**2.1 Measurements of GIC**

The usual place for installing GIC recording equipment in a power network is the earthing lead of a transformer neutral. In the normal situation, this particular lead carries no 50/60 Hz current because the sum of the ac currents in the three phases is equal to zero. Furthermore, measuring GIC in the neutral lead directly gives information about the currents flowing through transformer windings, where they can result in harmful saturation. Recordings of GIC can be performed with a coil around the earthing lead. However, for example in the Finnish 400 kV network, a small shunt resistor is utilised in the lead (e.g. Elovaara et al., 1992). The largest GIC magnitudes measured in Finland and in

Geomagnetically Induced Currents as Ground Effects of Space Weather 31

a role. However, it is important to note that the geoelectric field and GIC are not directly proportional to the geomagnetic time derivative but the relation is more complicated (see Section 2.2). Pirjola (2010) investigates the relation between geomagnetic variations and the geoelectric field (and GIC) in the case of a simple two-layer Earth. He explicitly shows that a poorly-conducting upper layer above a highly-conducting bottom is favourable to the geoelectric field (and GIC) being proportional to the geomagnetic time derivative at the Earth's surface whereas a thin highly-conducting upper layer above a less-conducting bottom results in the surface geoelectric field (and GIC) proportional to the geomagnetic variation. Trichtchenko & Boteler (2006; 2007) present an example from Canada in which GIC resembles the geomagnetic variation and another example also from Canada in which a correspondence between GIC and the geomagnetic time derivative exists. Watari et al. (2009) demonstrate that in recordings in the Japanese power network GIC show a high correlation with the geomagnetic variation field rather than with the geomagnetic time

Fig. 2. Measurement of GIC flowing in a power transmission line by using a magnetometer below the line and another magnetometer for reference data further away (Mäkinen, 1993;

Although GIC in transformer neutral earthing leads have a larger practical significance than GIC in transmission lines, both are of the same importance from the scientific point of view. This is a motivation for the measurements of GIC carried out in a transmission line in Finland for some time in the beginning of the 1990's (Mäkinen, 1993; Viljanen et al., 2009). Such measurements are possible to make by using two magnetometers, which behave slowly enough, so that the influence from the ac currents is not experienced. One magnetometer is installed very near the line, as shown in Figure 2. The other is located further away. The former records the sum of the natural geomagnetic field and the field due to GIC in the line whereas the latter only observes the natural field. If the distance of the two magnetometers is not too large (i.e. many tens of kilometres or more), the natural field can be regarded as the same at the two sites. Thus the difference of the magnetometer readings gives the field created by GIC flowing in the line, and by inverting the Biot-Savart law GIC data are obtained. It is naturally necessary to take into account that a transmission line consists of three phase conductors, each of which carries one third of the (total) GIC. The

derivative.

Viljanen et al., 2009).

Fig. 1. (*Top*) GIC recorded in the earthing lead of the Rauma 400 kV transformer neutral in southwestern Finland on March 24, 1991, (*Bottom*) north component (X) of the geomagnetic field, and (*Middle*) its time derivative at the Nurmijärvi Geophysical Observatory in southern Finland. The value of 201 A seen in the top plot is the largest measured in the GIC recordings in the Finnish 400 kV system started in 1977 (Pirjola et al., 2003; Pirjola et al., 2005).

Sweden are about 200 A and about 300 A, respectively (Pirjola et al., 2005; Wik et al., 2008). It should be noted that these values give the total GIC, i.e. the sum of GIC in the three phases. The per-phase values are obtained by dividing by three, being thus about 67 A and 100 A. To our knowledge, the Swedish value is the highest ever reported. It occurred during a great geomagnetic storm in April 2000. Figure 1 presents GIC recorded in the earthing lead of the Rauma 400 kV transformer neutral in southwestern Finland on March 24, 1991. It also includes the above-mentioned largest value of about 200 A just before 22 h Universal Time (UT).

The bottom and middle plots of Figure 1 show the recordings of the north component (denoted by X) of the geomagnetic field and its time derivative at the Nurmijärvi Geophysical Observatory located in southern Finland at a distance of about 200 km from Rauma. We see that the GIC curve resembles the derivative, but the behaviour of the geomagnetic field is more different. This would seem to be an expected result because GIC are created based on Faraday's law, in which temporal variations of the magnetic field play 30 Space Science

March 24, 1991

00:00 04:00 08:00 12:00 16:00 20:00 00:00

UT [h]

Fig. 1. (*Top*) GIC recorded in the earthing lead of the Rauma 400 kV transformer neutral in southwestern Finland on March 24, 1991, (*Bottom*) north component (X) of the geomagnetic

Sweden are about 200 A and about 300 A, respectively (Pirjola et al., 2005; Wik et al., 2008). It should be noted that these values give the total GIC, i.e. the sum of GIC in the three phases. The per-phase values are obtained by dividing by three, being thus about 67 A and 100 A. To our knowledge, the Swedish value is the highest ever reported. It occurred during a great geomagnetic storm in April 2000. Figure 1 presents GIC recorded in the earthing lead of the Rauma 400 kV transformer neutral in southwestern Finland on March 24, 1991. It also includes the above-mentioned largest value of about 200 A just

The bottom and middle plots of Figure 1 show the recordings of the north component (denoted by X) of the geomagnetic field and its time derivative at the Nurmijärvi Geophysical Observatory located in southern Finland at a distance of about 200 km from Rauma. We see that the GIC curve resembles the derivative, but the behaviour of the geomagnetic field is more different. This would seem to be an expected result because GIC are created based on Faraday's law, in which temporal variations of the magnetic field play

field, and (*Middle*) its time derivative at the Nurmijärvi Geophysical Observatory in southern Finland. The value of 201 A seen in the top plot is the largest measured in the GIC recordings in the Finnish 400 kV system started in 1977 (Pirjola et al., 2003; Pirjola et al.,

Nurmijärvi (10 s values)

00:00 04:00 08:00 12:00 16:00 20:00 00:00

Nurmijärvi

00:00 04:00 08:00 12:00 16:00 20:00 00:00

Rauma 400 kV transformer (60 s values)


2005).

before 22 h Universal Time (UT).


X [nT]

0




GIC [A]

0

dX/dt [nT/s]

a role. However, it is important to note that the geoelectric field and GIC are not directly proportional to the geomagnetic time derivative but the relation is more complicated (see Section 2.2). Pirjola (2010) investigates the relation between geomagnetic variations and the geoelectric field (and GIC) in the case of a simple two-layer Earth. He explicitly shows that a poorly-conducting upper layer above a highly-conducting bottom is favourable to the geoelectric field (and GIC) being proportional to the geomagnetic time derivative at the Earth's surface whereas a thin highly-conducting upper layer above a less-conducting bottom results in the surface geoelectric field (and GIC) proportional to the geomagnetic variation. Trichtchenko & Boteler (2006; 2007) present an example from Canada in which GIC resembles the geomagnetic variation and another example also from Canada in which a correspondence between GIC and the geomagnetic time derivative exists. Watari et al. (2009) demonstrate that in recordings in the Japanese power network GIC show a high correlation with the geomagnetic variation field rather than with the geomagnetic time derivative.

Fig. 2. Measurement of GIC flowing in a power transmission line by using a magnetometer below the line and another magnetometer for reference data further away (Mäkinen, 1993; Viljanen et al., 2009).

Although GIC in transformer neutral earthing leads have a larger practical significance than GIC in transmission lines, both are of the same importance from the scientific point of view. This is a motivation for the measurements of GIC carried out in a transmission line in Finland for some time in the beginning of the 1990's (Mäkinen, 1993; Viljanen et al., 2009). Such measurements are possible to make by using two magnetometers, which behave slowly enough, so that the influence from the ac currents is not experienced. One magnetometer is installed very near the line, as shown in Figure 2. The other is located further away. The former records the sum of the natural geomagnetic field and the field due to GIC in the line whereas the latter only observes the natural field. If the distance of the two magnetometers is not too large (i.e. many tens of kilometres or more), the natural field can be regarded as the same at the two sites. Thus the difference of the magnetometer readings gives the field created by GIC flowing in the line, and by inverting the Biot-Savart law GIC data are obtained. It is naturally necessary to take into account that a transmission line consists of three phase conductors, each of which carries one third of the (total) GIC. The

where and 

density = 

where 

across a boundary.

complex skin depth *p* = *p*(

wave case discussed briefly below.

field component *Ey* = *Ey*(

where *Z* = *Z*(

*Bx* = *Bx*(

Geomagnetically Induced Currents as Ground Effects of Space Weather 33

*0* and 

**jfree** 

the medium. An additional constitutive equation needed in the geophysical part is the

part are the continuity conditions that enable moving from one medium to another. Usually we utilise the continuity of the tangetial components of the **E** and **H** fields when moving

Different techniques and models for performing the geophysical part have been investigated for a long time (e.g. Pirjola, 2002, and references therein). An interesting approximate alternative is the Complex Image Method (CIM), in which the currents induced in the conducting Earth are replaced by images of ionospheric currents located in a complex space (Boteler & Pirjola, 1998a; Pirjola and Viljanen, 1998). A crucial parameter in CIM is the

), which depends on the angular frequency

( ) ( ) *<sup>Z</sup> <sup>p</sup> <sup>i</sup>*

0

) is the surface impedance at the Earth's surface relating a horizontal electric

0 ( ) () () *y x <sup>Z</sup> E B* 

It is implicitly required in equation (9) that the (flat) Earth surface is the *xy* plane of a righthanded Cartesian coordinate system in which the *z* axis points downwards. In practice, the surface impedance included in equation (9) and especially in equation (8) refers to the plane

CIM makes numerical computations much faster than with formulas obtained by a direct forward solution of Maxwell's equations and boundary conditions (Häkkinen & Pirjola, 1986; Pirjola & Häkkinen, 1991). However, it has been proved that, regarding the accuracy and fastness of computations required in GIC applications, the simple plane wave method to be applied locally in different areas covered by the particular network is the best and most practical technique (Viljanen et al., 2004). It should also be noted that, in GIC calculations, it is not necessary to know the spatial details of the geoelectric field exactly because the (geo)voltages driving GIC are obtained by integrating the geoelectric field (see Section 3.1).

In the plane wave method, the geoelectromagnetic disturbance produced by the (primary) magnetospheric-ionospheric currents is a plane wave propagating vertically downwards and the Earth's conductivity structure is layered (with a flat surface) enabling the Earth to be

in connection with geoelectromagnetic studies is that

) (see e.g. Kaufman & Keller, 1981; Pirjola et al., 2009)

assume a harmonic dependence on the time *t* given by exp(i

Maxwell's equations similarly to (1)-(4) but

Ohm's law that relates **jfree** and **E**

are the permeability and permittivity of the medium. The usual assumption

*free* and the current density **j** = **jfree** should only refer to charges moving freely in

is the conductivity of the medium. What is still required for solving the geophysical

 = 

*0* are replaced by

*t*))

) to the perpendicular horizontal magnetic field component

*<sup>0</sup>*. Macroscopically, we can write

, and the charge

 and 

**E** (7)

(8)

(9)

considered (i.e. we

geometries of the phases with respect to the nearby magnetometer are different, which must also be taken into account in the inversion.

A similar two-magnetometer technique has been used successfully to record GIC flowing along the Finnish natural gas pipeline since 1998 (Pulkkinen et al., 2001a; Viljanen et al., 2006). The largest GIC recorded so far is 57 A on October 29, 2003 (Pirjola et al., 2005). The pipe-to-soil voltage is also continuously monitored in the Finnish pipeline as well as in other oil and gas pipelines.

#### **2.2 Modelling of GIC**

As pointed out in the beginning of Section 2, GIC modelling is convenient to be carried out in two parts:


The geophysical part does not depend on the particular network and is thus the same for power networks, pipelines and other conductor systems. The input of the geophysical part consists of knowledge or assumptions about the Earth's conductivity and about the magnetospheric-ionospheric currents or about the geomagnetic variations at the Earth's surface. The solution is based on Maxwell's equations

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon\_0} \tag{1}$$

$$\nabla \cdot \mathbf{B} = 0 \tag{2}$$

$$
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \tag{3}
$$

$$
\nabla \times \mathbf{B} = \mu\_0 \mathbf{j} + \mu\_0 \varepsilon\_0 \frac{\partial \mathbf{E}}{\partial t} \tag{4}
$$

Maxwell's equations couple the electric field **E** [V/m] and the magnetic field **B** [Vs/m2] to each other as well as to the charge density [As/m3] and to the current density **j** [A/m2]. All these quantities are functions of space **r** and time *t*. The vacuum permeability and the vacuum permittivity are denoted by *0* (= 4 Vs/Am) and *<sup>0</sup>* (= 8.85412 As/Vm), respectively. In the form (1)-(4), Maxwell's equations are (microscopically) always valid. However, charges and currents are macroscopically usually divided into different types, and additional fields are introduced. The electric **D** field is related to **E** and the magnetic **H** field is related to **B** by constitutive equations, which are usually assumed to be linear and simple as follows

$$\mathbf{D} = \mathbf{c} \mathbf{E} \tag{5}$$

$$\mathbf{H} = \frac{\mathbf{B}}{\mu} \tag{6}$$

32 Space Science

geometries of the phases with respect to the nearby magnetometer are different, which must

A similar two-magnetometer technique has been used successfully to record GIC flowing along the Finnish natural gas pipeline since 1998 (Pulkkinen et al., 2001a; Viljanen et al., 2006). The largest GIC recorded so far is 57 A on October 29, 2003 (Pirjola et al., 2005). The pipe-to-soil voltage is also continuously monitored in the Finnish pipeline as well as in other

As pointed out in the beginning of Section 2, GIC modelling is convenient to be carried out

1. Determination of the horizontal geoelectric field at the Earth's surface ("*geophysical part*"). 2. Computation of GIC in the network produced by the geoelectric field ("*engineering part*"). The geophysical part does not depend on the particular network and is thus the same for power networks, pipelines and other conductor systems. The input of the geophysical part consists of knowledge or assumptions about the Earth's conductivity and about the magnetospheric-ionospheric currents or about the geomagnetic variations at the Earth's

> 0

> > *t*

0 00 *t*

*0* (= 4 Vs/Am) and

**E** (1)

**<sup>B</sup> <sup>E</sup>** (3)

[As/m3] and to the current density **j** [A/m2].

(5)

**<sup>B</sup> <sup>H</sup>** (6)

*<sup>0</sup>* (= 8.85412 As/Vm),

**<sup>E</sup> B j** (4)

0 **B** (2)

 

Maxwell's equations couple the electric field **E** [V/m] and the magnetic field **B** [Vs/m2] to

All these quantities are functions of space **r** and time *t*. The vacuum permeability and the

respectively. In the form (1)-(4), Maxwell's equations are (microscopically) always valid. However, charges and currents are macroscopically usually divided into different types, and additional fields are introduced. The electric **D** field is related to **E** and the magnetic **H** field is related to **B** by constitutive equations, which are usually assumed to be linear and

> **D E**

also be taken into account in the inversion.

surface. The solution is based on Maxwell's equations

each other as well as to the charge density

vacuum permittivity are denoted by

simple as follows

oil and gas pipelines.

**2.2 Modelling of GIC** 

in two parts:

where and are the permeability and permittivity of the medium. The usual assumption in connection with geoelectromagnetic studies is that = *<sup>0</sup>*. Macroscopically, we can write Maxwell's equations similarly to (1)-(4) but *0* and *0* are replaced by and , and the charge density = *free* and the current density **j** = **jfree** should only refer to charges moving freely in the medium. An additional constitutive equation needed in the geophysical part is the Ohm's law that relates **jfree** and **E**

$$
\mathbf{j}\_{\text{free}} = \sigma \mathbf{E} \tag{7}
$$

where is the conductivity of the medium. What is still required for solving the geophysical part are the continuity conditions that enable moving from one medium to another. Usually we utilise the continuity of the tangetial components of the **E** and **H** fields when moving across a boundary.

Different techniques and models for performing the geophysical part have been investigated for a long time (e.g. Pirjola, 2002, and references therein). An interesting approximate alternative is the Complex Image Method (CIM), in which the currents induced in the conducting Earth are replaced by images of ionospheric currents located in a complex space (Boteler & Pirjola, 1998a; Pirjola and Viljanen, 1998). A crucial parameter in CIM is the complex skin depth *p* = *p*(), which depends on the angular frequency considered (i.e. we assume a harmonic dependence on the time *t* given by exp(i*t*))

$$p(\alpha) = \frac{Z(\alpha)}{i\alpha\mu\_0} \tag{8}$$

where *Z* = *Z*() is the surface impedance at the Earth's surface relating a horizontal electric field component *Ey* = *Ey*() to the perpendicular horizontal magnetic field component *Bx* = *Bx*() (see e.g. Kaufman & Keller, 1981; Pirjola et al., 2009)

$$E\_y(\alpha) = -\frac{Z(\alpha)}{\mu\_0} B\_x(\alpha) \tag{9}$$

It is implicitly required in equation (9) that the (flat) Earth surface is the *xy* plane of a righthanded Cartesian coordinate system in which the *z* axis points downwards. In practice, the surface impedance included in equation (9) and especially in equation (8) refers to the plane wave case discussed briefly below.

CIM makes numerical computations much faster than with formulas obtained by a direct forward solution of Maxwell's equations and boundary conditions (Häkkinen & Pirjola, 1986; Pirjola & Häkkinen, 1991). However, it has been proved that, regarding the accuracy and fastness of computations required in GIC applications, the simple plane wave method to be applied locally in different areas covered by the particular network is the best and most practical technique (Viljanen et al., 2004). It should also be noted that, in GIC calculations, it is not necessary to know the spatial details of the geoelectric field exactly because the (geo)voltages driving GIC are obtained by integrating the geoelectric field (see Section 3.1).

In the plane wave method, the geoelectromagnetic disturbance produced by the (primary) magnetospheric-ionospheric currents is a plane wave propagating vertically downwards and the Earth's conductivity structure is layered (with a flat surface) enabling the Earth to be

Geomagnetically Induced Currents as Ground Effects of Space Weather 35

configuration and all resistance values of the network in question. The computation of GIC can be performed by applying electric circuit theory, i.e. Ohm's and Kirchhoff's laws. Because the frequencies in connection with geoelectromagnetic fields and GIC are very low, a dc treatment is appropriate to the engineering part (at least as the first approximation). Discretely-earthed networks, such as a power system, and continuously-earthed networks, such as a buried pipeline, need to have different calculation techniques. For the former, matrix formulas are available, which enable the computation of GIC between the Earth and the network at the nodes and in the lines between the nodes, whereas the latter can be treated by utilising the distributed-source transmission line (DSTL) theory. These methods

Assuming that the horizontal geoelectric field impacting a network is uniform and applying the engineering part techniques, we can easily identify the sites that will most probably experience the largest GIC magnitudes being thus risky for problems, but being also ideal GIC recording sites. With a uniform geoelectric field, we may also simply get a comprehension of the effect of disconnecting or connecting some lines on GIC values in the network. Performing both the geophysical and the engineering parts enables studies of GIC as functions of time at different sites of the system during large space weather storms. Using long-term geomagnetic data recorded at observatories and other magnetometer stations, it is possible to derive statistics of expected GIC values at different sites of a technological

For investigating the engineering part of GIC modelling in the case of a power system, we consider a network of conductors with *N* discrete nodes, called stations and earthed by the resistances *Re,i* (*i* = 1,…,*N*). Let us assume that the network is impacted by a horizontal geoelectric field **E**, which implies the flow of geomagnetically induced currents (GIC). Lehtinen and Pirjola (1985) derive a formula for the *N* 1 column matrix **Ie** that includes the currents *Ie,m* (*m* = 1,…,*N*) called earthing currents or earthing GIC and flowing between the

**Ie (1 YnZe )**

matrix **Yn** as well as the *N* 1 column matrix **Je** are explained below.

The current is defined to be positive when it flows from the network to the Earth and negative when it flows from the Earth to the network. The symbol **1** denotes the *N N* unit identity matrix. The *N N* earthing impedance matrix **Ze** and the *N N* network admittance

The definition of **Ze** states that multiplying the earthing current matrix **Ie** by **Ze** gives the voltages between the earthing points and a remote Earth that are related to the flow of the currents *Ie,m* (*m* = 1,…,*N*). Thus, expressing the voltages by an *N* 1 column matrix **U**, we have

Utilising the reciprocity theorem, **Ze** can be shown to be a symmetric matrix. The diagonal elements of **Ze** equal the earthing resistances of the stations. If the distances of the stations

**–1 Je** (12)

**U ZeIe** (13)

are discussed more in Section 3.

network.

**3. Calculation of GIC 3.1 Power networks** 

network and the Earth as follows

described by a surface impedance (see equation (9)). The contribution to the total geoelectromagnetic disturbance at the Earth's surface from (secondary) currents in the Earth is an upward-propagating reflected wave. This kind of a model is already included in the basic paper of magnetotellurics by Cagniard (1953). It is necessary to emphasise that the frequencies involved in geoelectromagnetic studies are typically in the mHz range and at least below 1 Hz, i.e. so small that the displacement currents (= t can practically always be neglected. It means that "geoelectromagnetic plane waves" are actually not "waves", so the terminology generally used in geoelectromagnetics is not completely correct in this respect.

Let us assume now that the Earth is uniform with the conductivity and consider a harmonic time dependence with the angular frequency . It is easy to show that the horizontal geoelectric field component *Ey* = *Ey*() at the Earth's surface is related to the perpendicular horizontal geomagnetic variation component *Bx* = *Bx*() by the following equation (e.g. Pirjola, 1982)

$$E\_{\text{y}} = -\sqrt{\frac{\alpha \nu}{\mu\_0 \sigma}} e^{\frac{\mu^2}{4}} B\_{\text{x}} \tag{10}$$

Equation (10) shows that there is a 45-degree (/4-radian) phase shift between the geoelectric and geomagnetic fields. We also see that an increase of the angular frequency and a decrease of the Earth's conductivity enhance the geoelectric field with respect to the geomagnetic field.

Noting that i*Bx*() is associated with the time derivative of *Bx*(*t*), equation (10) can be inverse-Fourier transformed to give the following time domain convolution integral (Cagniard, 1953; Pirjola, 1982)

$$E\_y(t) = -\frac{1}{\sqrt{\pi \mu\_0 \sigma}} \prod\_{0}^{\alpha} \frac{\mathbf{g}(t - \mu)}{\sqrt{\mu}} du \tag{11}$$

where the time derivative of *Bx*(*t*) is denoted by *g*(*t*). The derivation of equation (10) makes use of the neglect of the displacement currents, which thus also affects equation (11). If the displacement currents are included the kernel function convolved with *g*(*t*) in formula (11) is more complicated containing the Bessel function of the zero order (Pirjola, 1982). Equation (11) is in agreement with the causality, i.e. *Ey*(*t*) at the time *t* only depends on earlier values of *g*(*t*). The square root of the lag time *u* in the denominator means that the influence of a value of *g*(*t-u*) on *Ey*(*t*) decreases with increasing *u*. As indicated in Section 2.1, equation (11) shows that the relation of the geoelectric field (and GIC) with the geomagnetic time derivative is not simple, like for example a proportionality, not even in the present planewave and uniform-Earth situation.

Similarly to the inverse-Fourier transform of equation (10) leading to (11) in the time domain, we can inverse-Fourier transform equation (9) to get a convolution relation between *Ey* and *Bx* in the time domain, or as above in equation (11), perhaps rather between *Ey* and d*Bx*/d*t*.

The engineering part of GIC modelling utilises the horizontal geoelectric field to be provided by the geophysical part and also needs the knowledge of the topology, configuration and all resistance values of the network in question. The computation of GIC can be performed by applying electric circuit theory, i.e. Ohm's and Kirchhoff's laws. Because the frequencies in connection with geoelectromagnetic fields and GIC are very low, a dc treatment is appropriate to the engineering part (at least as the first approximation). Discretely-earthed networks, such as a power system, and continuously-earthed networks, such as a buried pipeline, need to have different calculation techniques. For the former, matrix formulas are available, which enable the computation of GIC between the Earth and the network at the nodes and in the lines between the nodes, whereas the latter can be treated by utilising the distributed-source transmission line (DSTL) theory. These methods are discussed more in Section 3.

Assuming that the horizontal geoelectric field impacting a network is uniform and applying the engineering part techniques, we can easily identify the sites that will most probably experience the largest GIC magnitudes being thus risky for problems, but being also ideal GIC recording sites. With a uniform geoelectric field, we may also simply get a comprehension of the effect of disconnecting or connecting some lines on GIC values in the network. Performing both the geophysical and the engineering parts enables studies of GIC as functions of time at different sites of the system during large space weather storms. Using long-term geomagnetic data recorded at observatories and other magnetometer stations, it is possible to derive statistics of expected GIC values at different sites of a technological network.
