Magnetic Dipole Source Research Articles

Linearized and nonlinear parameter variance estimationfor two-dimensional electromagnetic inductioninversion

Linearized and nonlinear techniques are presented fordetermining estimates of parameter uncertainty within atwo-dimensional iterative Born scheme. The scheme employslow frequency (<100 kHz) magnetic dipole sources in one well,and uses measurements of the vertical magnetic field in asecond well to invert for the electrical conductivitydistribution between the two boreholes. For computationalefficiency a localized nonlinear approximation is employed tocompute the sensitivity matrix. Parameter variance estimatesare determined using an iterative Monte Carlo technique thatassumes the data contain measurement noise, and that constraintassumptions imposed on the model are in error. The a posteriorimodel covariance matrix is determined statistically for thelinearized technique by rerunning the last iteration of thenonlinear inversion N times, each time adding random errors tothe data and constraints. The nonlinear approach involvesrerunning the full inversion N times. Two oil field examplesfrom California indicate that the linearized approach producesthe same general pattern in the uncertainty estimates as thenonlinear estimation process. However, the linearized estimatesare smaller in magnitude and show less spatial variationcompared to the full nonlinear estimates, and the deviationbetween the two techniques increases as the contrast betweenthe maximum and minimum conductivities within the inversiondomain becomes greater.

Electromagnetic edge diffraction revisited: the transient field of magnetic dipole sources

Summary A surprisingly simple exact solution is derived for the transient electromagnetic field scattered by a perfectly conducting half-plane, which is embedded in a uniformly conducting host and energized by a unit step impulse of an arbitrarily oriented magnetic dipole. Despite its simplicity, the model has some relevance for geophysical applications (e.g. mineral exploration), provides insight into the physics of the transient scattering process, and has merits in validating numerical 2.5-D or 3-D codes. The diffraction of electromagnetic waves at a perfectly conducting edge is one of the few vectorial diffraction problems that allows an exact treatment. In the past, attention has been confined to harmonic excitation in a lossless dielectric host, whereas the transient field in a lossy medium has escaped attention. In the quasi-static approximation in particular, this solution turns out to be simple compared to the explicit form of the field using harmonic excitation. However, even the inclusion of displacement currents, which may be necessary when applying transient electromagnetic methods to environmental geophysics, does not lead to complications. The electric field and the time derivative of the magnetic field are given explicitly both in the quasi-static limit and with the inclusion of displacement currents. The late-time behaviour of the field is remarkable: whereas the full-space parts of these fields show the well-known t− 5/2 decay, the diffracted wave emerging from the edge decays only as t− 2 and therefore dominates the field geometry at late × . The appendices briefly treat the quasi-static transient field of a grounded electric dipole and sketch the formal solution for a perfectly conducting half-plane in a layered host.

Terahertz emission fromYBa2Cu3O7−δthin films via bulk electric-quadrupole–magnetic-dipole optical rectification

We report the observation of terahertz emission from ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films excited by 1.5-eV, 150-fs pulses in the absence of external electric or magnetic fields. This emission is characterized for optimally doped $\ensuremath{\delta}=0$ films and underdoped $\ensuremath{\delta}=0.5$ films, over a range of temperatures T, $4\mathrm{K}&lt;T&lt;300\mathrm{K},$ where the films change from superconductors to correlated metals. It exhibits a pronounced 4\ensuremath{\varphi} dependence with respect to the azimuthal angle \ensuremath{\varphi}. We demonstrate that this emission is generated by optical rectification due to the bulk electric quadrupole and magnetic dipole source terms. A model of this emission, assuming that the nonlinearity results from transport of carriers with different masses and relaxation times in the three crystallographic directions, is consistent with the data. A fit of the data to this model yields values for the anisotropic masses and relaxation times in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films.

Computer simulations of asymmetric spontaneous fast reconnection

The spontaneous fast reconnection model is extended to the general asymmetric situations, where magnetic reconnection may take place between the field lines that are anchored in different magnetic dipole sources. It is demonstrated for a wide variety of parameters that the asymmetric fast reconnection mechanism can evolve as a nonlinear instability, so that an asymmetric plasmoid swells predominantly in the region of a weaker magnetic field and propagates along the field lines. In the central diffusion region, the secondary tearing is likely to take place and significant erosion of the stronger magnetic field occurs; accordingly, the X neutral point moves with time, where the (current-driven) anomalous resistivity is found to be always locally enhanced, allowing the fast reconnection mechanism to be sustained quasisteadily and extended outwards further. The associated shock structure standing at the boundary of the stronger magnetic field is identified with the ordinary slow shock, in general, combined with an intermediate wave in the presence of sheared field. On the other hand, the shock standing at the boundary of the weaker magnetic field has an intermediate shock-like structure near the diffusion region, which propagates along the shock layer to finally become the ordinary combination of a slow shock and a finite-amplitude rotational intermediate wave at the plasmoid boundary.

Analytical computation of EM field components in a uniform half-space

Analytical expressions for the electromagnetic field components at an arbitrary location in a half-space are presented for a vertical magnetic dipole source on the surface of the Earth. The Hankel transforms required in the computation are enumerated using expressions based on the modified Bessel functions of the first and second kind. For surface electromagnetic fields, the Bessel function expressions are shown to consistently produce results that are up to four orders of magnitude more accurate than the results commonly obtained using digital filters. In addition, initial speed tests reveal that considerable computational time is saved compared with the use of numerical routines based on digital filters. It is expected that the increased speed and accuracy of the analytical solution will find application in forward modelling and inversion routines where a half-space is considered to be a suitable model and Hankel transforms need to evaluated many times.

Faraday chiral media revisited. I. Fields and sources

Faraday chiral media, previously conceptualized as chiroplasmas or chiroferrites, are envisioned to combine the effects of Faraday rotation and chirality. Electromagnetic field representations for arbitrary sources are derived after the previous correct characterization of the constitutive relations of such media. The scalar Hertz potential (SHP) technique is employed and its applicability is thoroughly investigated. In particular, it is shown that all field components can be derived from one scalar Green function (plus so-called auxiliary source potentials) in source problems, whereas one scalar superpotential suffices for source-free problems. Expressions pertaining to radiation from electric and magnetic dipole sources are presented in a simple and compact form. Further generalizations of the results and the actual realizability of Faraday chiral media are discussed.

A Review Of Environmental Applications Of Quasi-Stationary Electromagnetic Techniques

Electromagnetic (EM) techniques are the most commonly used geophysical methods in mineral exploration. However, the use of EM measurements for environmental and engineering applications like the detection of contaminant plumes or the exploration of waste sites is relatively new. The reason for the success of the application of EM methods to environmental problems lies in the variation of conductivity caused by different geometry of pore fluids and clay contents in rocks, and by the presence of organic and inorganic contaminants. Many EM methods/instruments used for mapping near surface geology exist and nowadays they play a central role in environmental geophysics. In general, these methods can be classified in two blocks: EM methods using a plane wave source of excitation and EM methods using a controlled source like a magnetic dipole or a loop source. The Very Low Frequency (VLF, VLF-R) and Radiomagnetotelluric (RMT) methods are chosen as representative methods for plane wave techniques, while horizontal loop EM methods operating in low induction numbers (EM31, EM34) and Transient Electromagnetic methods (TEM) are chosen as representatives of magnetic dipole or loop source techniques. Basic principles, advantages and disadvantages of each technique as well as their connection to specific environmental problems will be discussed. Different successful applications of these methods are reported in the literature. However, this review will focus on three major subjects: waste site exploration, detection of contaminated earth layers, and groundwater exploration. Case histories are presented illustrating the suitability of EM methods for solving such problems.

A numerical and experimental investigation of planar asymmetric SQUID gradiometer characteristics

A low-cost, high-performance magnetic field sensor for applications such as biomagnetism and nondestructive evaluation can be fabricated by integrating a superconducting quantum interference device (SQUID) and a gradiometer on a single chip. Conventionally, the gradiometric pick-up loop would have a rectangular outline divided symmetrically about the midpoint of its length so that its spatial response was also symmetrical. However, it is also possible to divide the same outline asymmetrically, maintaining the field rejection order of the gradiometer by adding an extra crossover. The spatial response of this arrangement will also be asymmetric, which may be exploited to reduce the effects of the nearby SQUID as a magnetic anomaly or to enhance the sensitivity of the device to magnetic sources at a particular distance. The techniques to calculate the crossover positions are well established. Here we outline how different designs may be evaluated theoretically and report on first experimental results for three simple designs. Several devices have been fabricated using a well established trilayer process with high yields. The measurement of the spatial response of an asymmetric first-order gradiometer shows the expected magnetometer characteristics for a magnetic dipole source in the near field and first-order gradiometric characteristics for a far-field source. The balance of the integrated gradiometer appears to be better than one part in , and the magnetic field gradient sensitivity has been measured to be .

Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry

An iterative Born imaging scheme is employed to analyze the resolution properties of crosswell electromagnetic tomography. The imaging scheme assumes a cylindrical symmetry about a vertical magnetic dipole source and employs approximate forward modeling at each iteration to update the internal electric fields. Estimation of the anomalous conductivity is accomplished through least‐squares inversion. Much of the mathematical formulation of this diffusion process appears similar to the analysis of wavefield solutions, but the attenuation implicit in the complex propagation constant invalidates many of the accepted wavefield criteria for resolution. Images of illustrative models show that vertical resolution improves with increasing frequency and with increased spatial sampling density. In addition, greater conductivity contrasts between the target and the background can result in better resolution. The horizontal resolution depends on the maximum aperture that is employed and with increasing frequency, larger apertures are needed to obtain optimal results. However, the maximum aperture that can be employed, and thus the horizontal resolution, is limited by the rate of attenuation and the noise present in the measurements. Weighting the long‐offset data equally with the zero‐offset data can improve the resolution if the noise is not a function of the dynamic range of the measurement system. At lower frequencies, the resolution can be improved by measuring both the horizontal and vertical components of the magnetic fields. In addition, multiple frequencies can be employed to improve the resolution for limited aperture measurements. The general applicability of the cylindrically symmetric geometry is examined by comparing the 2-D sensitivity functions to those produced by a 2.5-D model, and by imaging a 3-D body with the 2-D iterative Born scheme. For borehole separations greater than five skin depths it is demonstrated that the measurements, and thus the images, are not affected by the geometry of the conductive zone outside of the interwell plane. Thus the 2-D imaging scheme can be employed in these situations. For borehole separations less than five skin depths, artifacts are produced in the images which will lead to faulty interpretations.

Electromagnetic modelling of buried line conductors using an integral equation

An integral equation is derived to represent the electromagnetic response of line conductors buried below the surface of a horizontally stratified earth. By permitting several finite-length line conductors of arbitrary topology, this representation is free of the limitations imposed by analytic solutions. The integral equation is formulated in terms of excess electric current (scattering current) flowing along the line conductor and is solved numerically by dividing the line conductor into many small segments. In general, the excess electric current is controlled by both the internal and external impedance of the line conductor. The internal impedance is the longitudinal resistance of the line conductor. The external impedance is caused by galvanic and inductive coupling between the line conductor and its local environment. The galvanic resistance to current channelling is spatially variable with a minimum in the centre of a uniform line conductor and is determined by conductor geometry and the host conductivity structure. The inductive external impedance is proportional to frequency and quadrature dominant. It is a function of line-conductor geometry, cross-section and burial environment. The inductive impedance effectively reduces the spatial dependence of the external impedance at high frequency by presenting a large reactance (which is uniform at all points along the conductor) to the exciting electric field. Within the quasi-static limit (i.e. where displacement current can be neglected), electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far field). The excess electric current in the line conductor will always be inversely proportional to frequency for these types of sources at sufficiently high frequencies where the inductive external impedance is dominant. Horizontal magnetic dipole and vertical electric dipole sources generate primary electric fields that are proportional to the square root of frequency in the high-frequency limit of the quasi-static domain and the excess electric current excited by such sources will decrease as the inverse of the square root of frequency.

Asymptotic expansion of the electromagnetic field induced by a dipole on the surface of a perfectly conducting convex body

The problem of the electromagnetic field generation by a magnetic dipole source on the surface of a perfectly conducting body is studied by using the boundary layer method. The field is first computed in the vicinity of the source, then matched with the creeping rays. The launching coefficients of these rays are computed up to the second order term, showing the effect of the difference of the principal curvatures of the surface.

Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth

Conversion of the measured voltages in direct current resistivity sounding methods into apparent resistivity [Formula: see text] is a useful step since [Formula: see text] data provide information about the subsurface resistivity variations with depth. This resistivity information then helps select a model for inverting the sounding data. In the controlled‐source electromagnetic method (CSEM), conversion of the measured electric and magnetic fields into apparent resistivity values has not been popular. This attitude may be attributed to the difficulties in the inversion of the resistivity of a half‐space from the electromagnetic (EM) field components as well as to the nonunique nature of the inversion giving two resistivity values for a single measurement. Two measured components—the vertical magnetic field [Formula: see text] and the tangential electric field [Formula: see text] as a result of a vertical magnetic dipole source—are combined to derive an exact apparent resistivity in a way similar to that used in direct current resistivity methods. Conversion of the measured [Formula: see text] and [Formula: see text] field components into apparent resistivity is found to be simple and can be carried out on a programmable pocket calculator. Theoretical apparent resistivity curves for frequency‐domain electromagnetic sounding show features similar to magnetotelluric (MT) and direct current dipole‐dipole apparent resistivity curves.

Frequency‐ and time‐domain electromagnetic responses of layered earth—A multiseparation, multisystem approach

EM depth soundings by controlled‐source electromagnetic methods (CSEM) are made to determine the vertical resistivity distribution of the earth. The two variations of soundings, namely frequency sounding and geometric sounding, are used for exploring the subsurface. Although in field applications electromagnetic (EM) sounding has relative advantages over direct current resistivity sounding, quantitative use of EM depth sounding has not been used as much as direct current resistivity sounding (Mundry and Bohlm, 1987). Mundry and Bohlm (1987) have pointed out that one of the problems in the application of frequency EM sounding is the lack of sophisticated interpretational tools. The interpretation of the mutual coupling ratio (MCR) from the EM field component measurements, [Formula: see text], invariably relies on numerical inversion routines. However, unlike the direct current (DC) or magnetotelluric (MT) apparent resistivity curves, MCR curves do not reflect the subsurface resistivity distributions, and an initial guess model from MCR required for its inversion is difficult. Conversion of single component EM measurements into apparent resistivity is ambiguous because for a single measurement, two apparent resistivity values are obtained. Combining the general expressions for MCR obtained from the quasi‐static tangential electric and vertical magnetic field components of a vertical magnetic dipole source on the surface of a half‐space, Das (1995) defined an apparent resistivity for the use of the CSEM. The CSEM apparent resistivity curves show features similar to DC and MT apparent resistivity curves and they greatly enhance the interpretation. I refer to this paper (Das, 1995, published in this issue) as Paper I. In the present paper, difficult measurements of the electric field have been avoided by combining [Formula: see text] and [Formula: see text] obtained from the magnetic field measurements of two different configurations, i.e., the horizontal coplanar loops (HCP) and vertical coplanar loops (VCP) systems, respectively. This combination of measurements provides operational simplicity in the field and gives the same CSEM apparent resistivity described in Paper I. However, complementary behavior of the two combinations would be realized.

Electromagnetic response of a discretely grounded circuit—An integral equation solution

We derive an integral equation to describe the electromagnetic response of a discretely grounded circuit. This investigation is relevant to the study of man‐made structures such as metallic fences, grounded powerlines, and pipelines, all of which may fall into the class of discretely grounded conductors. The solution developed here is an extension to existing circuit theory and takes into account the self and mutual interaction of the circuit elements. It is possible to ignore these interactions at low frequencies where the grounding impedances dominate the effective impedance of the circuit. However, at frequencies where the electromagnetic skin depth is comparable to the length between adjacent grounding points, the effective impedance of the circuit is proportional to frequency, and the inductance of the circuit dominates its electromagnetic response. Within the quasi‐static limit (i.e., where displacement currents can be neglected) electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far‐field). Thus, the electric current in the discretely grounded circuit will always be inversely proportional to frequency for these types of sources. Horizontal magnetic dipole or vertical electric dipole sources generate primary electric fields that are proportional to the inverse square root of frequency in the high frequency limit of the quasi‐static domain, and thus the current in a circuit excited by such sources will decrease as the inverse of square root of frequency. The integral equation solution derived here can be used to investigate the influence from cultural conductors on actual electromagnetic surveys and also provides further insights into the current channeling response of surficial conductors.

The fields from a finite electrical dipole—A new computational approach

Controlled‐source, frequency‐domain, and time‐domain electromagnetic methods require accurate, fast, and reliable methods of computing the electric and magnetic fields from the source configurations used. Except for small magnetic dipole sources, all electric and magnetic sources are composed of lengths of straight wire, which may be grounded. If the source‐receiver separation is large enough, the composite electrical dipoles may be considered to be infinitely small, and in a 1-D earth model the fields are expressed as Hankel transforms of an input function, which depends only on the model parameters. The Hankel transforms can be evaluated using the digital filter theory of fast Hankel transforms. However, the approximation of the infinitely small dipole is not always valid, and fields from a finite electrical dipole must be calculated. Traditionally, this is done by numerical integration of the fields from an infinitesimal dipole, thus increasing computation time considerably. The fields from the finite electrical dipole are expressed as Hankel transforms and as integrals of Hankel transforms. The theory of fast Hankel transforms is extended to include integrals of Hankel transforms, and a method is devised for calculating the filter coefficients. Unlike the fast Hankel transform, the computation involved in the integrated Hankel transforms is not a true convolution, and so a set of filter coefficients must be calculated for each source‐receiver configuration. Furthermore, the method is extended to include the calculation of potential differences where one more integration is involved, which is what is actually measured in the field. The computation of filter coefficients is very fast, and for standard configurations, the coefficients need be computed only once. The method is as fast, accurate, and reliable as the fast Hankel transforms method, and is up to an order of magnitude faster than the usual numerical integration.

Analysis of radiation from active microstrip antennas

The current interest in active microstrip antennas has highlighted the need for analysis of the radiation characteristics of such antennas. The paper describes the extension of the small magnetic dipole source analysis of microstrip line discontinuities to active devices. The analysis is then combined with the patch cavity model to form a flexible, approximate analysis suitable for implementation in active antenna computer-aided design packages. Computed results agree well with measurements and show that radiation from the active device and associated matching circuits can be significant. The analysis indicates that reduced radiation pattern perturbation will result from the active device being integrated within the periphery of the patch.

Three-dimensional electromagnetic cross-well inversion

An inversion algorithm for a vertical magnetic dipole source and a vertical magnetic field component receiver is presented. A three-dimensional integral equation algorithm is used for calculating the electromagnetic response of a particular trial reservoir model. The inversion formalism used is the Marquardt technique of nonlinear least-squares optimization. The system derivatives are calculated using an exact expression derived from reciprocity. The derivative calculation involves introducing sources at the receiver locations with subsequent back-substitution into the impedance matrix equation. The inversion algorithm was tested on data gathered with a laboratory scale model. Convergence to the neighborhood of the correct model from distant initial trial models is good. >

FIXED LOOP SOURCE EM MODELLING RESULTS USING 2D FINITE ELEMENTS1

AbstractAmong electromagnetic sounding techniques, the Mélos method possesses the specific feature of including an apparent resistivity computation. This acts as a normalizing scheme so that 2D modelling results can be obtained without accounting for a true 3D source. However, in order to get reliable numerical modelling results for a 2D magnetic dipole source, improved algorithms are required in order to apply the standard finite‐element technique: quadratic basis functions must be used in place of linear basis functions, and a more sophisticated method than conventional ones is necessary for properly solving the resulting system of linear equations.Such modelling results have been used to study theoretical responses for the Mélos method in the search for conductive bodies in mineral exploration. Two sets of models are presented and discussed. They show that the typical Mélos response to a conductive target is a bipolar anomaly on the apparent resistivity pseudo‐section, with a conductive pole at low frequency which is centred above the target.

Diffraction of nonaxisymmetric waves in cylindrically layered media by horizontal discontinuities

In this paper a numerically efficient algorithm is developed for solving the problem of nonaxisymmetric wave propagation in cylindrically layered media with horizontal discontinuities. For an off‐axis source in cylindrically layered media, because the nonaxisymmetry of the waves gives rise to the vectorial coupling between TE and TM waves, the modeling of the wave propagation becomes much more difficult than for a centered (axisymmetric) source. However, the numerical mode‐matching method proposed here calculates very efficiently the electromagnetic fields in cylindrically layered media with horizontal discontinuities. Several numerical examples are given to verify the numerical method and to illustrate the applications of this method in the calculation of the field generated by a magnetic dipole source.

Magnetic boundaries of the outer planets: A review

The static and dynamic characteristics of the magnetopauses of the outer planets, as well as their estimated large scale shapes, will be reviewed and compared to each other and to those of the earth. Various unique features will be stressed. For example, because of the severe asymmetric nature of the main magnetic fields of Uranus and Neptune (due to significantly displaced and tilted magnetic dipole sources), their magnetospheres are (rapidly) rotating obstacles to solar wind flow, and their magnetopauses respond to that large, rapid variation. Waves or wave-like features on Uranus' boundary and evidence for boundary layer plasmas at all of the outer planets will be reviewed. Fortuitously and unexpectedly, Voyager 2 encountered a magnetospheric cusp as it entered Neptune's magnetosphere. Observations of that region will be discussed, especially with regard to its structure and the apparent boundary layer plasmas around that complex boundary. Waves on the magnetopause of Saturn with periods of 5 to 30 min. have been observed (as at earth). These are probably due to the Kelvin-Helmholtz instability, but upstream perturbations are also possible causes. Comparisons of the estimated thicknesses of the observed magnetopauses will be made, including that of earth.