High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is 8 times lower, compared to analogous IE based algorithms, without additional restriction on the background media; (ii) accurate and stable method to compute matrix coefficients corresponding to the IE; (iii) high degree of parallelism. The solver's computational efficiency is shown on a problem of magnetotelluric sounding of the high conductivity contrast media. A good agreement with the results obtained with the second order finite element method is demonstrated. Due to effective approach to parallelization and distributed data storage the program exhibits perfect scalability on different hardware platforms.Comment: The main results of this paper were presented at IAMG 2015 conference Frieberg, Germany. 28 pages, 11 figure

Comparing Three Approaches to the Inducing Source Setting for the Ground Electromagnetic Field Modeling due to Space Weather Events

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 spatiotemporal 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 September 7–8, 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.publishedVersio

Preliminary Results of Marine Electromagnetic Sounding with a Powerful, Remote Source in Kola Bay off the Barents Sea

We present an experiment conducted in Kola Bay off the Barents Sea in which new, six-component electromagnetic seafloor receivers were tested. Signals from a powerful, remote super-long wave (SLW) transmitter at several frequencies on the order of tens Hz were recorded at the six sites along a profile across Kola Bay. In spite of the fact that, for technical reasons, not all the components were successfully recorded at every site, the quality of the experimental data was quite satisfactory. The experiment resulted in the successful simulation of an electromagnetic field by the integral equation method. An initial geoelectric model reflecting the main features of the regional geology produced field values that differed greatly from the experimental ones. However, step-by-step modification of the original model considerably improved the fit of the fields. Thereby specific features of the regional geology, in particular the fault tectonics, were able to be corrected. These preliminary results open the possibility of inverse problem solving with more reliable geological conclusions

3-D inversion of MT impedances and inter-site tensors, individually and jointly. New lessons learnt

Abstract A conventional magnetotelluric (MT) survey layout implies measurements of horizontal electric and magnetic fields at every site with subsequent estimation and interpretation of impedance tensors $${Z}$$ Z or dependent responses, such as apparent resistivities and phases. In this work, we assess advantages and disadvantages of complementing or substituting conventional MT with inter-site transfer functions such as inter-site impedance tensor, $${Q}$$ Q , horizontal magnetic, $${M}$$ M , and horizontal electric, $${T}$$ T , tensors. Our analysis is based on a 3-D inversion of synthetic responses calculated for a 3-D model which consists of two buried adjacent (resistive and conductive) blocks and thin resistor above them. The (regularized) 3-D inversion is performed using scalable 3-D MT inverse solver with forward modelling engine based on a contracting integral equation approach. The inversion exploits gradient-type (quasi-Newton) optimization algorithm and invokes adjoint sources approach to compute misfits’ gradients. From our model study, we conclude that: (1) 3-D inversion of either $${Z}$$ Z or $${Q}$$ Q tensors recovers the “true” structures equally well. This, in particular, raises the question whether we need magnetic field measurements at every survey site in the course of 3-D MT studies; (2) recovery of true structures is slightly worse if $${T}$$ T tensor is inverted, and significantly worse if $${M}$$ M tensor is inverted; (3) simultaneous inversion of $${Z}$$ Z and $${M}$$ M (or $${Z}$$ Z and $${T}$$ T ) does not improve the recovery of true structures compared to individual inversion of $${Z}$$ Z or $${Q}$$ Q ; (4) location of reference site, which is required for calculating inter-site $${Q}$$ Q , $${T}$$ T and $${M}$$ M tensors, has also marginal effect on the inversion results

High-Performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

ISSN:1874-8961ISSN:0882-8121ISSN:1874-8953ISSN:1573-886

A Proper Use of the Adjacent Land-Based Observatory Magnetic Field Data to Account for the Geomagnetic Disturbances During Offshore Directional Drilling

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 modeling results, thus without needing additional measurements at the seabed site.ISSN:1542-739

Real‐time 3‐D modeling of the ground electric field due to space weather events : A concept and its validation

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 (SM) and time series of respective expansion coefficients and exploits precomputed GEF kernels generated by corresponding SM. 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 International Monitor for Auroral Geomagnetic Effect 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 × 512 grid requires less than 0.025 s provided that GEF kernels due to pre-selected SM 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

Real-Time 3-D Modeling of the Ground Electric Field Due To Space Weather Events. A Concept and Its Validation

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 (SM) and time series of respective expansion coefficients and exploits precomputed GEF kernels generated by corresponding SM. 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 International Monitor for Auroral Geomagnetic Effect 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 s provided that GEF kernels due to pre-selected SM 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.ISSN:1542-739

Three‐Dimensional Modeling of the Ground Electric Field in Fennoscandia During the Halloween Geomagnetic Storm

In this study, we perform 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 International Monitor for Auroral Geomagnetic Effects (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

Multi-Site Transfer Function Approach for Real-Time Modeling of the Ground Electric Field Induced by Laterally-Nonuniform Ionospheric Source

We propose a novel approach to model the ground electric field (GEF) induced by laterally-nonuniform ionospheric sources in 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 Mantsala natural gas pipeline recording point and again observed remarkable agreement between modeled and measured GIC.Validerad;2023;Nivå 2;2023-11-15 (joosat);Funder: New Zealand Ministry of Business, Innovation, Employment (UOOX2002); ESA and EO Science for Society (4000109587); Academy of Finland (339329);License fulltext: CC BY</p