We use 10 s ground magnetic field measurements from the International Monitor for Auroral Geomagnetic Effects (IMAGE; https://space.fmi.fi/image/www/) magnetometers during 1994–2018. Currently, IMAGE consists of 41 stations that cover magnetic latitudes from the subauroral 47∘ N to the polar 75∘ N in an approximately 2 h magnetic local time (MLT) sector.

Because most IMAGE stations are variometers without absolute references to compensate for any artificial drift, we cannot use a model to subtract the baseline from the data. Instead, we have used the method of to remove the long-term baseline (including instrument drifts, etc.), any jumps in the data, and the diurnal variation. The diurnal quiet-time magnetic field variation in the IMAGE region is at most a few tens of nanotesla . We concentrate on studying large time derivatives of the horizontal magnetic field for which this effect is insignificant.

After the baseline subtraction, we applied the two-dimensional (2D) Spherical Elementary Current System (SECS) method e.g., to calculate the ionospheric and telluric current densities for each time step and to separate the magnetic field measured at each station into internal and external parts. To make sure that all the currents in space flow beyond the ionospheric equivalent current sheet and all telluric currents below the telluric equivalent current sheet, we place these sheets at 90 km altitude and 1 m depth, respectively. The actual depth distribution of the currents cannot therefore readily be concluded from this analysis. set the internal layer at the depth of 30 km, but such a choice omits induced currents close to the Earth's surface.

A change in the station configuration can, under certain conditions, result in an artificial time derivative peak in the separated magnetic field at the nearby stations. Because of this, we have discarded any station with data gaps during a day. The time derivative has been calculated so that values during successive days are not compared. This is a fairly strict approach, and wastes some usable data, but ensures that there will not be any artificial time derivative peaks due to changes in station configuration. We note that a possible way to mitigate the effect of data gaps, and at the same time enable the use of magnetometer data with different temporal resolutions, would be to add a temporal dimension to the SECS analysis, as recently demonstrated by . In general, representing temporal changes in terms of splines or similar nonlinear functions could lead to smoother time derivatives and/or changes in the frequency content of the signal, which should be avoided, for example, in GIC-related studies. These issues can be avoided by careful selection of the interknot frequency in the spline expansion based on previous knowledge of the largest frequencies of the target phenomena, as discussed by .

IMAGE data are provided in geographic coordinates, and we carry out the analysis using the same coordinate system. We use the notations Bx, By, and Bz for the north, east, and down components of the ground magnetic field. The horizontal magnetic field vector is denoted by H=Bxe^x+Bye^y and its amplitude by H=Bx2+By2. Similarly, the time derivative vector and its amplitude are dH/dt=dBx/dte^x+dBy/dte^y and dH/dt=(dBx/dt)2+(dBy/dt)2, respectively. The measured magnetic field is a sum of the telluric and ionospheric contributions, e.g., Bx=Bx,telluric+Bx,ionospheric. Although geographic coordinates are used to present the data, we have occasionally marked the magnetic coordinates in the plots. We have used the quasi-dipole (QD) coordinates , as given by the software available at https://apexpy.readthedocs.io/en/latest/ (last access: 10 September 2020). The code uses the 12th generation International Geomagnetic Reference Field IGRF-12;.

Figure  shows an example of the ionospheric (Fig. a) and telluric (Fig. b) equivalent current densities and their time derivatives (Fig. c–d) on 18 March 2018 at 21:22:30 UT. The arrows illustrate the vector quantity, and the color shows the corresponding horizontal component of the ground magnetic field. Magnetic latitude and magnetic local time are indicated by the blue grid. The locations of the IMAGE stations used to construct the maps are shown with black squares, and the Sodankylä (SOD) station is highlighted with a thicker line. The black vertical line passing through SOD indicates the meridian along which the horizontal ground magnetic field has been extracted in order to construct Fig. .

The telluric current density, and its time derivative, is mainly directed opposite to the driving ionospheric current density, and its time derivative, as expected. However, whereas the ionospheric currents are clearly oblivious to the conductivity structure of the Earth, the telluric currents are strongly affected by it. The peak of the telluric current density does not coincide with the peak of the westward electrojet but is displaced northward, favoring the high-conducting sea area over the more resistive land area. The difference in the driving and induced patterns clearly illustrates the coast effect, where the current flowing in the sea area encounters the highly resistive crust of the land area. The presence of high-conducting elongated structures within the land area is also evident in the induced currents. This behavior is in agreement with the modeling results by performed in the frequency domain with the plane wave assumption and 3D conductivity distribution. The amplitude of the horizontal ground magnetic field due to telluric currents (Fig. b) is clearly weaker than that which is due to the ionospheric currents (Fig. a). However, the telluric and ionospheric contribution to the time derivative of the magnetic field is of comparable strength.

The time development of the event surrounding the above example is illustrated in Fig.  and in the animation provided in the Supplement. Figure a shows the local IMAGE equivalents of the auroral electrojet indices , called IL and IU, as thick and thin black curves, respectively. The corresponding values derived from the ionospheric and telluric parts of the separated magnetic field are plotted in blue and red. The rest of the panels show the time series of the latitude profiles of the ionospheric (Fig. b) and telluric (Fig. c) contributions to the horizontal ground magnetic field and their time derivatives (Fig. d–e) along the longitude of SOD (black vertical lines in Fig. a–d). The time interval shown in Fig.  is 21:00–22:00 UT, and the time of the example in Fig.  is marked with the black vertical line. The animation consists of a time series of frames, showing plots similar to Figs.  and from 21:00 to 22:00 UT, with a 10 s time step.

The event consists of an intensification and subsequent decay of a westward electrojet (Fig. a) around the magnetic midnight. The example in Fig.  took place during the intensification, when the largest time derivatives (Fig. d–e) were observed at SOD (MLT ≈ UT+2.5 h). While the equivalent currents and ground magnetic fields change quite slowly in time and space, their time derivatives are highly dynamic. Although the ionospheric time derivative structures only live some tens of seconds, which is in agreement with , they still display a fairly smooth structure and time development. The telluric time derivative structures in the land area, on the other hand, are spatially much more variable because of the complex 3D conductivity distribution.

Figure a–c show the measured magnetic field components (black) and their ionospheric (blue) and telluric contributions (red) at SOD. As expected, the telluric currents strengthen the ionospheric Bx by a few tens of percent , while the ionospheric and telluric Bz are oppositely directed. For this event, By is relatively weak, as expected for a westward electrojet. Figure d–f show the time derivative of the magnetic field. Unlike the horizontal magnetic field components, the time derivatives of Bx and By are mostly dominated by the telluric component.

In order to examine what the relevant periods for the ionospheric and telluric magnetic fields and their time derivatives are, we perform wavelet transforms e.g., on the measured, ionospheric, and telluric Bx and dBx/dt. We use continuous wavelet transform with Morlet wavelets, as given by the software available at https://pywavelets.readthedocs.io/en/latest/ (last access: 10 September 2020; ). The results are shown in Fig. . Note that the periodic structures visible in the plots are artificial. They are caused by the definition of the wavelets used and would be different for other wavelets. In addition to the 1 h interval shown in Fig. a and d, we have included 1 h of data before and after the interval of interest, i.e., analyzed a 3 h interval but limited the periods shown in Fig.  to 1 h. The black vertical line in Fig.  indicates the time shown in Fig. . The period ranges of the ultra-low frequency (ULF) pulsation classes Pc4 (45–150 s) and Pc5 150–600 s; are shown with the white horizontal dashed lines.

While most of the measured (Fig. a) and ionospheric Bx (Fig. b) signals consist of longer periods above the Pc5 threshold of 600 s, the shorter periods in the Pc5 range are somewhat more relevant for the telluric Bx (Fig. c) and clearly more relevant for the measured (Fig. d) and ionospheric dBx/dt (Fig. e). For the telluric dBx/dt (Fig. f) signal, on the other hand, periods in the Pc5 and even Pc4 range are very significant, with only some contributions from the longer periods. This behavior is in agreement with our discussion on the relevant frequencies in the Introduction. It can also be seen that changes in the ionospheric Bx power (Fig. b) at a certain frequency are associated with intensifications in the ionospheric dBx/dt power (Fig. e), as expected. However, when comparing the power of ionospheric (Fig. e) and telluric dBx/dt (Fig. f) at the Pc5 band around 21:15 and 21:25 UT, it can be seen that the ratio of the ionospheric and telluric contributions is not constant. Rather, it must depend on the spatiotemporal structure of the ionospheric current system. The telluric Bx power tends to, more or less, follow the behavior of the ionospheric dBx/dt with a small delay. This delay is a consequence of the induction in a realistic 3D earth with a finite conductivity and will be discussed further in Sect. .

In order to further examine the relative contributions of ionospheric and telluric currents to the horizontal components of the ground magnetic field and their time derivatives, Fig.  shows the telluric contribution to Bx, By, and their time derivatives as a function of the measured value at SOD in 1996–2018. Only values with large time derivatives of the horizontal magnetic field (dH/dt=(dBx/dt)2+(dBy/dt)2>1 nTs-1) are included to concentrate on time steps where large GICs are most likely to occur. This is roughly 1 % of the total number of data points. The black line in Fig.  is the line of unity, and the red line is a least squares fit to the data points. The slope of this line is given at the top right corner of the panel, indicating a typical telluric contribution of 29 % to Bx, 46 % to By, 54 % to dBx/dt, and 65 % to dBy/dt. While the telluric contribution to Bx is fairly modest, and in agreement with earlier results , the other contributions, especially those to the time derivatives, are quite high.

So far we have concentrated on one IMAGE station only. We will now extend the analysis to the rest of the stations available during 1994–2018. The station of LOZ has been omitted from the analysis because the data showed some nonphysical behavior, and the newest IMAGE stations of RST, HAR, BRZ, HLP, SUW, WNG, NGK, and PPN were omitted because there were not enough data available from them to produce reliable statistics. In this section, we have again only considered measurements that have large horizontal time derivatives, i.e., dH/dt>1 nTs-1. The number of such data points for each station is listed in Table .

Figure a shows the slope, k, of the fitted line Bx,telluric=k⋅Bx+const. for each IMAGE station. The slopes for By, dBx/dt, and dBy/dt are shown in Fig. b–d. Magnetic coordinates are indicated by the blue grid, with the separation of the constant latitude lines corresponding to 1 h in MLT. Numerical values of k are listed in Table .

The smallest induced contribution can be observed at stations KIL, ABK, MUO, and KIR. These stations are (1) typically located below the driving ionospheric currents. The internal contribution tends to increase away from the main ionospheric current system , which is also visible in the simplified model applied by . This effect is probably at least partly responsible for the larger telluric contribution at the more southern IMAGE stations. For a 1D earth and a plane wave primary field, the secondary contribution would be 50 %. Moreover, the stations are (2) located away from the coastline. There is a clear increase in the internal contribution to By and Bx at the Norwegian coastal stations, due to the typical primary ionospheric currents flowing in the east–west direction and the secondary induced currents turning to follow the coastline. Finally, the stations are (3) located away from the conductivity anomalies on land. There are two prominent conductivity anomalies (see Fig. ), namely one related to the Archean–Proterozoic boundary and directed approximately from northwest to southeast, affecting Bx and By – at least at RVK, DON, LYC, OUJ, and MEK. The other conductivity structure is directed from north to south and affects By – at least at KEV, IVA, and SOD. It should be noted that recent studies indicate a much more complex structure of the abovementioned conductivity anomalies.

Finally, we will examine the effect of the field separation on the direction of the horizontal ground magnetic field vectors and their time derivatives at the IMAGE stations. Because the typical direction of the field is strongly dependent on MLT, we have divided the data into 1 h MLT bins. Figure  shows the results for the 23–24 h MLT bin. Plots for the other MLTs are provided in the Supplement, together with a table listing the number of data points in each bin. Figure a shows histograms of the direction of the telluric (red) and ionospheric (blue) contribution to H. The blue histograms in Fig. b–c are the same as in Fig. a, but the red histograms illustrate the direction of the ionospheric (Fig. b) and telluric (Fig. c) contribution to the time derivative vector, dH/dt.

The telluric H is typically, more or less, in the same direction as the ionospheric H, and none of the stations stands out by behaving radically different from other nearby stations. The number of data points decreases southward, and consequently, the histograms of the southern IMAGE stations are clearly more noisy than those of the northern stations. Because large time derivatives tend to occur around midnight and morning hours , the histograms for all stations tend to be relatively noisy at other times.

The ionospheric dH/dt also tends to be, more or less, aligned with the ionospheric H, except at auroral latitudes during morning hours when the ionospheric dH/dt tends to be more strongly east–west directed than the ionospheric H. This behavior is in agreement with .

The telluric dH/dt histograms tend to be wider than the ionospheric ones. They also reveal some clear anomalies. The most pronounced ones are at MAS and LYR, where the telluric dH/dt has a preferred direction that, at many MLTs, differs markedly from those of the ionospheric H and dH/dt. At the coastal stations of RVK, DON, AND, LEK, TRO, SOR, and NOR, the telluric dH/dt shows a preference for a direction perpendicular to the local coastline, most likely because of strong induced currents flowing along the coast. At IVA, KEV, and SOD, the telluric dH/dt tends to prefer a more east–west-aligned direction than the driving ionospheric field. This is most likely due to the local north–south-aligned conducting belt. list AND, LYC, MAS, and TRO as stations where the directional distribution of the measured dH/dt is strongly rotated or scattered by telluric currents. An examination of the MLT dependency of the telluric dH/dt at LYC shows that the presence of the nearby northwest–southeast-aligned conducting belt tends to rotate the vectors accordingly.

Although the significance of the telluric currents to the time derivative has, according to our knowledge, not been considered until now, the qualitative explanation is quite straightforward. It is well known that the electromagnetic field penetrates into the Earth in a diffusive manner. The penetration depth depends on the subsurface conductivity (σ) and period (T) of the electromagnetic field, as described by the skin depth s=σ-1T. Thus, faster variations have a shallower penetration depth.

Penetration depth does not directly describe the depth of the induced current, which creates the telluric part of the magnetic field, but the depth at which the inducing field has lost most of its energy. Thus, the majority of the induced current should flow above the penetration depth. Significant induced current density can be produced if there is a sufficiently sized structure of sufficiently good conductivity at a suitable depth, considering the period of the inducing field and the conductance structure through which it needs to diffuse to reach that structure.

Generally, conductivity is very low at the Earth's surface and increases with depth. Hence, the slower variations that dominate the ionospheric part of H would be expected to induce currents that are stronger (relative to the primary wave energy) and located deeper than those induced by the faster variations that dominate the ionospheric part of dH/dt. However, the high-conducting sea and near-surface conductivity anomalies change the picture dramatically. The conductivity anomalies are typically not large enough to catch the slower variations, and the sea, although it can cover large areas, is most likely too shallow to catch a very large portion of the wave energy. For the faster variation, on the other hand, the sea and the anomalies are very good conductors at an optimal depth, catching the majority of the wave energy. Thus, in a realistic 3D earth, faster magnetic field variations would be expected to induce stronger (relative to the primary wave energy) currents closer to the surface than slower variations. Thus, the Earth would be expected to amplify ground dH/dt more strongly than H.

The simplest model to explain the effect of the telluric currents is to assume a perfect conductor at some depth in the Earth e.g.,, or, in a special case, a 2D structure is also possible . Such models give a qualitative understanding of the internal contributions to the magnetic field, but they can be very misleading when applied to the time derivative. For simplicity, consider planar geometry with a perfect conductor; the induced currents could be replaced by mirror images of the external currents. The induced fields follow the temporal behavior of the external currents strictly; then, the relative internal contribution at a given location is the same for both the magnetic field and its time derivative.

Contrary to this idealized case, induction in a realistic 3D earth with a finite conductivity is much more complex, and there is a significant contribution from the anomalous part of the induced (secondary) field due to conductivity anomalies. Realistic induction is a diffusive phenomenon. It means that there is always some delay in the formation of the induced currents and related internal fields after a change in the external field. This can be seen when inspecting the animation provided in the Supplement. An extreme example in the time domain is a step-like change in the amplitude of the external current, which the Earth would respond to by more slowly decaying induced currents. It would mean that, after the step change in the external field, dH/dt would solely consist of the internal contribution. In turn, the variation field H would finally be produced only by the external currents that would remain at the enhanced level.

The resolution of the small-scale structures is limited by the station separation of the magnetometer array. We examine this effect by performing a test with the station of KIR. As can be seen in Fig. , it is located in the densest part of the network and typically has a relatively low induced contribution. By removing the three nearest stations of ABK, KIL, and MUO, we can significantly decrease the density of the network around KIR. We run the magnetic field separation with this reduced network and then compute k, similar to the analysis presented in Sect.  and . The resulting internal contributions are 26 % (22 %) for Bx, 39 % (30 %) for By, 58 % (47 %) for dBx/dt, and 66 % (51 %) for dBy/dt. The numbers in parentheses give the corresponding contribution for the intact network (Table ). There is some increase in the internal contribution with the reduced network, indicating that structures smaller than what the network can resolve at 90 km altitude may be mapped underground instead. However, the relative behavior of the different parameters remains unchanged. This indicates that although our numbers are somewhat sensitive to the station configuration, the conclusions drawn from them should still be valid.

have shown that perfect separation of the ground magnetic field into internal and external parts is not possible using spherical cap harmonics. The separation should be possible globally, but, in a regional case, the two sources will be partially mixed, most likely due to boundary conditions, i.e., currents outside of the examined region. Nonetheless, the separation has been considered useful . It is likely that the same fundamental problem concerns the regional field separation carried out using the SECS method and affects our results. The effect of remote currents might be reduced, and the separation improved, by expanding the analysis region and magnetic input data to cover the whole auroral region where the most intense ionospheric currents flow . This would lead to uneven spatial distribution of magnetic data over the entire auroral region, but that could be reasonably handled by using variable density in the SECS grid e.g.,. However, in this study, we limit the analysis to the IMAGE network and examine the effect of imperfect separation into internal and external parts on our results by performing a small test on our example event. We give the separated external (internal) field as input to the SECS method and examine the resulting internal (external) part. For a perfect separation, this should be zero, of course. The results for the external and internal input field are illustrated in Figs.  and , respectively.

Figures  and show that the field separation performed using the SECS method and IMAGE data is indeed not perfect. The reanalysis of the external field produces a small internal part and, vice versa, reanalysis of the internal field produces a small external part. Nonetheless, both the magnetic field and its time derivative are strongly dominated by the field contribution used as input, indicating that although our numbers must be affected by the imperfect field separation, the conclusions drawn from them should still apply.

The significant role of the induced component in the time derivative of the ground magnetic field has some interesting implications. First of all, observations of the time derivative should be considered highly local, and any results derived from them should not be generalized to other locations without caution. It is well known that the electric field at the Earth's surface is highly local, and 3D conductivity structures strongly affect its variability . When comparing simultaneously measured time derivative values at different locations, it should be kept in mind that they do not necessarily provide a comparable measure of the dynamics of the driving ionospheric currents because they are affected by the internal anomalous fields. Second, attempts to predict the time derivative of the ground magnetic field using global simulations have not been considered very successful . According to our results, one significant source of difference between the simulated and measured values is that the simulations typically do not include a conducting ground. Thus, while the simulated magnetic field time derivatives mainly represent the ionospheric currents, the measurements with which they are compared may be dominated by the telluric currents. Lately, there have been some studies in which a 3D conducting ground has been included in a magnetohydrodynamic (MHD) simulation e.g.,.

When the magnetic field is separated into telluric and ionospheric parts, short period and small-scale variations are seen to be amplified by the internal field contribution. Thus, the ionospheric equivalent current density and especially its time derivative have a more regular spatiotemporal structure than could be concluded if they were derived without the field separation. However, the lifetimes of the ionospheric structures are still very short, comparable with the 80–100 s limit derived by for predictable behavior of the measured ground magnetic field time derivatives. Thus, learning to predict the occurrence of large time derivatives of the ground magnetic field still requires more work.

From the GIC modeling viewpoint, the (horizontal) geoelectric field is the primary quantity as it is the driver of induced currents in technological conductors. While the internal contribution to the magnetic field is only produced by telluric currents, due to the inductive nature of the magnetic field, the electric field is affected by galvanic effects as well, due to charge accumulation across lateral conductivity gradients. This adds a lot of spatial complexity to the electric field compared to the magnetic field e.g., and is responsible for the strong amplification of the electric field on the less conductive side of a conductivity contrast (e.g., the coast effect). The behavior of dH/dt falls between the rather smoothly varying magnetic field and the spatially very inhomogeneous electric field.