We propose a novel approach to model the ground electric field (GEF) induced by laterally-nonuniform ionospheric sources in the real-time. The approach exploits the multi-site transfer function concept, continuous magnetic field measurements at multiple sites in the region of interest, and spatial modes describing the ionospheric source. We compared the modeled GEFs with those measured at two locations in Fennoscandia and observed good agreement between modeled and measured GEF. Besides, we compared GEF-based geomagnetically induced current (GIC) with that measured at the M\“ants\”al\”a natural gas pipeline recording point and again observed remarkable agreement between modeled and measured GIC.

In this study, we perform rigorous three-dimensional (3-D) ground electric field (GEF) modeling in Fennoscandia for three days of the Halloween geomagnetic storm (29-31 October 2003) using magnetic field data from the IMAGE magnetometer network and a 3-D conductivity model of the region. To explore the influence of the inducing source model on 3-D GEF simulations, we consider three different approaches to source approximation. Within the first two approaches, the source varies laterally, whereas in the third method, the GEF is calculated by implementing the time-domain realization of the magnetotelluric intersite impedance method. We then compare GEF-based geomagnetically induced current (GIC) with observations at the Mäntsälä natural gas pipeline recording point. We conclude that a high correlation between modeled and recorded GIC is observed for all considered approaches. The highest correlation is achieved when performing a 3-D GEF simulation using a “conductivity-based” laterally nonuniform inducing source. Our results also highlight the strong dependence of the GEF on the earth’s conductivity distribution.

Imaging Earth's electrical conductivity at mantle depths requires accurate models of the spatial-temporal structure of external (ionospheric and magnetospheric) currents. Such models can also be useful for better retrieving core and crustal fields. Three ionospheric current systems-equatorial electrojet (EEJ), polar electrojet (PEJ), and mid-latitude current system (MLCS; in quiet time called Sq) produce quasi-periodic diurnal variations (DV). The signals at longer periods (LP) are due to primarily irregular fluctuations of magnetospheric currents. Conventionally, DV and LP signals are treated separately. For example, the analysis of LP signals is often based on night-time data to diminish the effects from ionospheric sources. However, due to EM induction in the Earth, the signals of ionospheric origin also persist during the night. As for DV, their analysis is usually  performed in the frequency domain. However, the morphology of all ionospheric sources varies from day to day, depending on the solar activity and the Earth’s orbital position,  advocating analysis of DV in the time domain. Besides, the analysis of EEJ and MLCS signals is usually based on non-polar data to diminish the effects from PEJ. In this study, we present a methodology to simultaneously model magnetic fields from all the sources directly in the time domain using night- and day-time as well as non-polar and polar data. An approach exploits two types of source parameterisation (data-based and physics-based) and accounts for 3-D electromagnetic induction effects. Using observatory data, we obtain continuous spatio-temporal models of multi-source external and induced magnetic fields for 1998-2021. We also discuss an adaptation of the approach to analyse satellite data.

Directional drilling in the oil fields relies particularly on the “on-fly” measurements of the natural magnetic field (measurements while drilling; MWD); the MWD are eventually used to construct the well path. These measurements are the superposition of the signals from the internal, core and crustal, and external, ionospheric and magnetospheric sources and the noise from magnetic elements in the borehole assembly. The internal signals are mostly constant in time and accounted for through the Earth’s internal field models. The signals of external origin give rise to diurnal and irregular spatio-temporal magnetic field variations observable in the MWD. One of the common ways to mitigate the effects of these variations in the MWD is to correct readings for the data from an adjacent land-based magnetic observatory/site. This method assumes that the land-based signals are similar to those at the seabed drilling site. In this paper, we show that the sea level and seabed horizontal magnetic fields differ significantly, reaching up to 30\,\% of sea level values in many oceanic regions. We made this inference from the global forward modeling of the magnetic field using realistic models of conducting Earth and time-varying sources. To perform such modeling, we elaborated a numerical approach to efficiently calculate the spatio-temporal evolution of the magnetic field. Finally, we propose and validate a formalism allowing researchers to obtain trustworthy seabed signals using measurements at the adjacent land-based site and exploiting the modelling results, thus without needing additional measurements at the seabed site.

We present a methodology that allows researchers to simulate in real time the spatiotemporal dynamics of the ground electric field (GEF) in a given 3-D conductivity model of the Earth based on continuously augmented data on the spatiotemporal evolution of the inducing source. The formalism relies on the factorization of the source by spatial modes and time series of respective expansion coefficients and exploits precomputed frequency-domain GEF generated by corresponding spatial modes. To validate the formalism, we invoke a high-resolution 3-D conductivity model of Fennoscandia and consider a realistic source built using the Spherical Elementary Current Systems (SECS) method as applied to magnetic field data from the IMAGE network of observations. The factorization of the SECS-recovered source is then performed using the principal component analysis. Eventually, we show that the GEF computation at a given time instant on a 512 x 512 grid requires less than 0.025 seconds provided that frequency-domain GEF due to pre-selected spatial modes are computed in advance. Taking the 7-8 September 2017 geomagnetic storm as a space weather event, we show that real-time high-resolution 3-D modeling of the GEF is feasible. This opens a practical opportunity for GEF (and eventually geomagnetically induced currents) nowcasting and forecasting.

There is significant interest in constraining mantle conductivity beneath oceans. One data source to probe oceanic mantle conductivity is magnetic fields measured at island observatories. From these data local responses are estimated and then inverted in terms of conductivity. However, island responses may be strongly distorted by the ocean induction effect (OIE) originating from conductivity contrasts between ocean and land. Insufficiently accurate accounting for OIE may lead to wrong interpretation of the responses. OIE is generally modeled by global simulations using relatively coarse grids to represent bathymetry. We explore whether very local bathymetry influences island responses. To address this question we developed a methodology for efficient modeling of effects of bathymetry of any resolution. On an example of two island observatories we demonstrate that small-scale bathymetry dramatically influences the responses. Using new methodology we obtain new conductivity models beneath considered islands and observe remarkable agreement between modeled and experimental responses.

Ground-based technological systems, such as power grids, can be affected by geomagnetically induced currents (GIC) during geomagnetic storms and magnetospheric substorms. This motivates the necessity to numerically simulate and, ultimately, forecast GIC. The prerequisite for the GIC modeling in the region of interest is the simulation of the ground geoelectric field (GEF) in the same region. The modeling of the GEF in its turn requires spatio-temporal specification of the source which generates the GEF, as well as an adequate regional model of the Earth’s electrical conductivity. In this paper we compare results of the GEF (and ground magnetic field) simulations using three different source models. Two models represent the source as a laterally varying sheet current flowing above the Earth. The first model is constructed using the results of a physics-based 3-D magnetohydrodynamic (MHD) simulation of near-Earth space, the second one uses ground-based magnetometers’ data and the Spherical Elementary Current Systems (SECS) method. The third model is based on a “plane wave” approximation which assumes that the source is locally laterally uniform. Fennoscandia is chosen as a study region and the simulations are performed for the 7-8 September 2017 geomagnetic storm. We conclude that ground magnetic field perturbations are reproduced more accurately using the source constructed via the SECS method compared to the source obtained on the basis of MHD simulation outputs. We also show that the difference between the GEF modeled using laterally nonuniform source and plane wave approximation is substantial in Fennoscandia.

Most of the existing three-dimensional (3-D) electromagnetic (EM) modeling solvers based on the integral equation (IE) method exploit fast Fourier transform (FFT) to accelerate the matrix-vector multiplications. This in turn requires a laterally-uniform discretization of the modeling domain. However, there is often a need for multi-scale modeling and inversion, for instance, to properly account for the effects of non-uniform distant structures, and at the same time, to accurately model the effects from local anomalies. In such scenarios, the usage of laterally-uniform grids leads to excessive computational loads, both in terms of memory and time. To alleviate this problem, we developed an efficient 3-D EM modeling tool based on a multi-nested IE approach. Within this approach the IE modeling is first performed at a large domain and on a (laterally-uniform) coarse grid, and then the results are refined in the region of interest by performing modeling at a smaller domain and on a (laterally-uniform) denser grid. At the latter stage, the modeling results obtained at the previous stage are exploited. The lateral uniformity of the grids at each stage allows us to keep using the FFT, and thus attain the remarkable performance of the developed tool. An important novelty of the paper is a development of a “rim domain” concept which further improves the efficiency of the multi-nested IE approach.

We present a methodology that allows real-time simulation of the geoelectric field (GEF) spatiotemporal evolution in a given 3-D conductivity model of the Earth based on continuously augmented inducing source data. The presented concept is validated using Fennoscandia as a test region. The choice of Fennoscandia is motivated by several reasons. First, it is a high latitude region, where the GEF is expected to be particularly large. Second, there exists a 3-D ground electrical conductivity model of the region. Third, the regional magnetometer network, IMAGE, allows us to build a realistic model of the source for a given geomagnetic disturbance. Taking the 7-8 September 2017 geomagnetic storm as a space weather event, we show that real-time high-resolution 3-D modeling of the GEF is feasible and requires only a few tens of seconds.

In this study we develop a tool to simultaneously invert multi-source magnetic transfer functions (TFs), including magnetotelluric (MT) tippers (with period ranging from a few minutes to 3 hours), solar quiet (Sq) global-to-local (G2L) transfer functions (TFs; with period ranging from 6 hours to 24 hours) of ionospheric origin, and magnetospheric global Q-responses (with period ranging from a few days to a few months). We further jointly invert the aforementioned multi-source TFs to constrain the local conductivity structures beneath three islands located in South Atlantic, Indian Ocean and North Pacific. The recovered conductivity profiles suggest upper mantle plumes beneath Tristan da Cunha and Oahu islands. Besides, our results indicate resistive lithosphere of different thicknesses beneath these three islands, showing a progressive thickening of oceanic lithosphere with age.