1 Introduction

The Sun continuously blows ionized particles known as ‘solar wind’ in the interplanetary space. Following intense coronal mass ejection (CME), the compression of the magnetosphere by the solar wind and the interaction with the geomagnetic field intensify currents in the magnetosphere and high latitude ionosphere (Bogdan 2007). The subsequent intense fluctuations of the geomagnetic field during the disturbance periods (geomagnetic storms) induce electric field and currents within the earth (Boteler et al. 1998; Pirjola 2000; Pirjola et al. 2005). These currents are designated as ‘geomagnetically induced currents (GIC)’. The flows of GIC in technological infrastructures, such as buried pipelines, power transmission system, transformers and telecommunication cables, are known to possibly cause their disruption. Such damages have been experienced at high latitudes since mid XIXth century (Bolduc 2002; Boteler 2001). The disruptions of Hydro–Quebec (Canada) power grid on March 13th, 1989, which resulted in a 9-h power outage (Boteler et al. 1998) and that in Sweden on October 30th, 2003, are noticeable GIC effects that occurred in the modern days (Kappenman 2005). At high latitudes, magnetosphere–ionosphere coupling through geomagnetic field lines generates intense currents such as auroral electrojets (Viljanen and Pirjola 1994; Pulkkinen et al. 2003). These currents are extremely enhanced during geomagnetic storms and sub-storms and cause very intense geomagnetic field variations. Thus, most investigations on GICs have been focused on high latitudes (Bolduc 2002; Lam et al. 2002; Pirjola 2005; Pulkkinen et al. 2005; Wik et al. 2009). There are only few reports on important \(GIC\) occurrence in low- and mid-latitudes (Trivedi et al. 2007; Ngwira et al. 2008, 2015; Torta et al. 2012). However, several transformer failures due to GIC associated with geomagnetic storms occurred in South Africa between 2003 and 2004 (Gaunt and Coetzee 2007). Trivedi et al. (2007) estimated the \(GIC\) amplitudes during the November 7–10, 2004 geomagnetic storm in Brazil. They obtained \(GIC\) values between 15 and 20 A. Impulsive variations of the geomagnetic field like sudden storm commencement (ssc) and solar flare effects (sfe) are the possible sources of significant GICs at low latitudes (de Villiers et al. 2016; Kappenman 2003, 2005). In a recent study, Doumbia et al. (2017) analyzed the low latitude geoelectric field variations observed in West Africa in 1993. In that study, enhanced geoelectric field variations have been associated with impulsive geomagnetic field variations like sscs and \(sfes\). However, the GICs associated with those variations have not been estimated.

It is worth to notice that GIC estimations in most previous studies are inferred from geomagnetic field variations (Koen 2000; Bernhardi et al. 2008, 2010; Liu et al. 2009; Barbosa et al. 2015). The approach consists of estimating the horizontal components (\(Ey\) and \(Ex\)) of the geoelectric field variations from the time derivatives of the geomagnetic field variations based on a given earth conductivity model. The resulting geoelectric field components are then used to calculate the GIC. This approach assumes the local earth’s conductivities are known before.

In the present work, the disturbed geomagnetic field variations and associated geoelectric field variations observed at different stations in West Africa are analyzed. In addition, variations of the GIC was estimated from the respective measured geoelectric field components \(Ey\) and \(Ex\).

2 Data and data processing

2.1 Data

During the International Equatorial Electrojet Year (IEEY), 10 stations devoted to recording the geomagnetic and geoelectric field variations were deployed along a meridian chain across the geomagnetic dip-equator in West Africa (Amory-Mazaudier et al. 1993; Doumouya et al. 1998; Vassal et al. 1998; Doumbia et al. 2017). The stations were located along the 5°W meridian, from Lamto (Cote d’Ivoire, –6.30° dip-latitudes) to Tombouctou (Mali, +6.76° dip-latitudes). Figure 1 shows the IEEY network of the stations in West Africa. The coordinates of the stations are given in table 1. Variations of the horizontal northward (\(H\)), eastward (\(D\)) and vertical (\(Z\)) components of the geomagnetic field, as well as the north–south (\(Ex\)) and east–west (\(Ey\)) components of the geoelectric field were recorded at a sampling rate of 1 min from November 1992 to December 1994. The \(H\) and \(D\) components were measured with suspended magnet variometers with an accuracy of about \(\pm 0.2~\,{\text{nT}}\) and thermal sensitivity of 0.02 nT/°C. The \(Z\) component was recorded with a fluxgate magnetometer with an accuracy of \(\pm \,0.1~\,{\text{nT}}\). Geoelectric field variations were measured as potential differences between electrodes installed at the ends of two 200 m long lines oriented along N–S and E–W magnetic directions, respectively. The measured potential differences resulted from the circulation of the geoelectric field between the two ends of the line, and were therefore proportional to the average value of the geoelectric component along the line (Ex for the N–S line and Ey for the E–W line, respectively). Each electrode was made from five thin sheets of lead metal (20 cm × 10 cm) buried at a depth of 50 cm. The measured geoelectric signal was amplified, with the resultant output being in the range of \(\pm\)250 mV/km with 0.13 mV/km sensitivity. In-situ measurements showed that differential variations of temperature between two electrodes set 50 cm deep were about 0.2°C for a daily temperature variation of about 15°C at the surface, thereby resulting in a negligible thermal drift of 5–10 µV (Vassal et al. 1998). The schematic diagram of the measurement is shown in figure 2.

Figure 1
figure 1

The West African network of 10 stations for the geomagnetic and geoelectric field measurements during the International Equatorial Electrojet Year (IEEY).

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Table 1 Geographic coordinates of the magnetic stations installed along the meridian 5°W in West Africa during the International Equatorial Electrojet Year. The geomagnetic dip-latitudes of the stations at epoch 1993.5 are shown.
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Figure 2
figure 2

Synoptic scheme of a geomagnetic-telluric station used to measure the variations of the east–west \(D\) (channel 1), horizontal \(H\) (channel 2), and vertical \(Z\) (channel 5) components of the geomagnetic B field and the north–south (NS) (channel 3) and east–west (EW) (channel 4) components of the telluric B field (Doumouya 1995).

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2.2 Data processing

2.2.1 Geoelectric field data

The total geoelectric field component \({Ex}_{tot}\) measured in each station can be expressed by:

$$ Ex_{{tot}} \left( t \right) = Ex\left( t \right) + Ex_{{bl}} \left( t \right) $$
(1)

where \(Ex\) is the geoelectric field fluctuations that are superimposed on the geoelectric field diurnal variation \({Ex}_{bl}\). \({Ex}_{bl}\) was removed by polynomial fitting of degree 16. The degree 16 is chosen after many iterations from 0 to 50. \(Ex\) is obtained by substracting the base line \({Ex}_{bl}\) from \({Ex}_{tot}\):

$$Ex\left(t\right)={Ex}_{{tot}}\left(t\right)-{Ex}_{bl}\left(t\right).$$
(2)

Similar calculation is made for \(Ey\) component.

2.2.2 Geomagnetically induced current calculation methods

The geomagnetically induced current in any technological system can be calculated by the following equation:

$$GIC\left(t\right)=aEx\left(t\right)+bEy\left(t\right)$$
(3)

where \(Ex\) and \(Ey\) are the fluctuations of the horizontal geoelectric filed components, and \(a\) and \(b\) are designated as system parameters. \(a\) and \(b\) depend on the topology and the electrical characteristics of the system concerned. In practice, \(a\) and \(b\) can be determined if GIC and the geoelectric field or GIC and the geomagnetic field variations are known. When the values of the geoelectric field components and the GIC are known, \(a\) and \(b\) can be estimated as follows (Pulkkinen et al. 2007; Ngwira et al. 2008):

$$ a = \frac{{\left\langle {GICE_{y} } \right\rangle \left\langle {E_{x} E_{y} } \right\rangle - \left\langle {GICE_{x} } \right\rangle \langle {E_{y}^{2} } \rangle }}{{\left\langle {E_{x} E_{y} } \right\rangle ^{2}\, - \, \left\langle {E_{x}^{2} } \right\rangle \langle {E_{y}^{2} } \rangle }} $$
(4)
$$ b = \frac{{\left\langle {GICE_{x} } \right\rangle \left\langle {E_{x} E_{y} } \right\rangle - \left\langle {GICE_{y} } \right\rangle \left\langle {E_{x}^{2} } \right\rangle }}{{\left\langle {E_{x} E_{y} } \right\rangle ^{2}\, - \,\left\langle {E_{x}^{2} } \right\rangle \langle {E_{y}^{2} } \rangle }} $$
(5)

where \(a\) and \(b\) are expressed in \({\text{A}}.\,{\text{km/V}}\) and the symbol ‘.’ indicates the expectation values of the parameters.

3 Results

3.1 Geomagnetic and geoelectric field variations during quiet periods

In this section, quiet period geomagnetic and geoelectric field data are analyzed. \(H\), \(D\) and \(Z\) components on 23 February, 1993 with Ap = 9 nT are shown in figure 3. Figure 4(a and b) shows variations of the total geoelectric field, the baseline and the fluctuations on 23 February, 1993. The baseline shows a high variability from one station to another. The amplitudes of the fluctuations are weak, including at LAM where it appears to have strong amplitude. The storm effects on \(Ex\) and \(Ey\), are shown on the composite hourly mean and the standard deviation of these components during quiet and disturbed periods in figure 5(a and b). It appears that the amplitudes of the standard deviation of the fluctuations \(Ex\) and \(Ey\) are higher during storm periods than on quiet days. \(Ex\) and \(Ey\) data are far away from the mean value during the disturbed period than during a quiet period.

Figure 3
figure 3

The geomagnetic components \(H\), \(D\) and \(Z\) at West African stations during the quiet day of 23 February, 1993. The Ap value (9 nT) of this day is shown.

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Figure 4
figure 4figure 4

(a) The daily geoelectric field \({Ex}_{tot}\) (left column), the isolated baseline \({Ex}_{bl}\) (middle column) and the fluctuations \(Ex\) (right column) on 23 February, 1993. (b) The daily geoelectric field \({Ey}_{tot}\) (left column), the isolated baseline \({Ey}_{bl}\) (middle column) and the fluctuations \(Ey\) (right column) on 23 February, 1993.

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Figure 5
figure 5figure 5

(a) The \(Ex\) composite hourly mean and standard deviation estimated with five quiet days in January, 1993 and that of the disturbed day of January 10, 1993. In each panel of the figure, the name and the dip latitude value of the station are indicated. (b) Same as figure 5(a), but for \(Ey\).

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3.2 Geomagnetic and geoelectric field variations during disturbed periods

In the present study, geomagnetic field and geoelectric field variations during 11 disturbed days with the daily Ap index higher than 20 nT are considered. The tri-hourly ap indices and the daily \(\rm{Ap}\) index shown in table 2 were downloaded from http://swdcwww.kugi.kyoto-u.ac.jp/index.html.

Table 2 Tri-hourly ap index and the daily mean Ap index for the selected days.
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Figure 6 shows variations of the \(H\) (a), \(D\) (b) and \(Z\) (c) components of the geomagnetic field, the time derivatives \(dH/dt\) (d), \(dD/dt\) (e) and \(dZ/dt\) (f) and the fluctuations of the geoelectric field components \(Ex\) (g) and \(Ey\) (h) observed at LAM, respectively on 10 January 1993 (left column), on 20 February, 1993 (middle column) and 15 March, 1993 (right column). The geoelectric field fluctuations were isolated from the daily variations of \(Ex\) and \(Ey\) according to the method described in equation (2). On the three days shown in figure 6, the daily Ap indices are respectively 25, 26, 45 nT with 80, 39 and 67 nT as highest values of tri-hourly \(ap\). The high values of the ap indices indicate significant geomagnetic field disturbances, which are confirmed by the geomagnetic field components \(H\), \(D\) and \(Z\) and their time derivative \(dH/dt\), \(dD/dt\) and \(dZ/dt\) that exhibit important fluctuations. As a consequence, significant variations of the geoelectric field components \(Ex\) and \(Ey\), associated with these fluctuations are observed. Indeed, variations of \(Ex\) and \(Ey\) clearly reflect respectively the fluctuations of the time derivatives \(dD/dt\) and \(dH/dt\) of the geomagnetic field components. The correlation between \(Ex\) and \(dD/dt\), and Ey and \(dH/dt\) is shown in figure 7. The correlation coefficient between \(Ey\) and \(dH/dt\) is about – 0.87 during the three storms, while that of \(Ex\) and \(dD/dt\) is greater than or equal to 0.60.

Figure 6
figure 6

The geomagnetic field components \(H\) (a), \(D\) (b) and \(Z\) (c), the time derivatives \(dH/dt\) (d), \(dD/dt\) (e) and \(dZ/dt\) (f) and the geoelectric field components \(Ex\) (g) and \(Ey\) (h) recorded at LAM during three disturbed days: 10 January (left column), 20 February (middle column), and 15 March (right column), 1993.

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Figure 7
figure 7

Correlations between \(Ey\) and \(dH/dt\), and \(Ex\) and \(dD/dt\) at LAM during the disturbance periods of 10 January 1993, 20 February 1993 and 15 March 1993.

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3.3 Induction effects associated with disturbed fluctuations of the geomagnetic field

3.3.1 Geoelectric field variations associated with disturbed geomagnetic fluctuations

In this section, variations of the geoelectric field horizontal components \(Ex\) and \(Ey\), recorded during 11 geomagnetically disturbed days (table 2), are analyzed. Figure 8(a and b) shows fluctuations of the geoelectric field components \(Ex\) and \(Ey\) associated with geomagnetic disturbances on 10 January and 15 March, 1993 (first two columns on the left), and 20 February and 24 March, 1993 (last two columns on the right), at different stations of the network. For these disturbed days, the geoelectric field components exhibit rapid fluctuations that were isolated from the measured geoelectric field components, by subtracting the baseline (Doumbia et al. 2017). These fluctuations associated with geomagnetic variations are observed at all the stations of the network. The magnitudes of the fluctuations show a diurnal trend with most significant amplitudes observed during the daytime. In addition, strong impulses due to brisk changes in the magnetic field variations are observed. More attention is paid to these impulses in this study. On 10 January, 1993, the crest-to-crest amplitudes of the strongest impulse at LAM are \(Ex = 369\,{\text{mV/km}}\) and \(Ey = 289\,{\text{mV/km}}\) around 11.00 LT. On 20 February, 1993, \(Ex = 352\,{\text{mV/km}}\) and \(Ey = 186\,{\text{mV/km}}\) around 12.00 LT. The most important amplitudes of fluctuations and impulses are observed at LAM. However, they are also observed at all the stations. In section 3.2.3, the latitudinal trend of the impulses of the geoelectric field component are examined.

Figure 8
figure 8figure 8

(a) Fluctuations of the geoelectric field components \(Ey\) and \(Ex\) associated with geomagnetic field disturbances on 10 January and 20 February, 1993. The vertical dashed lines indicate the selected impulses considered for the latitudinal variations of \(Ey\), \(Ex\) and \(GIC\) in figure 10. (b) Same as figure 8(a), but during the 15 and 24 March, 1993.

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3.4 Geomagnetically induced currents estimated from geoelectric field variations

In this section, the geomagnetically induced current (GIC) within a ground-based network of conductors is estimated from the horizontal components \(Ex\) and \(Ey\) of geoelectric field variations, and \(a\) and \(b\) using the equation (3). Different values of \(a\) and \(b\) are found in literature (Liu et al. 2009; Pulkkinen et al. 2007, 2012; Matandirotya 2016). For example, Matandirotya et al. (2015) used \(a = - 94~\,{\text{A}}.\,{\text{km/V}}\) and \(b = 24~\,{\text{A}}.\,{\text{km/V}}\) for the power grid in South Africa; Pulkkinen et al. (2007) used \(a = - 70\,{\text{A}}.\,{\text{km/V}}\) and \(b = 88~\,{\text{A}}.\,{\text{km/V}}\) for the Finnish natural gas pipeline and Liu et al. (2009) used \(a = - 3.5~\,{\text{A}}.\,{\text{km/V}}\) and \(b = - 256~\,{\text{A}}.\,{\text{km/V}}\) for the Chinese power grids. It is to be noticed that other values of \(a\) and \(b\) have also been used for the GIC investigation (Bernhardi et al. 2008; Ngwira et al. 2008; Wik et al. 2009).

It is to be noticed that the system parameters \(a\) and \(b\) of the conductor systems are not determined during the IEEY campaign. For this study, the configuration of system parameters with \(a = b = 50~\,{\text{A}}. \,{\text{km/V}}\) is considered to estimate the GIC at different stations. This choice is based on the recommendation made by Pulkkinen et al. (2012), who demonstrated that a good approximation of the GIC is obtained when both a and b are set to \(50~\,{\text{A}}.\,{\text{km/V}}\) for unknown conductor systems (Zois 2013). Same value of \(a\) and \(b\) can also be justified by the fact that during the IEEY campaign, the same electric wires of 200 m and electrodes were used in north–south and east–west directions for \(Ex\) and \(Ey\) measurements.

The GIC variations associated with the fluctuations of the geoelectric field components \(Ex\) and \(Ey\), are estimated from equation (3), with more emphasis on the strong impulses. Figure 9(a and b) shows the estimated \(GIC\) variations on 10 January and 20 February 1993 (figure 9a), and 15 and 24 March, 1993 (figure 9b). Like that of geoelectric field components, the GIC variations exhibit a daily trend with higher magnitudes of the fluctuations during the daytime. The strongest amplitudes of the GIC are linked to the strong impulses in the geoelectric field components. At LAM, \(GIC = 32.0~\,{\text{A}}\) at 11:00 LT on 10 January; \(GIC = 27.0~\,{\text{A}}\) at 12:00 LT on 20 February, 1993. Although the most important amplitudes of the GIC associated with the impulses in the geoelectric field components are observed at LAM, same impulses with weaker amplitudes are observed at the other stations of the network.

Figure 9
figure 9figure 9

(a) Geomagnetically induced current (\(GIC\)) estimated from measured geoelectric field components \(Ex\) and \(Ey\) associated with geomagnetic field disturbances on 10 January and 20 February, 1993. (b) Same as figure 9(a), but on 15 and 24 March, 1993.

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3.4.1 Latitudinal trends of the induction effects of disturbed geomagnetic variations

The magnitudes of \(Ex\) and \(Ey\) as well as in the \(GIC\) are relatively more important in the southern stations than in the northern stations. Figure 10 shows the latitudinal trends of the strongest impulses of the geoelectric field components \(Ex\) and \(Ey\). The crest-to-crest amplitudes of these strongest impulses are shown in table 3. The amplitudes of the impulses decrease from LAM, where the largest amplitudes of \(Ex\) and \(Ey\) are observed, to the weakest amplitudes at KOU and SAN. A slight increase in \(Ey\) is noticed at SIK with \(Ey = 127\,{\text{mV/km}}\), on 17 and \(Ey = 51\,{\text{mV/km}}\) on 20 February, 1993, while \(Ex\) remains relatively weak, with \(Ex = 25\,{\text{mV/km}}\) and \(Ex = 8\,{\text{mV/km}},\) respectively. At KOR and TOM, the magnitudes of the impulses in \(Ex\) slightly increase, while \(Ey\) remains decreasing.

Figure 10
figure 10

Latitudinal trends of the impulses associated with brisk geomagnetic field variations during disturbance periods. The colored dots correspond to the impulses of individual events and the solid lines correspond to the averages of individual impulses. The geoelectric field components and the estimated \(GIC\) are shown: (a) \(Ex\) and \(Exm\), (b) \(Ey\) and \(Eym\), and (c) \(GIC\) and \(GICm\).

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Table 3 Maximum crest to crest amplitudes of geoelectric field components during geomagnetic disturbances in West African stations. The dash indicate no data recorded.
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The features of latitudinal trends of \(Ex\) and \(Ey\) are reflected in that of the GIC (figure 10). Table 4 displays the crest-to-crest amplitudes of the highest GIC impulses during the selected disturbed days. The southern stations are subject of most significant GIC amplitudes, which decrease from LAM, with slight increases at KOR, SIK and TOM. The highest amplitudes are observed at LAM with mean \(GIC = 30\,{\text{A}}\). Non-negligible values of GIC are also observed at TIE, with mean \(GIC = 10\,{\text{A}}\). KAT and KOR experience GIC amplitudes that attain sometimes 5 A. From NIE to TOM, the GIC amplitudes are less important, with values weaker than 1 A at KOU and SAN.

Table 4 Maximum and average GIC amplitudes estimated from geoelectric field components recorded in West African stations during the geomagnetic disturbances from January, 1993 to April, 1993. The blank boxes indicate no GIC values available because no geoelectric field data recorded in the station.
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4 Concluding discussion

The induction effects of disturbed geomagnetic field variations were examined through measured geoelectric field variations and associated geomagnetically induced current (GIC) in West Africa. Eleven geomagnetically disturbed days were selected with Ap index higher than 20 nT. The geomagnetically induced current (\(GIC\)) was estimated according to equation (1), from the observed geoelectric field components \(Ey\) and \(Ex\) associated with geomagnetic disturbances based on the system parameters configuration of \(a = b = 50\,{\text{A}}. \,{\text{km/V}}\). Similar fluctuations in the time derivatives \(dH/dt\) and \(dD/dt\) of the geomagnetic field components were observed in the horizontal components \(Ey\) and \(Ex\) of the geoelectric field and the GIC variations. This similarity confirms that geoelectric field and estimated GIC fluctuations are induction effects due to geomagnetic disturbed variations. The disturbance fluctuations in the geoelectric field components and the GIC exhibit higher amplitudes during the daytime, especially between about 8:00 and 16:00 LT. These daytime amplifications are likely linked with the daytime ionospheric currents, which are associated with increasing conductivity in the low latitude ionosphere (Sastry 1970; Subbaraya et al. 1972). Especially enhanced Cowling conductivity in the equatorial electrojet (EEJ) current belt is known to magnify geomagnetic field disturbances near the magnetic dip-equator which in turn intensifies the geoelectric field and GIC fluctuations during the daytime. The processes that underlay these effects may be analogous to ionospheric drivers of large GIC at high latitudes. Huttunen et al. (2002) and Pulkkinen et al. (2003) demonstrated the effects of high latitude ionospheric drivers of large GIC by analyzing the GIC amplifications due to the intensifications of auroral electrojets during geomagnetic storms. The impulses in the geoelectric field components and the estimated GIC during this timeframe are stronger in the southern stations than in the northern stations. On the average, these impulses decrease from LAM to TOM, with a slight enhancement near the magnetic equator. Doumbia et al. (2017) attributed these important latitudinal variations to the lateral variations of the earth resistivity. Indeed, Vassal et al. (1998) considered two models of stratified Earth corresponding to the average resistive structure of the two tectonic provinces across the area of concern: a sedimentary basin in the north and a cratonic shield in the south. The apparent resistivity computed according to those models was found to be stronger in the cratonic shield in the south, than in the sedimentary basin in the north. The slight enhancement near the magnetic equator can also be attributed to the effect of the ionospheric conductivity at this area. In fact, Onwumechilli (1960), and Onwumechilli and Ogbuehi (1962) showed that ionospheric conductivity increases rapidly to a maximum at the EEJ dip latitude and decreases at other latitudes.