Induction Vector Research Articles

Sq effect on the electromagnetic response functions in the period range between 104 and 105 s

SUMMARY Geomagnetic induction responses such as geomagnetic depth sounding (GDS), magnetotelluric (MT), and horizontal geomagnetic transfer function (HTF) at long periods are used to estimate the electrical conductivity in the deep mantle. The responses in the period range that are shorter than 10 5 s (about 1 day) are in many cases considered to be local or regional induction problems in which the source field is approximated by plane waves and therefore the sphericity of Earth is not taken into account. In the period range between 10 4 and 10 5 s, the most dominant signature of the magnetic field variation is the solar quiet daily (Sq) variation and its higher harmonics. Therefore, when we obtain the responses due to the quasi-white background spectrum composed of plane waves, we regard the Sq field variations as noises in estimating the responses, and line spectra of the variations are removed from the observed time-series before the responses are calculated. However, with this approach, the calculated responses tend to possess a discontinuity at a period of about 10 4 s, and the response functions show common features at longer periods irrespective of the location of the observation site. It is particularly well known that the imaginary part of the induction vector tends to have a significant westward component for periods ranging between 10 4 and 10 5 s. Such features cannot be easily explained by the effect of the electrical conductivity structure alone. Examination of the phase of the HTF implies that the responses in the same period range are affected by the signature of sources of finite wavelength moving westward. Thus, it is suggested that the response functions in this period range were under the effect of the Sq field variations, even though the line spectra of them were removed and the responses were estimated at periods separate from the harmonic periods of Sq field variation. We examined how the influences of the Sq field appear on the responses numerically by a forward modelling. Results show most of the characteristic features in observed response functions can be ascribed to Sq source effects.

Multipole expansions in magnetostatics

Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out.

On magnetic field of ring current

The explicit expression for magnetic induction vector of a ring current at arbitrary point in toroidal coordinates is presented in terms of the full elliptic integral of the first kind and its derivative over integral modulus. There is a conjugated point for any observation point: it is an image of the latter in a sphere with the ring current as its equator. The conjugated point lies on the same vector and has the same integral modulus as the initial point.

Attitude control system of the first Russian nanosatellite TNS-0 no. 1

The results of designing the attitude control system of the first Russian nanosatellite TNS-0 no. 1 providing orientation of its longitudinal axis along the local geomagnetic field induction vector are presented. The system consists of a permanent magnet and two sets of hysteresis rods. The magnetic and geometric parameters of the magnet and rods are calculated. The influence of the permanent magnet field on the hysteresis rods and mutual influence of the rods in the case of compact satellite packaging are analyzed. Examples of calculations of transient processes and steady-state angular satellite motion are presented.

Erratum to: ”Fast Calculation of the Sensitivity Matrix for Responses to the Earth’s Conductivity: General Strategy and Examples”

Modern electromagnetic studies of the Earth deal with three-dimensional data sets and their inversion in the class of three-dimensional models. Due to the large scale of the 3D inverse problem, it is usually solved using gradient-type iteration techniques. These techniques require repeated calculations of the gradient of the penalty function (i.e., the sum of the misfit and the regularization term) with respect to the model parameters that describe the spatial distribution of conductivity. Since there are generally no analytical tools for calculating the misfit gradient, its computation requires the application of some numerical techniques. Unfortunately, it is impossible to perform mass calculations of the misfit gradient even using modern computing if one applies conventional numerical differentiation. In reality, in this case the number of calls of the forward problem is proportional to the number of the sought parameters, which is very large in case of a 3D inversion. However, there is a much more efficient method for calculation of the misfit gradient, namely, the adjoint-field technique. At present, this technique is widely used in the numerical schemes of the 3D inversion of electromagnetic and other data. With this technique we can calculate the misfit gradient with the same computational burden as that required for the solution of a single additional forward problem. Although this technique is widely used, we failed to find any comprehensive description of this technique in the literature that would allow one to apply this approach for any particular scheme of sounding, profiling, or transillumination as easily as a general formula is applied for a given case. In the present paper, we obtain general formulas for the quick calculation of the derivatives of the frequency-domain responses and the derivatives of the misfit function with respect to the variations in conductivity. We also show how the derived general formulas are transformed into particular expressions when we consider the response functions of the conventional and generalized magnetotelluric methods. In addition, we demonstrate how to apply our general methodology to the inversion of magnetovariational induction vectors (tippers), the phase tensor, and multipoint transfer functions, namely, the horizontal magnetic and telluric tensors.

On magnetic field of ring current

The explicit expression for magnetic induction vector of a ring current at arbitrary point in toroidal coordinates is presented in terms of the full elliptic integral of the first kind and its deri...

Development and laboratory verification of control algorithms for formation flying configuration with a single-input control

Once been orbited, the technological nanosatellite TNS-0 no. 1 is supposed to be used in one of the next missions for the demonstration of orbital maneuvering capability to eliminate a secular relative motion of two satellites due to the J2 harmonic of the Earth gravitational field. It is assumed that the longitudinal axis of the satellite is stabilized along the induction vector of the geomagnetic field and a thruster engine is installed along this axis. Continuous and impulsive thruster control algorithms eliminating the secular relative motion have been developed. Special equipment was developed in ZARM for demonstration and laboratory testing of the satellite motion identification and control algorithms. The facility consists of a horizontal smooth table and mobile mock-up that enables to glide over the table surface due to compressed air stored in on-board pressure tanks. Compressed air is used to control the translation and attitude motion of the mock-up equipped with a number of pulse thrusters. In this work a dynamic model for mock-up controlled motion over the table is developed. This allows us to simulate a relative motion of a pair of TNS-0 type nanosatellites in the plane of the orbit.

Method of first integrals and interface, surface waves

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or based on the one for the traction vector was introduced recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves, the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii) Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

Application of the 3D magnetotelluric inversion code in a geologically complex area

ABSTRACTThe WSINV3DMT code makes the implementation of 3D inversion of magnetotelluric data feasible using a single PC. Audio‐magnetotelluric data were collected along two profiles in a Cu‐Ni mining area in Xinjiang, China, where the apparent resistivity and phase curves, the phase tensors and the magnetic induction vectors indicate a complex 3D conductivity structure. 3D inversions were carried out to reveal the electrical structure of the area. The final 3D model is selected from the inversion results using different initial Lagrange values and steps. The relatively low root‐mean‐square (rms) misfit and model norm indicate a reliable electrical model. The final model includes four types of low resistivity areas, the first ones coincide with the known location of an orebody and further forward modelling indicates that they are not in full connectivity to form a low resistivity zone. The second ones are not controlled by magnetotelluric sites and embody little information of the observed data, they are considered as tedious structures. The third one is near to the regional Kangguer fault and should be treated carefully considering the effect of the fault. The last ones are isolated and existing at a limited level as the first ones, they should be paid more attention to.

Algorithm of the analytic solution of magnetostatic inverse problem in magnetocardiography

Event Abstract Back to Event Algorithm of the analytic solution of magnetostatic inverse problem in magnetocardiography Michael Primin1*, Igor Nedayvoda1 and Yury Maslennikov2 1 Academy of Science of Ukraine, Institute of cybernetics, Ukraine 2 Cryoton Ltd, Russia Development of analytical method of magnetostatic inverse problem solution is proposed for investigation of magnetic field of human heart. Set of N different dipole sources is ascribed to spatial distribution of heart magnetic field parameters, measured in observation plane. Every dipole is supposed to have at least one point in the measurement plane, where the dipole’s magnetic field coincides with known (calculated on the basis of observed data) magnetic induction vector values and with all of it's spatial first-order derivates. Estimations of sources quantity for investigated timepoint of cardiocycle, their mutual locations and relative powers are obtained as a result of magnetic gradient intensity's spatial analysis in the signal's measuring plane and as a result of the Voronoy's diagram construction.Conditions and the correct magnetostatic inverse problem solution for several signal sources distributed independently in heart's three-dimesional volume are obtained through investigations. An algorithm of a system of cross-sections corresponding to a set of F-planes parallel to the measurement plane and forming a virtual three-dimensional space with the magnetic signal source was developed for the visualization of magnetostatic inverse problem solution results. In standard display mode 20 equidistant cross-sections with 1 centimeter step are used. In the “nonregular grid” display mode the distance between cross-sections is 0,5 centimeter whereas their quantity is determined in the process of the inverse problem solution's spatial analysis. Algorithm of inverse problem solution is realized in magnetocardiograph software and is used in real magnetocardiogramm investigation and analysis. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: MCG: Instrumentation, Modeling, Basic and Clinical Studies Citation: Primin M, Nedayvoda I and Maslennikov Y (2010). Algorithm of the analytic solution of magnetostatic inverse problem in magnetocardiography. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00318 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 06 Apr 2010; Published Online: 06 Apr 2010. * Correspondence: Michael Primin, Academy of Science of Ukraine, Institute of cybernetics, Kiev, Ukraine, prima_m@voliacable.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Michael Primin Igor Nedayvoda Yury Maslennikov Google Michael Primin Igor Nedayvoda Yury Maslennikov Google Scholar Michael Primin Igor Nedayvoda Yury Maslennikov PubMed Michael Primin Igor Nedayvoda Yury Maslennikov Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

DC corona discharge ozone production enhanced by magnetic field

We have studied the effect of a stationary magnetic field on the production of ozone from air at atmospheric pressure by a negative corona discharge in a cylindrical electrode configuration. We used a stainless steel hollow needle placed at the axis of the cylindrical discharge chamber as a cathode. The outer wall of the cylinder was used as an anode. The vector of magnetic induction was perpendicular to the vector of current density. We found that: (a) the magnetic field extends the current voltage range of the discharge; (b) for the discharge in the Trichel pulses regime and in the pulseless glow regime, the magnetic field has no substantial effect on the discharge voltage or on the concentration of ozone that is produced; (c) for the discharge in the filamentary streamer regime for a particular current, the magnetic field increases the discharge voltage and consequently an approximately 30% higher ozone concentration can be obtained; (d) the magnetic field does not substantially increase the maximum ozone production yield. A major advantage of using a magnetic field is that the increase in ozone concentration produced by the discharge can be obtained without additional energy requirements.

The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data

SUMMARY An existing time-domain spectral-finite element approach for the forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite is, in this paper, supplemented by a new method of computing the sensitivity of the CHAMP electromagnetic induction data to the Earth's mantle electrical conductivity, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data at the satellite's altitude are the X magnetic component measured by the CHAMP vector magnetometer along the satellite track for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of these differences summed up over all CHAMP tracks determine the misfit. The sensitivities of the CHAMP data, that is the partial derivatives of the misfit with respect to mantle conductivity parameters, are then obtained by the scalar product of the forward and adjoint solutions, multiplied by the gradient of the conductivity and integrated over all CHAMP tracks. Such exactly determined sensitivities are checked against numerical differentiation of the misfit, and good agreement is obtained. The attractiveness of the adjoint method lies in the fact that the adjoint sensitivities are calculated for the price of only an additional forward calculation, regardless of the number of conductivity parameters. However, since the adjoint solution proceeds backwards in time, the forward solution must be stored at each time step, leading to memory requirements that are linear with respect to the number of steps undertaken. Having determined the sensitivities, we apply the conjugate gradient method to infer 1-D and 2-D conductivity structures of the Earth based on the CHAMP residual time series (after the subtraction of static field and secular variations as described by the CHAOS model) for the year 2001. We show that this time series is capable of resolving both 1-D and 2-D structures in the upper mantle and the upper part of the lower mantle, while it is not sufficiently long to reliably resolve the conductivity structure in the lower part of the lower mantle.

Two-dimensional problem of electromagnetoelasticity for multiply connected media

We propose a method for the solution of connected two-dimensional and plane problems of electromagnetoelasticity for multiply connected domains. Basic relations of two-dimensional and plane problems are obtained. Generalized complex potentials of electromagnetoelasticity are introduced and investigated. Boundary conditions for their determination and, using them, expressions of main characteristics of the electromagnetoelastic state (stresses, displacements, electromagnetic field intensity vectors, induction vectors, potentials of the electric and magnetic fields) are obtained. We present a solution of the problem for a plate with an elliptic hole or a crack.

Hydrothermal system beneath the crater of Tarumai volcano, Japan: 3-D resistivity structure revealed using audio-magnetotellurics and induction vector

Audio-magnetotelluric (AMT) measurements were recorded in the crater area of Tarumai volcano, northeastern Japan. This survey brought the specific structures beneath the lava dome of Tarumai volcano, enabling us to interpret the relationship between the subsurface structure and fumarolic activity in the vicinity of a lava dome. Three-dimensional resistivity modeling was performed to achieve this purpose. The measured induction vectors pointed toward the center of the dome, implying the topographic effect. However, estimation of the topographic effect showed that the measured vector was not explained only by this effect. This suggested that the distribution of induction vectors still held information of the subsurface structure and could be helpful in determining the geometry of 3-D bodies. The 3-D modeling was based on a quasi-one-dimensional layered structure that included topography. The final model revealed that the andesitic lava dome is characterized by comparatively low resistivity (50 Ωm), and that two conductive bodies (50 and 1–5 Ωm) are present beneath the lava dome. The shallower of these conductors is interpreted as an aquifer, such as a buried crater lake. The deeper, extremely conductive body corresponded to a convecting zone containing rising hydrothermal fluid. The shallower aquifer critically controls the temperature and chemical components of the fumarolic gasses. High-temperature gas supplied from deeper part that encounters the shallow aquifer loses its water-soluble components and heat, resulting in weak and low-temperature fumaroles. In contrast, most of the gas, which ascends outside the area of the shallower aquifer, is released as high-temperature fumaroles. This study provides an insight that the shallow aquifer in the crater area plays a significant role in the property of fumaroles at the volcanic surface.

A discussion of bias in magnetotelluric responses

Magnetic-field noise biases magnitudes of magnetotelluric response functions such as resistivity, impedance, and the induction vector (tipper). This is particularly severe in the so-called dead band between about 1- and [Formula: see text] periods. The standard approach to remove these biases is to use a magnetic remote reference. In cases where this is unavailable or does not work because noise is correlated at the local and remote sites, it is possible to extract unbiased estimates using an inversion algorithm that predicts the magnitude from the phase. However, an important condition for this to be successful is that phase estimates are unbiased. Phase can be biased if parallel components of the electric and magnetic fields are correlated. This arises when the structure is 3D or when a 2D response is estimated in coordinates not parallel to strike. Improvements in electric field measurements make electric field references a viable option for estimating low-bias responses up to periods approaching [Formula: see text].

The wideband [0.001 Hz–100 kHz] interferometry project in Central Italy

ABSTRACTWe are reporting some results and future planning of the Magnetic and Electric fields Monitoring Project. The principal purpose of the project is to create a network of observatories for monitoring the electromagnetic signals in the 0.001 Hz–100 kHz frequency bands in Central Italy. These bands include both natural and artificial signals. The technological objectives of the project are the development of new instrumentation and the know‐how transfer to the industry. These instruments were tested in the Geomagnetic Observatory of L'Aquila, the first station of the network. Here we show some examples of the developed electric and magnetic sensors. These instruments are designed for the automatic long‐term recording of the electromagnetic fields in a wide band of frequency. The preliminary results of the first operating station of the network are shown taking into account, in the signal elaboration, the single station approach. Here we are reporting some examples concerning the calculation of the ground electric resistivity profile, the evaluation of the magnetic induction vectors and the study of the magnetic sources by the eigenvectors calculation. When all the stations of the network will be in operation, the use of an innovative technique, the wideband interferometry will be proposed. Combining the simultaneous observations of the electromagnetic field measured in each station, we will be able to obtain detailed information about the investigated electromagnetic sources.

Characteristics of the statistical distribution of the current transmitted by a cathode spot of a vacuum arc in variously oriented magnetic fields

The influence of variously oriented uniform magnetic fields on the cathodic attachment of a low-current vacuum arc with electrodes made of oxygen-free copper and CuCr30 composition is studied. It is found that, if the current is fixed, cathode spots in the arc attachment are distributed by the normal law in the entire range of variation of the amplitude of magnetic induction vector B and angle α between this vector and the normal to the cathode surface. The parameters of the distribution depend on the magnetic field and cathode material. The magnetic field dependence is appreciable only when angle α exceeds some critical value α* (α* ≈ 30° and ≈45° for cathodes made of copper and CuCr30, respectively). At α > α*, the parameters of the distribution become strongly dependent on α, while the B dependence remains weak. Only when α → π/2 does the field amplitude have a pronounced effect on the parameters of the distribution. From the obtained results, we determine the statistical characteristics of the distribution of the mean current transmitted by a cathode spot in variously oriented magnetic fields. The found relationships make it possible to explain the peculiarities of the structure of the cathodic attachment of the high-current vacuum arc stabilized by an external axial magnetic field.

Orbital corrections by a single-input impulsive control applied along the geomagnetic field

This paper examines the possibility of regular orbital corrections for a satellite controlled by an impulsive force applied along the induction vector of the local geomagnetic field. The main purpose of the correcting considered in the paper is to eliminate the drift in secular variation of the relative orbital parameters over the orbital period. The obtained results are applied to the formation flying problem. The developed method is tested using numerical simulation.

The Jeju dataset: Three-dimensional interpretation of MT data from mid-mountain area of Jeju Island, Korea

Magnetotelluric (MT) surveys have been performed along five lines in the Jeju volcanic island located at South Sea of Korea. The purposes of the MT surveys are to see if there still remains thermal regime and if there exist deeply extended fractures or an aquifer system beneath the mid-mountain region of Mt. Halla in Jeju. By performing Audio-frequency MT (AMT) surveys together with MT surveys at each site and by operating far-remote reference site of approximately 480 km apart, we could get a broadband (10 − 4 –10 4 Hz) MT dataset of totally 108 sites with very good quality. 3D inversion of MT data from 88 measurement sites gives a reasonable estimation of the subsurface structures beneath the island. An induction vector analysis and 3D inversion results commonly indicate the existence of a conductive anomaly extended down to a few-kilometer depth beneath the central part of the island, which can be related to ancient volcanic activities. Because the island is surrounded by electrically conductive sea and has steep topographic variation, measured MT data in terms of impedance is seriously biased by distortion of electric fields and is suffered from the static shifts. The Jeju MT dataset is valuable for the research purpose in the sense that the dataset contains so many problems, some of which can frequently be observed in every field data, and that the geology of Jeju Island is relatively simple.

Phenomenological approach on wave propagation in dielectric media with two relaxation times

Abstract In this paper dielectric phenomena with two relaxation times are discussed. By assuming a sinusoidal form for induction vector D a sinusoidal electric field is generated and it depends on unknown phenomenological coefficients whose expressions together to their numerical values as functions of frequency are obtained. Moreover, electromagnetic wave propagation is analysed obtaining wave vector as function of the aforementioned coefficients. The results are applied to a Vinylidene Chloride-Vinyl Chloride (VDC–VC) to test the applicability of the model.