external current vortex is above the Eurasian continent. To check whether this enhancement is caused by the finite conductivity (0.01 S m-') used for the land, we examined the effect of the shell consisting of land only, but the results of this simulation were same as those of the simulation without the shell. Therefore, our introduction of the finite conductivity for the land has no effect on the simulated induced currents. Another feature is that there is 2 0 -60 0 W 0 - 9 4 ' ' 6 . ' . 12 ' . -,3 , I8 , 1 24 MAGNETIC LOCAL T I M E Figure 3. Same as Fig. 2 but at 22 hr UT. only slight enhancement of the induced currents when the centre of the external current vortex is above the Atlantic Ocean. These features seem to result from the fact that the horizontal wavelength of the Sq field is so large that the induced currents respond only to the gross sea-land distribution. Even when the external current vortex comes above the Eurasian continent, the effects of the Pacific Ocean remain and cause the enhancement of the total internal field, although it is possible that the enhancement may be due to the existence of the Indian Ocean in the southern hemisphere. On the other hand, the longitudinal scale of the Atlantic Ocean is smaller (1/6 of the Earth) than the wavelength of fourth harmonic of the Sq field which is the maximum cycle wave actually appearing in the Sq field. Inclusion of the shell enhances the internal current vortex and it is expected that this affects the estimation of the mantle conductivity. This is discussed in the next section. 4 EFFECT OF THE CURRENTS IN THE OCEANS ON THE ESTIMATION OF MANTLE CONDUCTIVITY Now we have got the electric currents induced in the shell representing the sea-land distribution, we can discuss their effects on the internal Sq field and on the estimation of the mantle conductivity. We first estimated the conductivity and the depth of the conductor from the amplitude ratio of the 100 3> tl-l 9 50 W t- z OO MAGNETIC LOCAL T I M E 12 18 U N I V E R S A L T I ME 24 ur variation of northern internal current intensity obtained by the simulations with (thin solid line) and without (dashed line) the shell representing the sea-land distribution above the uniformly conducting mantle of 500 km depth and 0.1 S m-'. The thick solid line shows the UT variation of the simulation with the shell above the uniformly conducting mantle of 780 km depth and 1 Sm-'. Figwe 4. Flgwe 2. Current function representing the calculated induced currents in the shell at 1 0 h r m . Ordinate and abscissae are geomagnetic latitude and geomagnetic local time at the equinox, respectively. Contours are drawn at every 10 kA. 6 384 M. Takeda 2 0.0 , 0 ,o. , , 1 2 0 0 4 0 0 6 0 0 a00 1000 E ( : I 34, (a) I I l 4 $ 1 , 0 60.0 0 , , 1 2 0 0 4 0 0 600 800 1000 (b) ment of the total induced currents by the existence of the shell makes the estimated depth of the sphere shallower. A more clear feature appears in this figure. An apparent distribution of the conductivity with depth is found. That is, the shorter the period of the Sq harmonics, the smaller estimated conductivity, and the shallower the depth. This is also caused by the response of the shell to the inducing field. For the external fields of shorter period, more of the induced currents flow in the finitely conductive shell and the effects of the shell become larger. Thus, it is possible that the previous conductivity distribution by depth obtained from the response of the Sq harmonics does not reflect the real conductivity distribution in the mantle, but only the effect on the shell or oceans. How can the real conductivity distribution from the observed Sq field be obtained? For this purpose, we calculated the conductivity and depth of the uniform geocentric conductor by using the fields which are obtained by subtracting the effects of the currents in the shell from the total observed fields. The effects of the currents in the uniformly conductive sphere induced by the fields generated by the currents flowing in the shell are also taken into consideration. This procedure should be iterated until the estimated conductivity and depth agree with those of the conductive sphere used for the calculation of the currents in the shell. It was found that for the l d a y period variation field of Pi mode, a uniformly conductive sphere of 1S m-' below the depth of 780km can explain the observed response if the effects of the shell are considered. This depth of 780 km is an interesting value, because from the study of the seismic precursors it is shown that there is a transition region of the Earth's upper mantle at about 670 km depth. It is possible that the estimated depth is related to the sudden increase of the electric conductivity accompanied by this transition. However, we do not have enough data to discuss this problem further. Figure 5(c) gives the conductivity and depth of the conductor estimated from the field generated by currents induced in both the shell and the conductive sphere on the assumption that the total induced fields are generated by a uniformly conductive sphere only. This figure resembles Fig. 5(a) not only in the estimated conductivity and depth for the 1 day period variation field of the P: mode but also in the apparent dependence of the conductivity and depth on the period as the shorter period gives smaller conductivity and shallower depth, except that the 114 day period variation field of the mode gives a shallower depth than the 1/3 day period variation field of the mode in Fig. 5(a). Therefore, it is possible that the depth variation of the mantle conductivity obtained by the geomagnetic induction fields of various periods is not realistic but reflects the effects of the currents induced in the oceans. This change of the mantle parameters varies the induced currents. However, it is found that the currents induced in the shell are almost the same as those for the previous parameters (the difference is less than 10 per cent) and are not shown here. Newly estimated UT variation of the intensity of the internal current vortex in the northern hemisphere in the daytime is presented by the thick line in Fig. 4. Comparing the thick and thin solid lines, it is clear that the general overestimation of the internal current intensity is removed by the change of the mantle o'21 O.] tI . : ' , o.oo , , 1 2 0 0 4 0 0 6 0 0 8 0 0 1000 DEPTH ( k m l (C) Figare 5. (a) Conductivity profile estimated by the application of the uniform-conductivity sphere model to the result of the data analysis by Takeda (1985, 1989). The result of simulation in which the effects of the shell are considered in addition to the uniformly conducting mantle of (b) 500km depth and 0.1Sm-' and (c) 780 km depth and 1 S m-'. internal field to the external field and their phase difference obtained by data analysis on the assumption that the induced currents flow in a uniformly conductive sphere, by using the method shown in Campbell & Anderssen (1983). Fig. 5(a) shows the conductivity and the depth of the conductor. Symbols 1, 2, 3 and 4 represent the values estimated from the 1cpd term of the Pi mode, the 2cpd term of the P', mode, the 3 cpd term of the Pj mode and the 4cpd term of the mode, respectively. Those terms are chosen because they are the principal terms of each frequency and have large amplitudes. Figure 5(b) shows the same profile calculated from the current distribution obtained by the present simulation, assuming that the calculated internal field, which is affected by the shell in reality, is generated by the induced currents in a uniformly conductive sphere without the shell. If the effects of the shell representing the sea-land is negligible, the resultant conductivity and depth for all terms should be 0.1 S m-I and 500 km, respectively because these are the parameters of the uniformly conductive sphere used in the present simulation. However, the results show clear effects of the shell. The 1 day period of the Pi mode gives the result of 0.05Sm-' and 240km depth, and the higher harmonics gives less conductivity and a shallower depth. The estimated conductivity and depth from the 1 day period variation field of the Pi mode are 0.05S m-' and 240 km, respectively, and conductivities and depths from higher modes are smaller and shallower, respectively. This is caused by the currents induced in the shell, almost all in the oceans. That is, the phase difference of the currents in the shell due to the finite conductivity makes the total phase difference larger and estimated conductivity of the sphere smaller, and enhance- e Induced oceanic currents and mantle conductivity parameters. The amplitude of the UT variation becomes larger and more similar to the observational result, although inclusion of the shell itself does not improve the agreement with the observational result so conspicuously. Disparity between the observational and simulated results may be due to the insufficient number of the observatories in the oceanic region. We have shown that electric currents in the oceans have a significant effect on the estimation of the mantle conductivity for the Sq field. Usually, variation with depth of the electric conductivity of the mantle was mainly estimated by using the response of geomagnetic variation field of the mode of the period from a few to several hundred days (e.g. Banks 1%9; Campbell & Anderssen 1983) ignoring the effects of the oceans. However, Roberts (1984) found that the Oceans have a considerable effect on the response even at the periods of 2-200 days, by comparing of the responses at different stations. It will be necessary to simulate the effects of the electric currents induced in the Oceans for the Pi mode up to the period of several hundred days for the precise estimation of the mantle conductivity. We will discuss this problem in a subsequent paper. 5 CONCLUSIONS We have simulated the electric currents induced in the Ocean by using the model of a shell conductor representing the sea-land distribution and a finitely conductive sphere representing the mantle. This study reveals the following major points. (1) The simulation results show that at 22 hr UT currents in the ocean have maximum intensity of 54kA in the northern Pacific Ocean and enhance the total induced fields by about 60 per cent. This shows that the induced currents in the Oceans cannot be neglected for the estimation of the conductivity in the mantle. (2) Even when the external current vortex is located above the Eurasian continent, the internal current vortex is enhanced by about 10 per cent by the existence of the shell. (3) Electric currents induced in the ocean cause less-conductive and shallower estimation of the mantle conductor and apparent depth dependence of the conductivity. The conductivity and depth estimated from the data analysis for the 1 day period variation field of the P i mode without the consideration of the oceanic currents are 0.1 S m-' and 500 km, respectively, but it would be 1S m-' and 780km if the effects of the currents in the shell representing the sea-land are considered. Apparent dependence of the conductivity and depth on the period can be made by the effect of the oceanic currents even if the mantle is a uniform conductor. 385 ACKNOWLEDGMENTS The bathmetry data used in this study are E T O P O J of NOAA presented through Japan Oceanographic Data Center of Maritime Safety Agency, Japan. The author wishes to thank Professor T. Araki for valuable discussions. The geomagnetic data used in the present study were obtained through the World Data Center C2 for Geomagnetism, and the data processing was performed using facilities at the Data Processing Center, both at the Kyoto University. REFERENCES Banks, R. J., 1%9. Geomagnetic variations and the electrical conductivity of the upper mantle, Geophys. J. R. asfr. SOC.,17, 457-487. Beamish, D., Hewson-Browne, R. C., Kendall, P. C., Malin, S. R. C. & Quinney, D. A., 1980a. Induction in arbitrarily shaped oceans-IV. Sq for a simple case, Geophys. 1. R. astr. SOC.,60, 435-443. Beamish, D., Hewson-Browne, R. 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