Geomagnetically induced currents (GICs) are directly described by ground electric fields, but estimating them is time-consuming and requires knowledge of the ionospheric currents and the three-dimensional (3D) distribution of the electrical conductivity of the Earth. The time derivative of the horizontal component of the ground magnetic field (

Fast geomagnetic variations at periods from seconds to hours and days are primarily produced by currents in the ionosphere and magnetosphere. There is always an associated secondary (internal, telluric) current system induced in the conducting ground and contributing to the total variation field measured by ground magnetometers. Mathematically, it is possible to fully explain the variation field by two equivalent current systems, namely one at the ionospheric altitude and another just below the Earth's surface

Geomagnetically induced currents

Geomagnetic induction is a complicated phenomenon with intricate dependencies between the scale sizes of the ground conductivity structures and the spatiotemporal composition of the ionospheric primary fields. A widely used simplification in the frequency domain is considering the effects of a primary plane wave field on a one-dimensional (1D; i.e., variation as a function of depth only) electrical conductivity distribution of the Earth. In such a case, the contribution of the secondary field is 50 %

A well-known example of the strong influence of the 3D conductivity distribution is the so-called “coast effect”

The nonplanar wave primary field, together with the effects of the 3D conductivity distribution, typically reduces the secondary contribution to

There are two key factors that determine the distribution of the telluric current density and, thus, the secondary induced magnetic field. One is the time-varying external magnetic field that drives the induction. The main origin of this primary field is the ionospheric current density, with some contribution from the more distant magnetospheric currents. The other factor is the Earth's conductivity distribution. A conductance map of the Fennoscandian Shield and its surrounding oceans, sea basins, and continental areas (S-map) has been presented by

Conductance of the upper crust (0–10

Key features of the conductivity model relevant for telluric currents are the well-conducting seawater and sea sediments surrounding the Fennoscandian Shield, which consist of a highly resistive crust with imbedded, well-conducting belts.

The International Monitor for Auroral Geomagnetic Effects (IMAGE;

The Earth's conductivity distribution is occasionally considered to consist of two components, namely a normal 1D component and an anomalous 3D component. Similarly, the induced field is considered to consist of a normal part and an anomalous or scattered part. We have not made this separation but consider the normal and anomalous parts together. Unless otherwise mentioned, all analyses in this study are carried out in the time domain, i.e., by considering the time series.

We use 10

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

After the baseline subtraction, we applied the two-dimensional (2D) Spherical Elementary Current System (SECS) method

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

IMAGE data are provided in geographic coordinates, and we carry out the analysis using the same coordinate system. We use the notations

Figure

Ionospheric equivalent current density (arrows) on 18 March 2018 at 21:22:30 UT

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

The time development of the event surrounding the above example is illustrated in Fig.

Upper (IU – thin black curve) and lower (IL – thick black curve) envelope curves of the magnetic field

The event consists of an intensification and subsequent decay of a westward electrojet (Fig.

Figure

Magnetic field north 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

Wavelet transform of the magnetic field north component

While most of the measured (Fig.

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.

Telluric contribution to

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.,

IMAGE station, start and possible end year of operation, number of 10 s data points

Figure

Slope,

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

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

Histograms of the direction of the ionospheric (blue) and telluric (red) horizontal ground magnetic field, when

The telluric

The ionospheric

The telluric

We have used 10

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 (

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

The simplest model to explain the effect of the telluric currents is to assume a perfect conductor at some depth in the Earth

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,

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.

Magnetic field at SOD in the same format as Fig.

Magnetic field at SOD in the same format as Fig.

Figures

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 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

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

We have examined the relative contribution of the telluric (secondary, induced) and ionospheric (primary, inducing) electric currents to the variation magnetic field measured on the ground in the time domain. We have used 10

The time derivative of the measured horizontal magnetic field (

The horizontal magnetic field (

The coast and conductivity anomalies

The

Our results have been derived using IMAGE data and are thus only valid for IMAGE stations. Some uncertainty in the numbers is caused by the imperfect separation of the magnetic field into telluric and ionospheric parts due to the spatial resolution of the magnetometer network and the boundary conditions. However, it is likely that the main principles, although not the exact numbers, apply and are relevant to other areas as well.

Our results imply that measurements of

A natural next step for this study would be to apply a 3D ground conductivity model, together with a given external (equivalent) ionospheric current system, in the time domain and to calculate the external and internal parts of the ground magnetic field and their time derivatives. The approach could be as seen in

IMAGE data are available at

IMAGE_20180318T210000_10sec_20180318T220000.mp4 illustrates the time development of the ionospheric and telluric equivalent currents, their time derivatives, and corresponding horizontal ground magnetic fields on 18 March 2018, from 21:00 to 22:00 UT, with a 10

LJ prepared most of the material and wrote the paper with contributions from HV, AV, and MS. HV provided expertise on the theoretical discussion, and AV provided expertise on the GIC application of the results. MS provided expertise on the magnetotelluric viewpoint and prepared the conductance maps.

The authors declare that they have no conflict of interest.

We thank the institutes that maintain the IMAGE Magnetometer Array, namely the Tromsø Geophysical Observatory of UiT the Arctic University of Norway (Norway), Finnish Meteorological Institute (Finland), Institute of Geophysics Polish Academy of Sciences (Poland), German Research Centre for Geosciences (GFZ, Germany), Geological Survey of Sweden (Sweden), Swedish Institute of Space Physics (Sweden), Sodankylä Geophysical Observatory of the University of Oulu (Finland), and Polar Geophysical Institute (Russia).

This research has been supported by the Academy of Finland, Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta (grant no. 314670).

This paper was edited by Georgios Balasis and reviewed by J. Miquel Torta and one anonymous referee.