Secondary Electric Field Research Articles

Accurate Interpolation at Receiver Positions: A Novel Method for Frequency-Domain Marine CSEM Finite-Difference Modelling

We present an accurate interpolating method for calculating electric and magnetic fields at the seafloor with a resistivity contrast. This method is applied to the three-dimensional (3D) frequency-domain marine controlled-source electromagnetic (CSEM) modeling with the towed transmitters and receivers located at the seafloor. We simulate the 3D marine CSEM responses by the staggered finite-difference method with a direct solver. The secondary-field approach is used for avoiding the source singularities and the primary fields excited by the electric dipole source could be calculated quasi-analytically for the one-dimensional layered background. Therefore, in this study, we focus on interpolating of electric and magnetic fields to the receiver locations at the seafloor interface between the conductive seawater and resistive seafloor formation. Considering the discontinuity of the normal electric fields, we use the normal current electric density for interpolation. The secondary electric and magnetic fields are also used for interpolation instead of the total fields for high numerical accuracy. The proposed interpolation only utilizes the nodes below/above the seafloor interface and is approved to be much more accurate than other tested interpolating methods, i.e., the conventional linear interpolation and the rigorous interpolation.

Mask-assisted electrospray for superoleophobic surfaces: An experimental and numerical study

This paper presents both experimental work and numerical simulations of formation of superoleophobic surfaces created by mask-assisted electrospraying, followed by a second layer overlay and fluoropolymer treatment. The primary electric field focusing in the mask-assisted electrospray effectively guides the electrosprayed particulates into the mesh openings, forming characteristic pyramid-shaped pillars. The secondary focusing occurs during the overlay deposition when the electrosprayed particulates favorably deposit onto the pre-patterned pillars. Systematic studies were conducted on the effects of mask-substrate-gap and duration of the overlay deposition on the pattern morphology and wetting performance. A shorter mask-substrate-gap results in a stronger focusing effect and pillars with a larger aspect ratio. The overlay deposition firstly increases the pillar height and then changes the pillar shape from pyramids to domes with overhangs due to electrostatic interactions. All the surfaces are superhydrophobic, however, superoleophobicity varies. Surfaces that have tall pillars and overhang structures demonstrate robust superoleophobicity when compared to their counterparts with shorter pillars and absence of overhang structures. The primary and secondary electric field focusing effects exerted by the mask and the pre-patterned pillars, and their roles in pattern formation have been numerically investigated by COMSOL Multiphysics simulation. A reasonable agreement has been obtained between the numerical predictions and experimental results.

3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

The controlled source extremely low frequency (CSELF) electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) inversion of CSELF electromagnetic data is presented (in which the sources, or primary fields, are included), with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.

3D parallel inversion of time-domain airborne EM data

To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical.

Interference from the sea surface near the electrostatic system location

The solution of the problem of the spatial structure of the secondary electric field due to rough sea surface in the field of third-party sources. It is shown that the energy spectrum of two-dimensional components of the electric field is determined as a result of the two-dimensional spatial filter filters the energy spectrum of sea surface height. Shows the frequency characteristics of the spatial filter and temporal power spectra of the components of the electric field when driving electrostatic locator over the sea surface.

Feasibility of Fiber-Deposition Control by Secondary Electric Fields in Near-Field Electrospinning

Product miniaturization has become a trending technology in a broad range of industries and its development is being pushed by the requirements for complexity and resolution of micromanufactured products. However, there still exists a gap in the manufacturing spectrum for complex three-dimensional (3D) structure generation capabilities with micron and submicron resolution. This paper extends the near-field electrospinning (NFES) process and develops a direct-writing (DW) technology for microfiber deposition with micrometer resolution. The proposed method presented uses an auxiliary electrode to generate an electric field perpendicular to the fiber flight path. This tunable electric field grants the user real-time control of the fiber flight path, increasing the resolution of the deposited structure. The use of an auxiliary electrode ring for fiber manipulation is proposed to further improve control over the deposition process.

On smoke rings produced by a loop buried in a conductive half-space

The transient electromagnetic (TEM) response of a wire loop at the surface of the earth has been studied in detail for several decades. When current in the loop is rapidly switched off, an identical system of current, commonly referred to as a “smoke ring,” is induced in the conductive subsurface and diffuses downward and outward into the earth. What has not been studied as thoroughly is the response of a loop buried within a conductive medium, as might be the case in the marine environment or when TEM prospecting systems are placed in mine tunnels or horizontal boreholes. We have examined the TEM response of a horizontal wire loop buried within a conductive half-space. Expressions were derived for the azimuthal electric field and corresponding vertical and radial magnetic fields. Our results showed that when the loop is far from the earth-air interface, a single smoke ring system diffuses radially outward from the transmitter, while the electric field and corresponding current density decays away in the vertical direction. As the loop approaches the interface, the smoke ring system diffuses radially at early times, but gradually, the complex image of the loop in the air produces a system of secondary azimuthal electric fields, which, when combined with the primary field, adds a vertical component to the field diffusion. At late times, the field behavior reduces to the well-known surface case and the maximum current system diffuses downward at a constant angle of 26° with respect to the plane of the loop. We concluded that it was the effect of the interface that produces the downward migration of a smoke ring system, whereas the outward migration is mainly generated by the primary field.

Electrospun Poly(3‐hexylthiophene) Nanofibers with Highly Extended and Oriented Chains Through Secondary Electric Field for High‐Performance Field‐Effect Transistors

An extra electric field is introduced below the spinneret in an electro­spinning setup for producing poly(3‐hexylthiophene) (P3HT) nanofibers. The liquid jet is greatly prolonged by the additional extensional force and thinner fibers can thus be obtained. The chain conformation and orientation in fibers are probed by differential scanning calorimetry and X‐ray diffraction techniques. Under the influence of the secondary electric field, P3HT chains are extensively stretched and aligned along the fiber axis. The electrospun P3HT nanofibers are fabricated into field‐effect transistors and the charge carrier mobilities of the nanofibers with and without secondary electric field are found to be 1.54 × 10−4 and 1.62 × 10−1 cm2 V−1 s−1, respectively. The dramatic enhancement of mobility by more than 1000 times is due to the effective charge transport through the delocalization of electrons along the highly extended and oriented P3HT backbones rather than the ordinary π–π stacking. In addition to P3HT, it is found that this simple method also works for poly(3‐alkylthiophene).

Three‐dimensional modelling of controlled‐source electromagnetic surveys using an edge finite‐element method with a direct solver

ABSTRACTA fully three‐dimensional finite‐element algorithm has been developed for simulating controlled‐source electromagnetic surveys. To exploit the advantages of geometric flexibility, frequency‐domain Maxwell's equations of the secondary electric field were discretised using edge‐based finite elements while the primary field was calculated analytically for a horizontally layered‐earth model. The resulting system of equations for the secondary field was solved using a parallel version of direct solvers. The accuracy of the algorithm was successfully verified by comparisons with integral‐equations and iterative solutions, and the applicability to models containing large conductivity contrasts was verified against published data. The advantages of geometry‐conforming meshes have been demonstrated by comparing different mesh systems to simulate an inclined sheet model. A comparison of the performance between direct and iterative solvers demonstrated the superior efficiency of direct solvers, particularly for multisource problems.

Effects of near-surface inhomogeneities on MT responses: An analytical model

An analytical model is suggested to describe the electrostatic field produced by near-surface inhomogeneities responsible for galvanic shift in magnetotelluric (MT) apparent resistivity sounding curves. The near-surface inhomogeneities are modeled in thin-sheet approximation with laterally variable longitudinal conductance and transverse resistance. The model accounts for the TM (transverse magnetic) mode secondary electric field in the conductive layered subsurface below the thin sheet. Equations have been obtained to relate the subsurface geoelectric parameters and the spatial harmonics of the secondary electrostatic field. This secondary field, which is the source of galvanic shift in MT data, turns out to be in-phase with the primary field. The equations derived to simulate galvanic distortions are applicable to long-period MT data acquired by a synchronous array.

Backflow-mediated domain switching in nematic liquid crystals.

We study the dynamics of the nematic liquid crystal kickback effect upon removal of a primary electric field and its amplification by a perpendicular secondary electric field resulting in the formation of domains with a reverse director orientation. Using computational fluid dynamics, we show that the domain formation is a robust phenomenon that takes place also in the complex case of multiple irregular random Freedericksz domains in three dimension as they appear in a realistic experimental situation. We propose domain switching by kickback amplification as a tool for self-insertion of shell-like inhomogeneities into an otherwise perfectly uniform director field configuration.

3D MT Data Modelling using Multi-order Hexahedral Vector Finite Element Method, including Anisotropy and Complex Geometry

We will present the progress made on the development of a computational algorithm to model 3D Magnetotelluric data using Vector Finite Element Method (VFEM). The differential equations to be solved are the decoupled Helmholtz equations for the secondary electric field, or the secondary magnetic field, with a symmetric conductivity tensor. These equations are modified to include anisotropic earth and complex geometry (such as surface topography, and subsurface interfaces). The primary field is the solution of an air domain, homogeneous half-space or layered earth. This study will compare the application of two boundary conditions, the Generalize Perfect Matched Layers method (GPML) versus Dirichlet boundaries. Dirichlet boundary conditions are applied on the tangential fields, assuming that the boundaries lie far away from the inhomogeneous model. The GPML scheme defines an artificial boundary zone that absorbs the propagating and evanescent electromagnetic fields, to remove boundary effects (Fang, 1996). In this algorithm, high order edge elements are defined based on covariant projections for hexahedral elements (Crowley, et al., 1988). The vector basis functions are defined for the 12 edges (linear) element, 24 edges (quadratic) element, and 48 edges (cubic) element. By this definition, the vector basis will have zero divergence in the case of rectangular elements and relatively small divergence in the case of distorted elements. They are defined to study their numerical accuracy and speed, and to see if the divergence correction is automatically satisfied.

Theory of Cowling channel formation by reflection of shear Alfven waves from the auroral ionosphere

AbstractWe present the first complete formulation of the coupling between the ionospheric horizontal currents (including Hall currents) and the field‐aligned currents (FAC) via shear Alfven waves, which can describe the formation of a Cowling channel without any a priori parameterization of the secondary (Hall polarization) electric field strength. Our theory reorganizes the Cowling channel by “primary” and “secondary” fields. Until now there are no theoretical frameworks, which can derive these separated components from observed or given total conductance, electric field, and FAC distributions alone. But when a given incident where Alfven wave is considered as the driver, the reflected wave can be uniquely decomposed into the primary and secondary components. We show that the reflected wave can, depending on actual conditions, indeed carry FAC that connect to divergent Hall currents. With this new method, we can identify how large the secondary electric field becomes, how efficiently the divergent Hall current is closed within the ionosphere, and how much of the Hall current continues out to the magnetosphere as FAC. In typical ionospheric situations, only a small fraction of FAC is connected to Hall currents at conductance gradients, i.e., the secondary field is relatively strong. But when conductances are relatively low compared with Alfven conductance and/or horizontal scales smaller than ~10 km, the Hall FAC may become significant.

A Low-Frequency Electromagnetic Near-Field Inverse Problem for a Spherical Scatterer

The interior low-frequency electromagnetic dipole excitation of a dielectric sphere is utilized as a simplified but realistic model in various biomedical applications. Motivated by these considerations, in this paper, we investigate analytically a near-field inverse scattering problem for the electromagnetic interior dipole excitation of a dielectric sphere. First, we obtain, under the low-frequency assumption, a closed-form approximation of the series of the secondary electric field at the dipole’s location. Then, we utilize this derived approximation in the development of a simple inverse medium scattering algorithm determining the sphere’s dielectric permittivity. Finally, we present numerical results for a human head model, which demonstrate the accurate determination of the complex permittivity by the developed algorithm.

3-D Modeling the Magnetic Field due to Ocean Tidal Flow O1

The tidal motion of the ocean water through the ambient magnetic field, generates secondary electric and magnetic field. The magnetic fields generated by the diurnal (O1) ocean flow can be clearly detected. We simulate the magnetic signals for tidal constituents –diurnal (O1) tides. The idea of exploiting tidal signals for EM studies of the Earth is not new, but so far it was used only for interpretation of inland and transoceanic magnetic field data due to O1. Emphasis in this work is made on a discussion of sea bottom electric field of the same origin.

An application of the finite length Cowling channel model to auroral arcs with longitudinal variations

A physical process for the latitudinal motion of an auroral arc based on the four‐side bound Cowling channel model is proposed. Assuming that an upward field‐aligned current (FAC) is associated with the auroral arc that forms a Cowling channel with finite lengths not only latitudinally but also longitudinally and that the upward FAC region is primarily embedded in a purely northward electric field, the primary Hall current driven by the northward electric field accumulates positive excess charges at the eastern edge of the channel and negative charges at the western edge for a perfect or partial Cowling channel with a nonzero Cowling efficiency. The charges produce a westward secondary electric field, indicating that a westward electric field can thus be produced by a purely northward primary electric field. This secondary electric field moves the arc with its magnetospheric source drifting together with the magnetospheric plasmas equatorward and simultaneously produces the electric field outside the channel that moves the downward FAC equatorward of the upward FAC region equatorward together with the upward FAC. Thus, the whole 3‐D current system is expected to move equatorward as often observed in the afternoon auroral zone.

Effect of A-site La and Ba doping on threshold field and characteristic temperatures of PbSc0.5Ta0.5O3 relaxor studied by acoustic emission

The structural transitions in Pb1−xLaxSc(1+x)/2Ta(1−x)/2O3, x = 0.08 (PLST) relaxor crystals were studied by means of acoustic emission (AE) under an external electric field (E) and compared with those observed in pure PbSc0.5Ta0.5O3 (PST) and Pb0.78Ba0.22Sc0.5Ta0.5O3 (PBST) [E. Dul'kin et al., EPL 94, 57002 (2011)]. Similar to both the PST and PBST compounds, in zero field PLST exhibits AE corresponding to a para-to-antiferroelectric incommensurate phase transition at Tn = 276 K, lying in the vicinity of dielectric temperature maximum (Tm). This AE signal exhibits a nontrivial behavior when applying E resembling the electric-field-dependence of Tn previously observed for both the PST and PBST, namely, Tn initially decreases with the increase of E, attains a minimum at a threshold field Eth = 0.5 kV/cm, accompanied by a pronounced maximum of the AE count rate Ṅ = 12 s−1, and then starts increasing as E enhances. The similarities and difference between PST, PLST, and PBST with respect to Tn, Eth, and Ṅ are discussed from the viewpoint of three mechanisms: (i) chemically induced random local electric field due to the extra charge on the A-site ion, (ii) disturbance of the system of stereochemically active lone-pair electrons of Pb2+ by the isotropic outermost electron shell of substituting ion, and (iii) change in the tolerance factor and elastic field to the larger ionic radius of the substituting A-site ion due to the different radius of the substituting ion. The first two mechanisms influence the actual values of Tn and Eth, whereas the latter is shown to affect the normalized Ṅ, indicating the fractions undergoing a field-induced crossover from a modulated antiferroelectric to a ferroelectric state. Creation of secondary random electric field, caused by doping-induced A-site-O ionic chemical bonding, is discussed.

A thin-sheet model for global electromagnetic induction

We consider the frequency domain electromagnetic (EM) induction problem in a layered spherical Earth overlain by an inhomogeneous thin sheet of finite conductance, and derive an integral equation for the secondary electric fields resulting from surface conductivity variations. The Green′s function kernel of the integral equation is singular, and must in practice be regularized for a numerical treatment. We compare two approaches: truncation of the spherical harmonic representation of the Green′s function, and projection onto a discrete spatial grid, with elements of the resulting discrete system matrix evaluated as contour integrals. In either case rotational symmetry and the fast Fourier transform (FFT) may be exploited to reduce computational costs, and Krylov space methods may be used to solve the resulting discretized integral equation efficiently. We illustrate the methods for several source field geometries. The two regularization schemes result in solutions that agree well at large scales, but exhibit substantial differences as the nominal resolution is approached. The agreement improves with increased resolution. Although the level of solution errors for the two approaches is likely comparable in an L2 sense, the truncation approach results in Gibb′s oscillations near sharp conductivity contrasts. These may be reduced by tapering the truncated kernel, essentially equivalent to low-pass filtering the solution.

The Modeling of 2D Controlled Source Audio Magnetotelluric (Csamt) Responses Using Finite Element Method

This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solution for homogeneous earth and it is used to calculate the secondary electric field in the inhomogeneous Helmholtz Equation. Calculation of Helmholtz Equation is carried out using the finite element method. Validation of this modeling is conducted by comparison of numerical results with 1D analytical response for the case of homogeneous and layered earth. The comparison of CSAMT responses are also provided for 2D cases of vertical contact and anomalous conductive body with the 2D magnetotelluric (MT) responses. The results of this study are expected to provide better interpretation of the 2D CSAMT data.

Effects of Head Geometry, Coil Position and CSF Displacement on Field Distribution Under Transcranial Magnetic Stimulation

In this study the effects of a realistic head geometry, coil position and head orientation on the spatial distribution of induced electric field, under TMS, have been investigated using statistical modalities such as RDM, MAG and CC. It has been observed that the secondary electric field, caused by the asymmetry of the geometry, leads to a dramatic drop in E-field magnitude, causes deviation in field focality and accelerates its decay. The results show that the head geometry, coil position and head orientation play an important role in shaping the spatial distribution of induced electric field