One of the key problems in the search for electromagnetic precursors of earthquakes is the possibility of separating magnetospheric and seismogenic disturbances. This paper presents the results of using a model that enables us to calculate the ultra-low-frequency (ULF) fields on the Earth’s surface created by a linear horizontal current of finite length. This model simulates the occurrence of mechano-electric transformers during a shift along a fault zone at the final stage of the earthquake preparation. The calculations show several characteristics of the field of the underground source in comparison with the field of ionospheric disturbances. If the vertical component B_z of the magnetic field of an ionospheric disturbance is small compared to the horizontal component 𝐁_ , then for an underground source | B_z| > | 𝐁_| in the vicinity of the source. For ionospheric sources, this apparent impedance (i.e., the μ_0| 𝐄_|/ . -0em| 𝐁_| ratio) coincides with the impedance of the Earth’s surface Zg, while the impedance of disturbances created by the lithospheric source may exceed Zg, up to order of magnitude in the source vicinity. An underground current source can create a vertical electric field E_z of significant magnitude. This is due to the vertical current continuity at the Earth–atmosphere interface, which acts as a powerful “amplifier” with a coefficient determined by the ratio of the complex conductivities of the Earth’s crust and air. Calculations have shown that these ideas are incorrect. The vertical component E_z on the Earth’s surface is of the same order of magnitude as the transverse component 𝐄_ . There have been suggestions to use short-baseline gradient measurements to reduce the contribution of large-scale ionospheric disturbances. The calculation of the field structure has revealed that amplitude-phase gradients in the vicinity of an underground source are highly variable and may provide ambiguous results.

A theoretical formalism has been developed to calculate the electromagnetic fields generated in the atmosphere–ionosphere system by a finitelength underground horizontal current source. A numerical model with a realistic profile of the ionosphere in a vertical geomagnetic field has been designed based on this theory. It is shown that the apparent impedance of the electromagnetic field created by an underground source on the Earth’s surface is one order of magnitude higher than the Earth’s impedance, which can be used to discriminate perturbations from seismogenic sources. The presented results of numerical modeling allow us to relate perturbations created by a large-scale underground source in the Earth surface magnetic field and in the electric field in the ionosphere. Based on these model estimates it is concluded that many of the ULF electric field perturbations detected in satellite data before earthquakes cannot be attributed to direct emission from seismogenic sources.

The extremely-low-frequency (ELF) response in the upper ionosphere to ground large-scale transmitter ZEVS on the Kola Peninsula has been detected by low-Earth orbiting satellite CSES (similar to 500 km altitude). When the satellite was in the vicinity of the ZEVS transmitter above the White Sea (horizontal distance similar to 400-900 km), the electric and magnetic sensors detected a narrowband 82 Hz emission with amplitudes E similar or equal to 1-3 mu V/m and B similar or equal to 0.5-1.0 pT. We modeled the ELF wave field spatial structure in the upper ionosphere excited by an oscillating 82 Hz linear current with the 60 km length suspended above a high-resistive ground. Realistic altitudinal profiles of the plasma parameters during events under study have been reconstructed with the use of the IRI ionospheric model. The modeled amplitudes of electromagnetic response of the upper ionosphere are in reasonable agreement with the 82-Hz emission power recorded by the CSES satellite for a typical transmitter current intensity >100 A.

AbstractA numerical model has been elaborated to calculate ULF electromagnetic fields in the ground-atmosphere–ionosphere system created by an underground horizontal current source of a finite length. The modeling has enabled us to examine in detail characteristic features of ULF response to an underground large-scale emitter that may be used for a search of electromagnetic earthquake precursors. The most promising features that might discriminate signals from an underground source and from a magnetosphere-ionosphere source are (a) the apparent impedance of the electromagnetic field derived from simultaneous observations of horizontal magnetic and electric fields, and (b) the ratio of vertical and horizontal magnetic component amplitudes. Besides that, the amplitude-phase gradients of signals from an underground source differ significantly from those of the magnetospheric source. For the same magnitude of horizontal magnetic disturbance on surface, an underground current source produces in a borehole a much larger vertical electric field Ez than a magnetospheric source does. At the same time, some properties, such as the ratio between the vertical and horizontal electric components, are shown to be ineffective. However, all these differences with ionosphere-magnetosphere source reveal themselves only in a vicinity of lithospheric source (< 30 km for depth 20 km). Graphical Abstract

A numerical model is developed for calculating the electromagnetic response in the ionosphere from ground-based ultra-low-frequency transmitters of finite length L. Such megatransmitters include the ZEVS transmitter with a carrier frequency of 82 Hz and the FENICS transmitter, which can generate artificial radiation at frequencies from fractions of 1 Hz to a several hundred Hz. The amplitude of radiation generated in the upper ionosphere by a grounded horizontal current suspended the high-resistive Earth’s surface is calculated. The altitude profile of the plasma parameters is reconstructed using the IRI model. The modeled amplitudes of the electromagnetic response in the nighttime ionosphere can reach 60 μV m−1 for the ZEVS transmitter (L = 60 km) powered by a current of 200 A, which is confirmed by observations on the DEMETER satellite. Calculations show that the FENICS transmitter (L = 100 km) powered by a current of 100 A can generate radiation with frequencies of 10–100 Hz and amplitudes of up to 60–70 μV m−1 in the upper nighttime ionosphere. The FENICS transmitter can be used to generate artificial Pc1 pulsations that can be detected on low-orbit satellites (e.g., CSES). Oscillations in the nighttime ionosphere at a frequency of 0.5 Hz with amplitudes >1 pT and >10 μV m−1 of the magnetic and electrical components, respectively, are generated in the FENICS transmitter by a current of >140 A.

A numerical model has been developed to calculate the electromagnetic response in the ionosphere from grounded ultra-low-frequency transmitters of finite length L. Such megatransmitters are the ZEVS installation with a carrier frequency of 82 Hz and the FENICS installation, which can generate artificial emissions at frequencies from fractions of a Hz to a few hundreds of Hz. The amplitude of radiation excited in the upper ionosphere by a grounded horizontal current suspended above a high-resistance earth’s surface has been calculated. The altitude profile of the plasma parameters was reconstructed using the IRI ionospheric model. For the ZEVS transmitter (L = 60 km) powered by a current of 200 A, the simulated amplitudes of the electromagnetic response in the nighttime ionosphere can reach ~60 μV/m, which was confirmed by observations on the DEMETER satellite. According to calculations, the FENICS facility (L = 100 km), powered by a current of 100 A, can generate radiation in the nighttime upper ionosphere with a frequency of 10—100 Hz and an amplitude of up to ~60—70 μV/m. The FENICS facility can be used to excite artificial Pc1 pulsations that could be detected on low-Earth-orbit satellites (e.g., CSES). To create pulsations in the nighttime ionosphere at a frequency of 0.5 Hz with the amplitudes of the magnetic component 1 pT and the electric component 10 μV/m, the current in the FENICS antenna is to be 100 A.

We consider the feasibility of detection of electromagnetic response in the upper ionosphere to ground-based large-scale extremely low-frequency (ELF) transmitters by low-orbiting satellites. As an example of such mega transmitters, we consider the ZEVS 82-Hz transmitter and the FENICS facility with decommissioned electric power lines driven by an 0.5–100 Hz oscillator. We numerically simulated the ELF wave energy leakage into the upper ionosphere, generated by an oscillating grounded linear current of finite length suspended above a high-resistance ground. An altitudinal profile of the plasma parameters has been reconstructed using the ionospheric IRI model. The main step in the analysis of the problem is the solution of Maxwell equations in the atmosphere–ionosphere system with the source in the form of a horizontal current dipole. The electromagnetic field is split into potential and vortex components using the potentials introduced. This problem is devoid of axial symmetry, but the potential and vortex components have this symmetry individually. This approach has enabled us to separate the variables and pass to a one-dimensional boundary-value problem using the Hankel transform. A perturbation excited by a horizontal current of finite length is calculated by summing the fields of horizontal current dipoles that are densely distributed along the current line. According to the model proposed, the horizontal ELF antennas with a length of 60 to 100 km driven by a 100–200 A current can provide electric response amplitudes of up to 60–70 μV/m in the upper nightside ionosphere.

We have analyzed geomagnetic variations in the 2.5–12 Hz frequency range in the ionospheric F layer above the electron density maximum, using data from two SWARM satellites. The analysis is based on the data obtained under weak and moderate magnetic activity for 12 days in September and December 2016. To separate spatial inhomogeneities from time variations of the magnetic field, we analyzed signal waveforms and cross-spectra in a 2.56 s sliding window. A maximum in the occurrence and power spectral density of the variations was found at latitudes above the polar boundary of the auroral oval, which correspond to the magnetospheric input layers and dayside polar cusp/cleft. Typical waveforms of the high-latitude variations are the wave packets lasting for 5–10 periods, recorded with a short time delay by two satellites spaced by 40–100 km. These variations might be the ionospheric manifestation of the electromagnetic ion-cyclotron waves generated at the non-equatorial magnetosphere near the polar cusp. The waveforms and cross-spectra of the variations are examined in more details for two cases with different spatial distributions of the magnetic field in the ionosphere. For the ionospheric conditions corresponding to event 1 (September 17, 80° geomagnetic latitude, afternoon sector), spatial distributions of wave magnetic field in the ionosphere and on Earth are estimated using a model of Alfvén beam with a finite radius incident on the ionosphere [Fedorov et al., 2018].

The feasibility of the detection of electromagnetic response in the upper ionosphere to ground large‐scale ultra‐low‐frequency (ULF) and extremely‐low‐frequency (ELF) transmitters by low‐Earth‐orbit (LEO) satellites is considered. As an example of such transmitters, we consider the ZEVS 82 Hz transmitter, FENICS installation driven by 0.5–150 Hz generator, and industrial 50 Hz unbalanced power transmission lines. We numerically model the ULF/ELF wave energy leakage into the upper ionosphere from an oscillating grounded linear power line of a finite length suspended above a ground with a finite resistivity. The numerical scheme is based on the theoretical formalism developed to describe the excitation of an electromagnetic field by a horizontal grounded dipole. A realistic altitudinal profile of the plasma parameters has been reconstructed with the use of the IRI ionospheric model. For the ZEVS transmitter powered by 200 A current the modeled amplitudes of electromagnetic response can reach in the upper nightside ionosphere up to 60 µV/m and 6 pT. The assumption of an infinite source scale overestimates the ionospheric response by a factor of ∼7 as compared with realistic scale 60 km of the ZEVS transmitter. Unbalanced 50 Hz current of 10 A in large‐scale (>100 km) power transmission lines can produce the electric response in the upper ionosphere that is sufficient to be detected by electric sensors at LEO satellite. The stimulation of artificial Pc1 pulsations (0.5 Hz) with amplitudes ∼1 pT and ∼10 µV/m by large‐scale (>100 km) power lines is possible with driving current >100 A. The use of decommissioned power lines can be a cheap and efficient tool to stimulate Pc1 pulsations in the ionosphere.

We examine magnetic field variations at 4–12 Hz frequencies in the upper ionosphere and on Earth. The ground response to the coherent oscillations at two SWARM satellites near and above the high frequency boundary of the nominal Pc1 range is studied. We use CARISMA data to analyze ground pulsations. Ionospheric oscillations are predominantly registered at geomagnetic latitudes above 65°, i. e. from the auroral zone to the polar cusp-cleft region. The oscillations at the same frequencies are recorded at auroral and subauroral ground stations at distances from 1500 to 3000 km from satellite footprint. Ratio RGI of the oscillation amplitude on Earth to that in the ionosphere retrieved from the observed data is compared to the values calculated for a finite radius Alfvén beam incident onto a quasi-real ionosphere. [Fedorov et al., 2018]. Radial distribution of RGI depends on the oscillation frequency and the altitude distribution of ionospheric parameters controlled mostly by season and local time. The most probable values of RGI range from 10–3 to 10–1. The RGI values obtained from the observed data agree with model ones at incident beam radius of about several hundred kilometers.

In September 2019, on the Kola Peninsula, an experiment was carried out to generate ULF–ELF signals at night using two decommissioned industrial power lines as a horizontal emitting antenna. The line current was supplied from an external 200 kW generator. The current strength varied from 240 A at low frequencies (0.382 Hz) to 20 A at the highest (194 Hz). The paper presents the results of recording ULF signals at the Staraya Pustyn magnetic station, which is 1610 km from the power line. Signals with frequencies from 0.6 to 6.4 Hz were recorded. The signal amplitudes, normalized to the emitter current, varied in the range of 0.4–0.7 fT/A. For theoretical estimates, two models were used: (1) formulas from the theory of ELF field excitation in the Earth–ionosphere waveguide and (2) a numerical model of the ULF field in the atmosphere and ionosphere created by a linear surface current of infinite length. The numerical model is based on calculation of the system of Maxwell equations in a vertically inhomogeneous atmosphere and ionosphere, the parameters of which are calculated using the IRI model. A fundamental feature of model 2 is that it takes into account the contribution of the ionospheric waveguide propagation to the excited field at large distances at frequencies above the critical waveguide frequency of ~0.5 Hz. The dependence of the amplitude of the recorded signals from an artificial source on a frequency of 2–8 Hz has a nonmonotonic character, which may be a manifestation of the effects of waveguide propagation along the ionosphere.

In September 2019, two out-of-service power transmission lines were used as a horizontal emitting antenna in an experiment conducted on the Kola Peninsula to generate ultra-low-frequency (ULF, 0.38–6.4 Hz) and extremely low–frequency (ELF, 9.4–194 Hz) signals during nighttime hours. The current ranged from 240 A at low frequencies (LF, 0.382 Hz) to 20 A at the highest frequencies (194 Hz). The results of the recording of ULF signals at Staraya Pustyn magnetic station, which is 1610 km away from the transmission line, are presented. The recorded signals had frequencies of 0.6–6.4 Hz and amplitudes normalized to the value of the emitter current ~0.4–0.7 fT/A. Three models were used for theoretical estimates: (1) formulas based on the theory of ELF field excitation over a conducting surface; (2) a numerical model of the ULF field in the atmosphere and ionosphere generated by a linear surface current of infinite length, and (3) a numerical model of a horizontal dipole in the multilayer Earth–atmosphere–ionosphere medium. Model 2 is based on the numerical solution of the system of Maxwell equations in the vertically inhomogeneous atmosphere and ionosphere; its fundamental feature is that it takes into account the contribution of ionospheric waveguide propagation to the excited field at large distances. Model 3 demonstrated the best agreement with the amplitudes of the recorded signals. However, contrary to the predictions of models 1 and 3, the frequency dependence of the amplitude of artificial signals in the 2–8 Hz range is non-monotonic, which may be a manifestation of the effects of waveguide propagation along the ionosphere.

We present an overview, based on satellite observations at low Earth orbits, on electromagnetic radiation from ground power transmission lines at an industrial frequency 50–60 Hz. Particular attention has been given to Chibis-M and DEMETER satellite observations. The electric 40-cm antenna of the micro-satellite often recorded 50–60 Hz radiation (known as Power Line Emission (PLE)) when it flew over industrialized areas of the planet. The PLE spectral amplitude varied from 1.2 to 18 (μV/m)/Hz0.5, which corresponds to the electric field amplitude E~1 μV/m. We report results of numerical calculations of the electromagnetic response of the atmosphere and ionosphere to a large-scale surface emitter at a frequency of 50 Hz. According to simulation results, PLE with an intensity of ~1 μV/m observed on satellites in the nightside ionosphere at midlatitudes can be excited by an unbalanced current 8–10 A in a power transmission line above the earth's crust with conductivity of 10–3 S/m. At middle and low latitudes with an inclined geomagnetic field, the maximum response in the upper ionosphere to the transmission line radiation should be seen shifted equatorward, although this shift is less than that upon guidance by the geomagnetic field. The maximum amplitude of the electromagnetic response of the ionosphere to the power transmission line emission decreases for an inclined geomagnetic field, but insignificantly. To date, the PLE intensity in near-Earth space has turned out to be higher than the intensity of natural radiation in this range (Schumann resonances and ion whistlers), and continues to grow with the technological development of mankind.

To foresee a plausible electromagnetic contamination of the near-Earth space by anthropogenic activity, a magnitude of electromagnetic response in the upper ionosphere to 50/60 Hz power line emission (PLE) is to be modeled. For that we have calculated the spatial structure of electromagnetic disturbance in the mid-latitude atmosphere and ionosphere immersed into an inclined geomagnetic field B0. The electromagnetic field is excited by a large-scale 50/150 Hz oscillating linear current suspended above the ground. The elaborated model is based on numerical solution of full-wave equations in a realistic ionosphere whose parameters have been reconstructed with the use of the International Reference Ionosphere (IRI) model. The PLE wave beam in the ionosphere is not guided by B0, but still is shifted equatorward from the vertical. The response of the nightside upper ionosphere is slowly decreasing with diminishing of latitude. The amplitude of PLE electric component in the upper ionosphere generated by the unbalanced power line current with intensity of similar to 10 Amperes can reach similar to 1 mu V/m which is sufficient to be detected by a low-Earth-orbit satellite. For a better insight into PLE transmission through the ionosphere a basic information about ELF waves in the multi-ion plasma is provided.

The expected magnitude of extralow-frequency (ELF) electromagnetic response in the upper ionosphere to ground large-scale power transmission lines at low Earth orbit (LEO) is modeled. The full-wave system of Maxwell's equations is numerically solved in a realistic ionosphere whose parameters have been reconstructed with the use of the International Reference Ionosphere (IRI) model. We have calculated the altitudinal structure in the atmosphere and ionosphere of electromagnetic field and Poynting flux excited by an oscillating 50/150 Hz linear current suspended above the ground. The leakage rate into the upper ionosphere was shown to increase during nighttime hours and above a high-resistive crust. The amplitudes of electromagnetic power line emission (PLE) detected by LEO satellites correspond to the unbalanced power line current intensity of about 1-10 A, depending on the crust resistivity.

We examine excitation of ultralow frequency (ULF) electromagnetic waves by an atmospheric lightning stroke in the upper ionosphere and the role of the ionospheric Alfven resonator (IAR) in this process. We have theoretically calculated with the developed numerical model the spatial and spectral structures of electromagnetic disturbance in the ULF frequency range 0.1-6.0 Hz excited by an atmospheric lightning stroke on the ground and at ionospheric altitudes. The frequency band under consideration comprises typical frequencies of the IAR and the ionospheric waveguide. The spectra of horizontal magnetic and electric components reveal a spectral multiband structure in the upper ionosphere. The form of spectra depends significantly on the horizontal distance rho from the source: spectral peaks associated with the IAR are evident at rho <= 400 km, whereas at rho >= 1,000 km the spectral peaks (>4 Hz) corresponding to the ionospheric waveguide modes can be seen. The model predicts that a vertical electric discharge with the charge moment M-Q = 10(6) C.m produces at altitude 500 km and rho = 40 km a pulse with electric and magnetic amplitudes of about 4mV/m and 4 nT, correspondingly, and duration similar to 0.2s. The pulse amplitude decays rather slowly with distance proportional to rho(-1). Detection of ULF response in the upper ionosphere to isolated intense lightning stroke by low-orbiting satellites with magnetic or electric sensors onboard is quite feasible.

Characteristic feature of the upper ionosphere is the occurrence of the ionospheric Alfvén resonator (IAR) and MHD waveguide, which can trap the electromagnetic waves in the frequency range from fractions of Hz to few Hz. The proposed numerical model is based on the solution of MHD equations in a realistic ionosphere, whose parameters are reconstructed from the IRI model. We estimated, both analytically and numerically, a critical, wave scale dependent, value of the Hall conductance when a wave equation for an uncoupled Alfvénic mode can be used to estimate the spectral parameters of the IAR. The model has enabled us to compare the contributions into the IAR Q-factor of the Joule dissipation in the lower ionosphere and a wave leakage into the magnetosphere. The first mechanism dominates during daytime, whereas the latter mechanism prevails during nighttime. The ground signatures of IAR can be used for monitoring of the F-layer plasma density and vertical total electron content on the basis of relationships derived from the developed IAR model.

The ionospheric Alfven resonator (IAR) and fast magnetosonic (FMS) waveguide, which can trap the electromagnetic wave energy in the range from fractions of Hz to several Hz, are characteristic features of the upper ionosphere. Their role in the electromagnetic impulsive coupling between atmospheric discharge processes and the ionosphere can be elucidated with a proper model. The presented model is based on numerical solution of coupled wave equations for electromagnetic modes in the ionosphere and atmosphere in a realistic ionosphere modeled with the use of IRI (International Reference Ionosphere) vertical profiles. The geomagnetic field is supposed to be nearly vertical, so the model can be formally applied to high latitudes, though the main features of ground ULF structure will be qualitatively similar at middle latitudes as well. The modeling shows that during the lightning discharge a coupled wave system comprising IAR and MHD waveguide is excited. Using the model, the spatial structure, frequency spectra, and polarization parameters have been calculated at various distances from a vertical dipole. In the lightning proximity (about several hundred kilometer) only the lowest IAR harmonics are revealed in the radial magnetic component spectra. At distances > 800 km the multiband spectral structure is formed predominantly by harmonics of FMS waveguide modes. The model predictions do not contradict the results of search coil magnetometer observations on Svalbard; however, the model validation demands more dedicated experimental studies.

A characteristic feature of the upper ionosphere is the occurrence of the ionospheric Alfven resonator (IAR) and MHD waveguide, which can trap electromagnetic wave energy in the range from fractions of a Hz to a few Hz. This wave trapping ensures the strong dependence of the ionospheric transmission/reflective properties on frequency. We have developed a numerical model of the magnetospheric Alfven wave interaction with the ionosphere and transmission to the ground based on the solution of multifluid magnetohydrodynamic (MHD) full wave equations in a realistic ionosphere, whose parameters were reconstructed from the International Reference Ionosphere model. The MHD modes are coupled owing to the frequency-dependent Hall conductivity and geomagnetic field line inclination. This model can be applied to the interpretation of the spectral structure of electromagnetic emissions of the magnetospheric origin in the band 0.1-10Hz observed at various latitudes. The model predicts that the upper part of the ULF spectrum (f > 1Hz) will be severely absorbed upon wave transmission through the daytime ionosphere to the ground. At nighttime the transmission coefficient of Alfven waves has an oscillatory dependence on frequency, with transmission windows at the lowest IAR eigenfrequencies (<3Hz). At higher frequencies (3-10Hz) the reflection/transmission coefficients are dominated by periodic scale-dependent modulation owing to the waveguide modes. Broad maxima/minima of the transmission coefficient are determined by the phasing between Alfven and fast magnetosonic waves at the bottom of the ionosphere.