Statistical Study of the Long-Period Induced Geoelectric Field Caused by Magnetic Storms and Its Implication on Mantle Exploration

The ground induced geoelectric ﬁeld caused by magnetic storms is not only a hazard, but also a helpful 7 tool to explore the underground conductivity. Especially, the long period ( > 10 5 s, LP) induced ﬁeld 8 deserves more concerns as it could reach the mantle. However, the occurrence rate and the period range 9 of the LP induced geoelectric ﬁeld during diﬀerent magnetic storms are unclear. This statistical work 10 examines the occurrence and the period upper limit in the whole solar cycle 23. The geoelectric ﬁeld 11 and geomagnetic ﬁeld measured continuously at Memambetsu observatory in Japan from 1989 to 2008 12 are studied. The LP electromagnetic ﬁeld is identiﬁed by the wavelet coherence spectra. The results 13 show that the LP induced geoelectric ﬁeld stably occurred during magnetic storms in the solar cycle. 14 The LP induced ﬁeld in the ﬁrst three months of each year is signiﬁcantly diﬀerent from that in the 15 three months around super magnetic storms. The longest period of the induced geoelectric ﬁeld during 16 the magnetic storms is 9 × 10 5 s. The period upper limit of the induced δ E y is larger than that of the 17 induced δ E x , which signiﬁcantly increases with the storm intensity range. The distribution of the LP 18 δ E x on the magnetic local time is asymmetric. To quantify the potential application of such a LP 19 electromagnetic ﬁeld on the mantle conductivity, we check the uncertainty of resistivity from inversion 20 under the condition of plane-wave for layered medium. We set the sources to be the ring current and 21 the ﬁeld-aligned current in their real scales. As a result, the apparent resistivity is obtained within 10% 22 uncertainty by δ E y , and within 20% by δ E x . 23


Introduction 26
The long-period (LP, > 10 5 s) induced geomagnetic field disturbances have been measured and studied 27 for many years (e.g. Lahiri and Price 1939;Banks 1969;Iyemori 1990;Constable and Constable 2004). 28 The LP induced geomagnetic field disturbances centred at the period of two days are related to the ring 29 current during the magnetic storms (e.g. Roberts 1984; Schultz and Larsen 1987; Banks and Ainsworth 30 1992). The induced geomagnetic field at the ground is dependent on both the current systems in the 31 ionosphere and in the magnetosphere, and the electrical conductivity structure in the deep earth (e.g. 32 Sun et al. 2015;Fujii and Schultz 2002). This LP geomagnetic field disturbance can be used by the 33 geomagnetic depth sounding (GDS) to deduce the electrical conductivity of earth interior (e.g. Banks 34 1969;Roberts 1984;Schultz and Larsen 1987;Banks and Ainsworth 1992;Olsen 1998). And the electric 35 conductivity of the earth mantle is a key factor in controlling the geomagnetic field reversal (Glatzmaier 36 et al. 1999). 37 Since the current source is not completely known, a simplified zonal dipole assumption for the long 38 period variation brings rather large error bars to the derived impedance (e.g. Schultz and Larsen 1987;39 Egbert and Booker 1992). Compared to the GDS method, the magnetotelluric (MT) method based 40 on the simultaneously measured geoelectric field and geomagnetic field could calculate the impedance 41 directly (e.g. Cagniard 1953;Tikhonov 1950;Rikitake 1951). 42 The induced EM field at period up to 10 4 s is widely used in crust exploration by MT (e.g. Egbert 2007;43 Fujii et al. 2015). According to Srivastava (1965), the assumption of uniform plane wave is valid for the 44 EM field at period below 10 5 s. It is still unclear that what is the period upper limit of the induced 45 geoelectric field related to magnetic storms, and if such field could be used as uniform plane wave in 46 layered-structure medium (e.g. Chave and Jones 2012; Simpson and Bahr 2005).

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As far as we know, the LP induced geoelectric field and its source have been rarely studied, as it is hard 48 to obtain the continuous long-term measurement (e.g. Fujii et al. 2015;Egbert et al. 1992). Recently, Wu  This statistical work, for the first time, shows the direct evidence of the stable existence of the LP 54 geoelectric field, and checks its period upper limit in the solar cycle 22 and 23. The results also 55 reveal the positive relation between the period limit of δE y and the ring current enhancement, with 56 the measurements from the same ground geomagnetic observatory. The power distribution of δE x along 57 the magnetic local time (MLT) indicates the domination by the field-aligned current. Considering the 58 scales of the RC and the FAC, the induced LP field caused by the magnetic storms is proved to satisfy the 59 plane-wave assumption for the layered medium. Therefore, this induced LP electromagnetic field during 60 the magnetic storms could be used to reveal mantle conductivity. The geomagnetic field and geoelectric 61 field measurements, the geomagnetic indices, and the way we study the induced LP electromagnetic field 62 are described in the section Data and Methods. The period upper limit and its relation to the storm 63 levels are shown in the section Results. The current source scale and the plane-wave test are provided in 64 the section Current Source Assumption and The Plane-wave Test. The superposition of the two current 65 sources, and the possible application on the mantle conductivity are stated in the section Discussion.

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Finally, the period upper limit, the relation between the period upper limit and the magnetic storm level, 67 and the applicability of the induced LP EM during on the layered medium are concluded.

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The geomagnetic indices SYM-H and AE are available from the World Data Center (WDC) for Geomag-78 netism in Kyoto at http://wdc.kugi.kyoto-u.ac.jp. They are used to reflect the enhancement of the ring 79 current (RC) and the auroral electrojet connected to the field-aligned current (FAC).

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Identification of the induced LP field on the ground 81 We use the criteria below to automatically identify the LP induced geoelectric field, and calculate its 82 period upper limit, the averaged power, and the duration in each magnetic storm. (1) The occurrence of 83 the LP induced geoelectric field. We first calculate the wavelet power spectra of the geomagnetic field 84 and the geoelectric field. One example of the super storm study is shown in Figure 1. Since the LP is 85 defined as the period is longer than 10 5 s, we focus on the spectra at period range from 26 to 250 hours. 86 Next, we calculate the coherence coefficients between the geomagnetic wavelet power spectra and those 87 of the geoelectric field. The areas having coherence coefficients larger than 0.8 at 95% significance level  is from the region-1.

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(2) The duration of the storm. We calculate the period-averaged power curves for each component of the represent the storm duration, which is defined as region-2.

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(3) The LP induced geoelectric field during magnetic storms. The intersections between region-1 and 96 region-2 are defined as region-3, when the LP induced geoelectric field occurs during the magnetic storms.

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The minimum SYM-H and the maximum AE are also chosen from region 3, respectively. The maximum 98 period in region-3 is taken as the period upper limit of the induced geoelectric field during each storm.

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In Figure 3(a), the period upper limit and the averaged power are from region-3. To exclude the power 100 of the solar diurnal variation (24 hours), the studied period range in Figure 3(a) starts from 35 hours 101 rather than 26 hours.

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Examination of plane-wave assumption

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To examine the uncertainty of the apparent resistivity in the layered medium, it is necessary to know 107 the period range and the source scale of the LP induced electromagnetic field. The theory is suggested 108 by Srivastava (1965) and Price (1962). The electromagnetic field is assumed to be plane-wave. Starting 109 from the Maxwell's equations, they obtained (in emu) Here the P , R, Q, and S are the real and imaginary parts of the right side in eq.(1).
In these equations, 2π/v is the horizontal scale of the source, σ n is the conductivity of the n th layer, h n is 117 the thickness of the n th layer, Z is the impedance, and θ n equals to √ v 2 + 4π iωσ n . The current source 2004. The lasting time of the δB y and δE x with period longer than 2.4×10 5 s is shorter than that of δB x 137 and δE y .

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Since the lasting time is rather short, it is shown as dotted area in the second panel of Figure 1(a). The 139 mean period varies from 1.1×10 5 s to 1.6×10 5 s. It is obvious that the LP geoelectric field occurs during 140 all the magnetic storms, though the period ranges of them are different. We would like to mention that 141 the LP induced field data is measured at the same observatory. Therefore, the period variation should 142 be only attributed to the source in magnetosphere and ionosphere.

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In both pairs of the LP induced field, the mean periods seem to be independent on the solar cycle. The   the storm is stronger. It means that the averaged period of LP induced field is linearly related to the 166 storm level. Therefore, the relation between period upper limit and SYM-H minimum is not one-to-167 one, but band-to-band. It could be seen that the period limit has a wide range for the storms having 168 minimum SYM-H from -210 nT to -50 nT. Similarly, the power of the LP induced δB x and δE y increases 169 with stronger storms. For the induced field of δB y and δE x , the band-to-band linear relation between 170 period upper limit and storm level becomes weaker. We could like to clarify that the storms happened 171 in the Group 1 could not be used to study the relation as they cover too small range of the minimum 172 SYM-H from -40 nT to -150 nT.

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The enhancement of LP induced field on local time 174 We next investigate the local time distribution of the LP induced field, which is shown in Figure 3(b).

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The studied storms are measured from 1998 to 2008 with minimum SYM-H varying between -150 nT that by the uniform plane wave at period of from 10 5 s to 10 6 s. It is known that the spacial scale of 223 FAC is smaller. As a result, the apparent resistivity is less than that obtained from ideal uniform plane 224 wave by 10% and 20% at period from 10 5 s to 5×10 5 s. The skin depth (D) of this long-period EM field 225 is estimated to be about 1500 km, assuming the resistivity being 100 Ω • m.

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In the equation, f is the frequency, µ 0 is permeability constant of free space (4π×10 −7 ) and ρ is the According to the source scales and the related period ranges, we check the plane-wave assumption for 250 the induced LP geoelectric and geomagnetic field during the magnetic storms. The result shows that the 251 LP δE y -δB x satisfies the plane-wave assumption in the period range from 10 5 to 10 6 s. However, the LP 252 δE x -δB y would generate an uncertainty from 10% to 20% on the apparent resistivity by inversion.

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This statistical work studies the LP induced geoelectric field caused by the magnetic storms at the same 255 ground observatory in the solar cycle 23. If such a field is stably generated during magnetic storms, it 256 could be an important tool to explore the mantle conductivity. It is known that the measured geoelectric 257 field is controlled by both the current sources and the underground conductivity. Thus, it is necessary to 258 investigate the source and the related period range before the application on mantle conductivity.

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To answer the above key questions, we analyze more than ten years' measurements of the geoelectric The former generates the uncertainty less than 10%, while the latter generates the uncertainty from 10% 273 to 20% on the apparent resistivity.

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The results indicate that not only the harmful geomagnetically induced current, but also the helpful .

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The authors declare no competing interests.

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Funding 306 The work on the induced geoelectric field during the magnetic storms is supported by the Chinese   The relation between the period upper limit and the SYM-H index Figure legends The sub-gure (a) shows he relations between the period length, the mean power of δBx, δEy, δBy, and δEx, and the minimum SYM-H. The x-axis is the period length in logarithm 2. The y-axis is the averaged power in logarithm 2. Four levels of the storm intensity classi ed by the SYM-H minimum are shown in the different colors. The storms having SYM-H minimum in the four ranges between -687 nT and -528 nT, -528 nT and -369 nT, -369 nT and -210 nT, -210 nT and -51 nT are shown in black, blue, yellow, and pink, respectively. All the storms happen in the three months including a super storm from 1989 to 2004. The square marks the mean value of each SYM-H range. The sub-gure (b) shows the distributions of the power and the period upper limit of δBx, δBy, δEy, and δEx along the local time. All the storms happen in the three months from 1998 to 2008, which have the SYM-H minimum varying from -40 nT to -150 nT. The x-axis is the local time from midnight to the next midnight. The color represents the period upper limit from 105 s to 5x105 s varying from blue to red.

Figure 4
The current source analysis The gure shows the superposition of the LP eld δBy generated by the RC and that by the FAC. The δBy caused by the RC is shown as a sinusoidal sequence in blue having the period of 105s and the unit amplitude in the sub-gure(a). The δBy caused by the FAC is shown as two opposite triangle signals in red lasting for 3x104 s having the amplitude of 5 times unit in the subgure(a). The superposition of the above two sequences is shown as black curve in the sub-gure(a). The wavelet power spectrum of δBy caused by the RC and by the FAC are shown in the sub-gure(b) and in the sub-gure(c), respectively. The right panels of the sub-gure(b) and (c) show the time averaged power. The bottom sub-panels of the sub-gure(b) and (c) show the period averaged power. The fourier spectra of the δBy caused by the RC and that caused by the FAC are shown as blue and red curves in the subgure(d). The fourier spectrum of the superposed δBy is shown as black curve in the sub-gure(d).

Figure 5
The apparent resistivity obtained by plane-wave assumption for layered medium This gure shows the inversed apparent resistivity by the LP electromagnetic eld under the uniform plane-wave assumption.
The larger sub-gure shows the apparent resistivity calculated by the EM eld having different source scales. The smaller gure focuses on the critical scales of the RC and the FAC under the uniform planewave assumption.

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