Earth Conductivity Research Articles

Analytic Calculation of Geoelectric Fields Due to Geomagnetic Disturbances: A Test Case

Geomagnetic field variations produce geoelectric fields that can affect the operation of technological networks at the Earth’s surface, including power systems, pipelines, phone cables and railway circuits. To assess the geomagnetic hazard to this technology, it is necessary to model the geomagnetically induced currents (GIC) produced in these systems during geomagnetic disturbances. This requires use of geomagnetic data with appropriate Earth conductivity models to calculate the geoelectric fields that drive GIC. To provide a way of testing geoelectric field calculation software, we provide a benchmark test case by defining a synthetic geomagnetic field variation and deriving exact analytic expressions for the Earth response based on both uniform and layered Earth conductivity models. These are then used to provide exact analytic expressions for the geoelectric fields that would be produced by the synthetic geomagnetic field variation. The synthetic geomagnetic data can be used as input to numerical geoelectric field calculation software, the output of which can be tested by comparison with the analytically-generated geoelectric fields.

Effects of Lateral Conductivity Variations on Geomagnetically Induced Currents: H-Polarization

H-polarization, along with E-polarization, indicates the lateral variations of the Earth conductivity, which influence the induced electric field distribution. The coast effect is a typical H-polarization phenomenon that causes local geoelectric field enhancement in coastal areas and significantly affects the geomagnetically induced currents (GIC) distributions in power grids. The influences of H-polarization on geoelectric fields and GIC form the basis for further research on power grid disasters resulting from magnetic storms. In this paper, block and thin-shell models of the coast effect are established, and the electric field distribution in the case of H-polarization is calculated using the finite element method. The results demonstrate the effects of the conductivity, frequency, and distance from the interface of a different conductivity on electric field distortion. Additionally, the relationship between H-polarization and GIC in power grids is investigated, demonstrating that the GIC can be influenced within 100 km in the H-polarization case. The methods and results provide a theoretical basis for GIC risk assessment and development of a control strategy for the power grid.

Proximity Effects of Lateral Conductivity Variations on Geomagnetically Induced Electric Fields

During a magnetic storm, the induced geoelectric field drives geomagnetically induced currents (GIC) in power transmission networks, railway systems, and pipelines, negatively affecting these systems. In regions with complex geological structures, the lateral earth conductivity changes influence the induced electric field distribution in the earth. H- and E-polarization are two cases of the orientation of the E-field vector relative to the lateral changes. A model of the earth with lateral conductivity changes is established in this paper to examine the effects of conductivity change across a discontinuity on the magnitude of the E-field for the case of the E-field parallel to the discontinuity. The electric field distribution with distance from the discontinuity is calculated, and the relationship between the lateral conductivity changes and electric field distortion is analyzed using the finite element method. In addition, the GIC variation in the power grid due to the lateral conductivity changes is examined. Then, the factors affecting GIC, including conductivity, frequency, and distance, are investigated. The results show that lateral conductivity changes can influence the GIC in power lines running parallel to the discontinuity up to 250 km from the discontinuity. The methods and results are significant for understanding how lateral conductivity changes influence GIC and will improve the accuracy of GIC calculations.

Numerical Calculation of Geoelectric Fields That Affect Critical Infrastructure

One of the modern applications of geomagnetism is determining the effect of geomagnetic disturbances on critical infrastructure such as power systems and pipelines. Assessing the geomagnetic hazard to such systems requires calculation of the geoelectric fields produced during geomagnetic disturbances. Such geoelectric fields can then be used as input to system models to calculate the impact on the system. This paper describes what is involved in calculating the geoelectric fields produced during real geomagnetic disturbances. The theory of geomagnetic induction is presented and used to derive the Earth transfer function relating the geoelectric and geomagnetic field variations at the Earth’s surface. It is then shown how this can be used to make practical calculations of the geoelectric fields and how the calculation process can be verified by comparison with analytic solutions obtained with synthetic geomagnetic variation data. The accuracy of the calculated geoelectric fields for geomagnetic risk assessments is limited, not by the accuracy of the calculation methods, but by the availability of geomagnetic field measurements and Earth conductivity information over the whole extent of the affected infrastructure.

Dark Matter that Interacts with Baryons: Density Distribution within the Earth and New Constraints on the Interaction Cross-section

Abstract For dark matter (DM) particles with masses in the 0.6–6m p range, we set stringent constraints on the interaction cross-sections for scattering with ordinary baryonic matter. These constraints follow from the recognition that such particles can be captured by—and thermalized within—the Earth, leading to a substantial accumulation and concentration of DM that interact with baryons. Here, we discuss the probability that DM intercepted by the Earth will be captured, the number of DM particles thereby accumulated over Earth’s lifetime, the fraction of such particles retained in the face of evaporation, and the density distribution of such particles within the Earth. In the latter context, we note that a previous treatment of the density distribution of DM, presented by Gould and Raffelt and applied subsequently to DM in the Sun, is inconsistent with considerations of hydrostatic equilibrium. Our analysis provides an estimate of the DM particle density at Earth’s surface, which may exceed 1014 cm−3, and leads to constraints on various scattering cross-sections, which are placed by (1) the lifetime of the relativistic proton beam at the Large Hadron Collider; (2) the orbital decay of spacecraft in low Earth orbit; (3) the vaporization rate of cryogenic liquids in well-insulated storage dewars; and (4) the thermal conductivity of Earth’s crust. For the scattering cross-sections that were invoked recently in Barkana’s original explanation for the anomalously deep 21 cm absorption reported by EDGES, DM particle masses in the 0.6–4m p range are excluded.

Telluric Field Variations as Drivers of Variations in Cathodic Protection Potential on a Natural Gas Pipeline in New Zealand

AbstractA study of variations in cathodic protection potential on a natural gas pipeline in the North Island of New Zealand is reported. Both the measured pipe‐to‐soil potential (PSP) and the current measured through an installed defect in the pipeline coating show strong correlations with variations in measured magnetic and telluric fields. Contrary to predictions from distributed‐source transmission line theory, analysis shows that the closest correlations of PSP and current are with the component of telluric field perpendicular to the pipeline. This orientation is close to perpendicular to major electrical conductivity contrasts associated with both the local coastline and with on‐shore Earth conductivity structure. It is therefore inferred the variations in PSP which drive the variations in defect current are the result of changes in the local Earth potential. While reporting on specific observations from New Zealand, these results should be applicable across a wide range of middle and high‐latitude global locations. Estimates of possible corrosion rates for the pipeline in question suggest that such enhancement of telluric field variations by conductivity structure may pose significant risk to pipelines in the event of defects in the pipeline coating.

Predicting Global Ground Geoelectric Field With Coupled Geospace and Three‐Dimensional Geomagnetic Induction Models

AbstractWe forecast the global effects of space weather on the geoelectric and geomagnetic fields using a novel combination of methods. We use a realistic three‐dimensional (3‐D) model of Earth's electrical conductivity and a realistic representation of magnetospheric and ionospheric current systems. Our scheme involves the following steps: (1) We run a global magnetohydrodynamic model of the magnetosphere coupled to an electrostatic model of the ionosphere. (2) We calculate a global time series of the ground magnetic field resulting from the ionospheric, field‐aligned, and magnetospheric currents of the global magnetohydrodynamic model. (3) We approximate this external field by an equivalent source current flowing in a thin shell above Earth. (4) We calculate a global time series of geoelectric and geomagnetic fields from the equivalent current and a 3‐D conductivity model of Earth that also takes into account the coast effect due to large horizontal conductivity gradient. We verify our implementation by comparing the results against known analytic and numeric solutions, and then apply our scheme to the geomagnetic storm of 14 and 15 December 2006. In particular, we show that accounting for 3‐D structure of Earth's conductivity results in significantly enhanced geoelectric field at large lateral gradients of conductivity, especially in coastal regions, both at middle and high latitudes. In the studied geomagnetic storm the largest values of 3‐D geoelectric field are detected at high latitudes reaching 2.5 V/km and the 3‐D effect extends inland by a few hundred kilometers.

Estimating ocean tide model uncertainties for electromagnetic inversion studies

Abstract. Over a decade ago the semidiurnal lunar M2 ocean tide was identified in CHAMP satellite magnetometer data. Since then and especially since the launch of the satellite mission Swarm, electromagnetic tidal observations from satellites are increasingly used to infer electric properties of the upper mantle. In most of these inversions, ocean tidal models are used to generate oceanic tidal electromagnetic signals via electromagnetic induction. The modeled signals are subsequently compared to the satellite observations. During the inversion, since the tidal models are considered error free, discrepancies between forward models and observations are projected only onto the induction part of the modeling, e.g., Earth's conductivity distribution. Our study analyzes uncertainties in oceanic tidal models from an electromagnetic point of view. Velocities from hydrodynamic and assimilative tidal models are converted into tidal electromagnetic signals and compared. Respective uncertainties are estimated. The studies main goal is to provide errors for electromagnetic inversion studies. At satellite height, the differences between the hydrodynamic tidal models are found to reach up to 2 nT, i.e., over 100 % of the local M2 signal. Assimilative tidal models show smaller differences of up to 0.1 nT, which in some locations still corresponds to over 30 % of the M2 signal.

A New Approximate Method for Lightning-Radiated ELF/VLF Ground Wave Propagation over Intermediate Ranges

A new approximate method for lightning-radiated extremely low-frequency (ELF) and very low-frequency (VLF) ground wave propagation over intermediate ranges is presented in this paper. In our approximate method, the original field attenuation function is divided into two factors in frequency domain representing the propagation effect of the ground conductivity and Earth’s curvature, and both of them have clearer formulations and can more easily be calculated rather than solving a complex differential equation related to Airy functions. The comparison results show that our new approximate method can predict the lightning-radiated field peak value over the intermediate range with a satisfactory accuracy within maximum errors of 0.0%, −3.3%, and −8.7% for the earth conductivity of 4 S/m, 0.01 S/m, and 0.001 S/m, respectively. We also find that Earth’s curvature has much more effect on the field propagation at the intermediate ranges than the finite ground conductivity, and the lightning-radiated ELF/VLF electric field peak value (V/m) at the intermediate ranges yields a propagation distance d (km) dependence of d−1.32.

The Thermal Conductivity of Earth's Core: A Key Geophysical Parameter's Constraints and Uncertainties

The thermal conductivity of iron alloys at high pressures and temperatures is a critical parameter in governing ( a) the present-day heat flow out of Earth's core, ( b) the inferred age of Earth's inner core, and ( c) the thermal evolution of Earth's core and lowermost mantle. It is, however, one of the least well-constrained important geophysical parameters, with current estimates for end-member iron under core-mantle boundary conditions varying by about a factor of 6. Here, the current state of calculations, measurements, and inferences that constrain thermal conductivity at core conditions are reviewed. The applicability of the Wiedemann-Franz law, commonly used to convert electrical resistivity data to thermal conductivity data, is probed: Here, whether the constant of proportionality, the Lorenz number, is constant at extreme conditions is of vital importance. Electron-electron inelastic scattering and increases in Fermi-liquid-like behavior may cause uncertainties in thermal conductivities derived from both first-principles-associated calculations and electrical conductivity measurements. Additional uncertainties include the role of alloying constituents and local magnetic moments of iron in modulating the thermal conductivity. Thus, uncertainties in thermal conductivity remain pervasive, and hence a broad range of core heat flows and inner core ages appear to remain plausible.

Effects of iron on the lattice thermal conductivity of Earth’s deep mantle and implications for mantle dynamics

Iron may critically influence the physical properties and thermochemical structures of Earth's lower mantle. Its effects on thermal conductivity, with possible consequences on heat transfer and mantle dynamics, however, remain largely unknown. We measured the lattice thermal conductivity of lower-mantle ferropericlase to 120 GPa using the ultrafast optical pump-probe technique in a diamond anvil cell. The thermal conductivity of ferropericlase with 56% iron significantly drops by a factor of 1.8 across the spin transition around 53 GPa, while that with 8-10% iron increases monotonically with pressure, causing an enhanced iron substitution effect in the low-spin state. Combined with bridgmanite data, modeling of our results provides a self-consistent radial profile of lower-mantle thermal conductivity, which is dominated by pressure, temperature, and iron effects, and shows a twofold increase from top to bottom of the lower mantle. Such increase in thermal conductivity may delay the cooling of the core, while its decrease with iron content may enhance the dynamics of large low shear-wave velocity provinces. Our findings further show that, if hot and strongly enriched in iron, the seismic ultralow velocity zones have exceptionally low conductivity, thus delaying their cooling.

Resistivity-Chemistry Integrated Approaches for Investigating Groundwater Salinity of Water Supply and Agricultural Activity at Island Coastal Area

Groundwater suitability for water supply and agriculture in an island coastal area may easily be influenced by seawater intrusion. The aim of this study was to investigate seawater intrusion to the suitability of the groundwater for water supply and oil palm cultivation on Carey Island in Malaysia. This is the first study that used integrated method of geo-electrical resistivity and hydrogeochemical methods to investigate seawater intrusion to the suitability of groundwater for water supply and oil palm cultivation at two different surface elevation and land cover. The relationship between earth resistivity, total dissolved solids and earth conductivity was derived with water type classifications and crop suitability classification according to salinity, used to identify water types and also oil palm tolerance to salinity. Results from the contour resistivity and conductivity maps showed that the area facing severe coastal erosion (east area) exhibited unsuitable groundwater condition for water supply and oil palm at the unconfined aquifer thickness of 7.8 m and 14.1 m, respectively. Comparing to the area that are still intact with mangrove (west area), at the same depth, groundwater condition exhibits suitable usage for both socioeconomic activities. Different characteristics of surface elevation and land cover are paramount factors influencing saltwater distribution at the west and east area. By the end of the twenty-first century there will no longer be suitable water for supply and oil palm plantation based on the local sea-level rise prediction and Ghyben–Herzberg assumption (sharp interface), focusing on the severe erosion area of the study site.

A method of moments approach to model the electromagnetic response of multiple steel casings in a layered earth

In oil and gas production environments, controlled-source electromagnetics can be used to aid brownfield exploration, development, and reservoir monitoring efforts. However, such environments typically have many highly conductive steel-cased wells in the area of interest. We have developed a modeling algorithm using a method of moments (MoM) approach to calculate the electromagnetic response of multiple 3D steel-cased wells of arbitrary geometry in a layered earth conductivity model. This approach involves dividing each casing into a collection of segments, each carrying a uniform current density. A matrix is computed that describes how the casing segments interact with each other electromagnetically. Then, we solve a linear system for the current within each casing segment, given a transmitter of arbitrary frequency and location. From these currents we are able to solve for the secondary electromagnetic fields produced solely by the casings at any point in our layered model, and we add these to the primary fields produced by the transmitter. To validate the algorithm, we compared results with a pseudoanalytic MoM algorithm for a single vertical casing in a half-space. We also compare results with a finite-element solution using Comsol Multiphysics for vertical and single tilted wells buried in various layered earth models. Our results indicate a good match between these different approaches, with tilted casings in a layered model requiring further study. Finally, we applied our algorithm to a realistic synthetic model with three casings (one vertical and two deviated) extending into a layered earth model containing the classic thin resistive layer. This example illustrates how the algorithm can be used to compute the electromagnetic response of multiple steel casings. The example also illustrates how the electromagnetic field changes due to the presence of the casings and how the casings may be used to inject the signal at depth.

Quantitative influence of coast effect on geomagnetically induced currents in power grids: a case study

In recent years, several magnetic storms have disrupted the normal operation of power grids in the mid-low latitudes. Data obtained from the monitoring of geomagnetically induced currents (GIC) indicate that GIC tend to be elevated at nodes near the ocean-land interface. This paper discusses the influence of the geomagnetic coast effect on GIC in power grids based on geomagnetic data from a coastal power station on November 9, 2004. We used a three-dimensional (3D) Earth conductivity model to calculate the induced electric field using the finite element method (FEM), and compared it to a one-dimensional (1D) layered model, which could not incorporate a coastal effect. In this manner, the GIC in the Ling’ao power plant was predicted while taking the coast effect into consideration in one case and ignoring it in the other. We found that the GIC predicted by the 3D model, which took the coastal effect into consideration, showed only a 2.9% discrepancy with the recorded value, while the 1D model underestimated the GIC by 23%. Our results demonstrate that the abrupt lateral variations of Earth conductivity structures significantly influence GIC in the power grid. We can infer that high GIC may appear even at mid-low latitude areas that are subjected to the coast effect. Therefore, this effect should be taken into consideration while assessing GIC risk when power networks are located in areas with lateral shifts in Earth conductivity structures, such as the shoreline and the interfaces of different geological structures.

A Comparison of Peak Electric Fields and GICs in the Pacific Northwest Using 1‐D and 3‐D Conductivity

AbstractGeomagnetically induced currents (GICs) are a result of the changing magnetic fields during a geomagnetic disturbance interacting with the deep conductivity structures of the Earth. When assessing GIC hazard, it is a common practice to use layer‐cake or one‐dimensional conductivity models to approximate deep Earth conductivity. In this paper, we calculate the electric field and estimate GICs induced in the long lines of a realistic system model of the Pacific Northwest, using the traditional 1‐D models, as well as 3‐D models represented by Earthscope's Electromagnetic transfer functions. The results show that the peak electric field during a given event has considerable variation across the analysis region in the Pacific Northwest, but the 1‐D physiographic approximations may accurately represent the average response of an area, although corrections are needed. Rotations caused by real deep Earth conductivity structures greatly affect the direction of the induced electric field. This effect may be just as, or more, important than peak intensity when estimating GICs induced in long bulk power system lines.

The influence of sulfur on the electrical resistivity of hcp iron: Implications for the core conductivity of Mars and Earth

AbstractCosmochemical and geochemical studies suggest sulfur (S) as a light alloying element in the iron‐rich cores of telluric planets, but there is no report of sulfur's alloying effect on the electrical and thermal transport properties of iron (Fe); a subject that is closely related to the dynamo action and thermal evolution of planetary cores. We measured the electrical resistivity of hexagonal‐closed‐packed (hcp) structured Fe alloy containing 3 wt. % silicon (Si) and 3 wt. % S up to 110 GPa at 300 K. Combined with the reported resistivities of hcp Fe and hcp Fe‐Si alloy, we determined the impurity resistivity of S in a hcp Fe matrix at high pressures. The obtained impurity resistivity of S is found to be smaller than that of Si. Therefore, S is a weaker influence on the conductivity of Fe alloy, even if S is a major light element in the planetary cores.

Modeling of the traction current harmonics distribution in rails

Electrified railways are one of the most powerful wide frequency range sources of disturbances that interference on signaling and radio communication systems. This is especially true for new types of vehicles equipped with electronic static converters with pulse width modulation (PWM), from which high-frequency interferences in rails can have frequencies up to several tens of kHz.To ensure the electromagnetic compatibility (EMC) of new types of rolling stock with signaling and radio communication systems, they are subjected to an acceptance procedure that includes on EMC tests in accordance with European and national regulatory standards and norms. But under some unfavorable operation conditions for the trains that were successfully tested and are in operation with old vehicles on the same lines (sometimes with old feeding system), the disturbing current generated by vehicles may reach values greater than the allowed values. As such unfavorable operational conditions may be considered increasing number of trains, low distance between track circuit receiver and vehicles or supply substation, low rail-to-earth conductivity and conductivity of earth. To proof the electromagnetic compatibility (EMC) between rolling stock and signalling systems it is need accurate modeling of the test cases with taking into account particular operation conditions.The aim of the work is to establish mathematical and computer model for distribution of traction current harmonics in direct feeding traction network with multiple vehicles in feeder zone. This model is an evolution and simplification of models represented earlier.The work has been performed in order to proof the electromagnetic compatibility of new trains equipped with electronic static converters with existing traction lines and has been used during tests of new types of train.The model has been simplified as follows. The lines with equal or close to each other potentials are represented as a single line with equivalent electrical parameters. The disturbing vehicles are modeled as sinusoidal current sources with several set of frequencies that are represented by currents vector. Only return current harmonics with frequencies that lie in frequency range of track circuit receiver were considered. Depended of simulation aim the values of harmonics are taken as values measured during train tests or as the maximum interference values according to norms.The distribution of the traction return current harmonics was computed for AC direct feeding traction network 1x25 kV with two-side ESS and with 1 to 5 vehicles in feeder zone. The maximum interference from trains is in the areas nearest to trains and also to the point of connection of return feeder to rails (at ESS terminals). The traction harmonic current in rails are increased with increasing of train number in feeder zone and with decreasing of the rail-to-earth conductivity.The interference at 25 Hz in the rails area near the ESS for one locomotive in feeder zone don’t exceed a limit value of 1 A even in unfavorable operation conditions for of the rail-to-earth conductivity equal 0.02 Sm/km. If number of trains are increased (from 1 to 5) the interference at 25 Hz also increased and it values at rail-to-earth conductivity equal 0.02 Sm/km reach to 1.073 A for two locomotives and to 1.233 A for five locomotives, that exceed the limit value of the interference in rails at 25 Hz.

The Development and Realization System for Calculating GIC of Pipelines

Geomagnetic disturbances (GMD)induce the pipe-to-soil potential(PSP) and geomagnetic induced current (GIC) in pipelines, which may trigger the pipeline steel corrosion. For accessing the impact of geomagnetic disturbances on pipelines, a system has been established to simulate the PSP and GIC. Based on magnetic dates from magnetic observatories, earth conductivity and pipeline parameter, this system has accomplished calculating the PSP and GIC in the pipeline and flowing to/from ground through ground resistances. We also have considered pipelines whether have branch or not, through time-variation and distance-variation such two forms to establish the computation system.

Modeling geomagnetically induced currents

AbstractUnderstanding the geomagnetic hazard to power systems requires the ability to model the geomagnetically induced currents (GIC) produced in a power network. This paper presents the developments in GIC modeling starting with an examination of fundamental questions about where the driving force for GIC is located. Then we outline the two main network modeling approaches that are mathematically equivalent and show an example for a simple circuit. Accurate modeling of the GIC produced during real space weather events requires including the appropriate system characteristics, magnetic source fields, and Earth conductivity structure. It is shown how multiple voltage levels can be included in GIC modeling and how the network configuration affects the GIC values. Magnetic source fields can be included by using “plane wave” or line current models or by using geomagnetic observatory data with an appropriate interpolation scheme. Earth conductivity structure can be represented by 1‐D, 2‐D, or 3‐D models that are used to calculate the transfer function between electric and magnetic fields at the Earth's surface. For 2‐D and 3‐D structures this will involve a tensor impedance function and electric fields that are not necessarily orthogonal to the magnetic field variations. It is now technically possible to include all these features in the modeling of GIC, and various software implementations are being developed to make these features more accessible for use in risk studies.

ANALYSIS OF ELECTROMAGNETIC INFLUENCE ON STEEL PIPELINES FROM THE ELEMENTS OF ELECTRIC POWER SYSTEM

A b s t r a c t: Power transmission lines often share same corridors with steel pipelines for oil and gas. When phase to ground fault occurs, high voltages may appear on the pipelines due to different mechanisms of mutual coupling. These voltages propagate at long distances from the fault location, and may pose a serious threat for the safety of the personnel and integrity of the pipeline. To provide adequate protection, calculation of the mutual coupling is required during the design stage of systems. Induced voltages are strongly influenced by the disposition of the both systems, their configuration and characteristics, elements that mutually interact etc. In this paper, we analyze induced voltages on practical pipeline system. Parametric analysis will show how far interventions on both systems can influence the induced voltages. Key words: electromagnetic influence; gas; oil; pipelines; safety REFERENCES: [1] Guide on the Influence of High Voltage AC Power Systems on Metallic Pipelines. Paris, CIGRE Working Group 36. 02, 1995. [2] Directives Concerning the Protection of Telecommunication Lines аgainst Harmful Effects from Electric Power and Electrified Railway Systems. Volume II: Calculating Induced Voltages and Currents in Practical Cases, Geneva, CCITT, 1989. [3] Guide for Assessment of Transferred EPR on Telecommunication Systems Due to Faults in A.C. Power Systems. Paris, CIGRE Working Group C4. 207, 2014. [4] Sunde. E. D.: Earth Conduction Effects in Transmission Systems. New York: Dover, 1968. [5] Wait, J. R.: Theory of Wave Propagation along a Thin Wire Parallel to an Interface. Radio Science. Vol. 7. pp. 675–679 (1972). [6] Directives Concerning the Protection of Telecommunication Lines against Harmful Effects from Electric Power and Electrified Railway Systems, Volume III, Capacitive, Inductive and Conductive Coupling: Physical theory and calculation methods, Geneva, CCITT, 1989. [7] Grcev, L., Dawalibi, F.: An Electromagnetic Model for Transients in Grounding Systems. IEEE Trans. on Power Delivery. Vol. 5. pp. 1733–1781 (1990). [8] Smith, A. A.: Coupling of External Electromagnetic Fields to Transmission Lines. New York: Wiley, 1977. [9] МКС EN 50443:2012 – Effects of Electromagnetic Interference on Pipelines Caused by High Voltage A.C. Electric Traction Systems and/or High Voltage A.C. Power Supply Systems, Brussels: CENELEC, 2011. [10] NACE SP0177-2014 – Mitigation of Alternating Current and Lightning Effects on Metallic Structures and Corroion Control Systems. Houston, Texas: NACE International, 2014. [11] Mangionem, S.: Compact Model of a Combined Overhead-Cable Line for Ground Fault Application Transfer Analysis, Proc. of the 5 th WHEAS Int. Conf. on Power Systems and Electromagnetic Compatibility. August 23–25, 2005, pp. 251–256.