Electromagnetic Inverse Problem Research Articles

Optimisation approach to the time-domain electromagnetic inverse problem for a bi-isotropic slab

A one-dimensional time-domain electromagnetic inverse problem for a bi-isotropic slab is solved using an optimisation approach. The bi-isotropy and dispersion result in time convolutions of four susceptibility kernels in the time-domain constitutive relations. To make the computation simpler, dual functions are introduced to derive an explicit expression for the gradient. A matrix formalism is introduced to derive the system of equations for the dual functions. After the gradient has been computed, a conjugate gradient method is used to reconstruct all the four susceptibility kernels simultaneously. Numerical results for the reconstruction are presented, and the algorithm is tested with both the clean and noisy data.

An analysis of the time-domain electromagnetic inverse problem of determining the susceptibility kernel for a stratified dispersive slab

Article An analysis of the time-domain electromagnetic inverse problem of determining the susceptibility kernel for a stratified dispersive slab was published on January 1, 1995 in the journal Journal of Inverse and Ill-posed Problems (volume 3, issue 6).

A Uniqueness Theorem for a Lossy Inverse Problem in Reflection Seismology

A nonlinear inverse problem is studied for recovering a stratified acoustic medium with attenuation (loss) from the medium's response to a point-source input introduced into the pressure field at the medium's surface. The primary focus is on applications in reflection seismology and oil exploration, where the medium is a model of the subsurface of the earth. The point-source response is the vertical component of the particle velocity at the earth's surface. It is shown that in the appropriate function spaces, if the wave speed is fixed, at most one pair of functions for density and attenuation, together with the fixed wave speed, could have produced the observed point-source response. This uniqueness result is based on a contraction mapping fixed-point argument in which the functional operator is derived from an analysis of two plane wave components of solutions to the model equations. The result is established in the time domain. This work also has direct application to some lossy inverse problems in electromagnetics.

Application of neural networks to inverse problems in electromagnetics

The paper presents a neural network approach for solving inverse problems in electromagnetics. In general, the measurements of the scattered electromagnetic fields can be related to the properties of the scatterer through integral equations. The energy minimization property of Hopfield neural networks is exploited to solve these integral equations. Results of implementing the method on an application problem involving reconstruction of material properties of multilayered media are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Detection of magnetic body using artificial neural network with modified simulated annealing

An artificial neural network is applied to the inverse electromagnetic fields problem. In the process of the training the network, it is suggested that the simulated annealing algorithm be used to smooth the output errors before the network is trained with the error back-propagation algorithm. And a general way of defining the control parameters of simulated annealing is presented. As numerical example, the artificial neural network with the suggested training algorithm is applied to the detection of the magnetic body in magnetic field. It is shown, through the numerical test, that the artificial neural network is very useful for the inverse electromagnetic field problems, especially in real-time system and the artificial neural network trained with the suggested training algorithm gives much less maximum errors than that trained with the error back-propagation algorithm only. >

PF coil voltage optimization for start-up scenarios in air core tokamaks

The basic features of a procedure for the optimization of the plasma scenario in an air core tokamak are presented. The method takes into account the eddy currents in the passive conducting structures. The problem is reduced to the synthesis of a time-varying magnetic field. The solution of this inverse electromagnetic problem is carried out by means of an optimization procedure based on the receding horizon approach. The paper includes an example of application to the ITER tokamak.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Practical strategies for the solution of large‐scale electromagnetic inverse problems

Nonlinear inverse problems in electromagnetics are typically solved by dividing the Earth into cells of constant conductivity, linearizing the equations about a current model, computing the sensitivities, and then solving an optimization problem to obtain an updated estimate of the conductivity. In principle, this procedure can be implemented for any size problem, but in practice the computations involved may be too large for the available computing hardware. In electromagnetics this is currently the situation irrespective of whether the interpreter has access to a workstation or a supercomputer. In addition to the demands imposed by the need to compute the predicted responses from a specified model (i.e., invoking a forward mapping) there are two computational roadblocks encountered when solving an inverse problem: (1) calculation of the sensitivity matrix and (2) solution of the resultant large system of equations. If either of these operations cannot be carried out in reasonable time then an alternate strategy is required. Such strategies include generalized subspace methods, conjugate gradient methods, or approximate inverse mapping (AIM) procedures. The theoretical foundations and computational details of these strategies are explored in this paper with the ultimate goal that the inversionist, after assessing his/her computing power and knowing the time required to perform forward modeling, can generate a methodology by which to solve the problem. The methodologies are compared quantitatively by considering an archetypal inversion problem in electromagnetics, the inversion of dc potential data to recover the electrical conductivity.

Inversion of conductivity profiles using the Volterra functional method.

The Volterra functional method is used for the electromagnetic inverse problem. A general analytical procedure and symbolic computer code implementation are successfully constructed that provides an alternative way for the inverse problem. The conductivity profiles, as an example, are reconstructed by the method. The results show that using only three terms of an expansion gives an obvious improvement when compared with former approximations.

Analysis of the Green’s function approach to one-dimensional inverse problems. II. Simultaneous reconstruction of two parameters

The wave-splitting Green’s function approach to one-dimensional electromagnetic inverse problems of simultaneous reconstructions with different types of scattering data is analyzed. Theorems of existence, uniqueness, and stability are given for the following types of scattering data: reflection and transmission data for one round trip, two-sided reflection data for one round trip, reflection data for two round trips.

Existence of an Optimal Conductivity and Fréchet Differentiability In 2-D Electromagnetic Inversion

SUMMARY A 2-D electromagnetic inverse problem relevant for geophysical exploration is considered. an exact theory is described which proves Frechet differentiability of the data and the existence of optimal, or best-fitting, solutions. the earth is represented by a 2-D electrical conductivity structure with a known, horizontal strike direction and the data are surface measurements of electric field due to telluric earth currents flowing along-strike. First, the TE-mode equations governing the forward problem are cast in variational form. It is then shown that there exists at least one admissible conductivity that minimizes the discrepancy between the observations and variational solutions to the forward problem. Admissible conductivities are drawn from any compact subset of the class of bounded, positive functions. Standard techniques from elliptic partial differential equations, non-linear functional analysis and optimization play key roles in establishing the result. In particular, the Lax-Milgram lemma assures that a unique solution to the forward problem exists. an implicit function theorem approach is used to establish the regularity of the mapping from the conductivity to the data. the existence of optimal models follows from the well-known fact that a continuous functional attains its minimum when varied over a compact set. Previously, Frechet differentiability and existence theories for geo-electromagnetic inverse problems have been limited to induction in 1-D media. However, characterization of the optimal models in two dimensions, analogous to Parker's D+ conductivity models in one dimension, is impeded by the lack of closed-form solutions to the forward problem.

Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction

An analysis of a Green’s function approach (based on wave splitting) to the one-dimensional electromagnetic inverse problem is given. The Green’s functions refer to split components of the fundamental solution. The linear system of equations for the Green’s functions is shown to be well-posed for the inverse problem and stability estimates, theorems on existence, uniqueness, local correctness, and convergence are given.

Advances in electromagnetic design of fusion devices

The specification of the large magnets needed in future fusion reactors based on the tokamak concept is presented as an inverse electromagnetic problem. The influence of the eddy currents flowing in the metallic structure is illustrated. Currently used computational tools and related mathematical formulations are reviewed. The behavior predicted by the numerical models is in agreement with experimental measurements, as demonstrated by a campaign of code validation. Recent progress on techniques for the identification of the plasma parameters and for scenario optimization is presented. >

Recovery of Perturbations in an Acoustic Medium with Attenuation from Several Plane Wave Responses

A linearized inverse problem is studied for recovering a stratified acoustic medium with attenuation from reflection data known at the medium’s surface. The inverse problem is based on a plane wave decomposition of the medium’s response to a point-source input. This paper shows that the inverse problem for recovering perturbations in density, wave speed, and the coefficient of attenuation from known perturbations in three plane wave responses is well posed in the appropriate function spaces. The question of whether the medium itself can be recovered from the point-source response is discussed. The primary focus of this paper is on applications in reflection seismology and oil exploration. The work also has direct application to some inverse problems in electromagnetics.

Artificial neural networks in the solution of inverse electromagnetic field problems

The use of artificial neural networks in the solution of inverse electromagnetic field problems is investigated. It is shown that artificial neural networks, while being no panacea, have a role to play in a limited domain of applications-that is, while it is ineffective to train networks to cover a broad class of devices, it is indeed possible to develop well-trained networks that function effectively over a narrow range of performance of a particular class of device. Particularly if one knows the desired geometry approximately and uses training sets around this geometry, simple neural networks with a few training sets can be used to do an effective job. However, neural networks cannot be used efficiently without such prior knowledge.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An electromagnetic inverse problem related to the non-invasive reconstruction of dielectric permittivity and electric conductivity in biomedical applications

A class of microwave imaging methods based on integral equations and the moment method is considered. In particular, a pseudoinversion-based multiview approach and an alternative version making use of the first-order Born approximation are presented. A probabilistic technique is also described, which is based on a simulated annealing approach and on a Markov random field model. Results are reported on dielectric reconstructions of cylindrical scatterers with complex dielectric permittivities consistent with those of human tissues.

An electromagnetic inverse problem solver for radar: aircraft rotation and tilt measurement

A Doppler radar is used to obtain the velocity, altitude, and distance of an aircraft with respect to the radar coordinates. It is shown that the reflected electromagnetic fields picked up by the receiver antenna also contain information on the rotation angle and tilt angle of the aircraft, which could be obtained using a maximum-likelihood estimation algorithm. The electromagnetic signal processing unit estimates the angles of rotation and tilt and the radius of the target modeled as a cylinder using the scattered magnetic field. Specific results showing the application of the estimator are given. >

Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering

The Born and Rytov approximations, widely used for solving scattering problems, are of limited utility for low‐frequency electromagnetic scattering in geophysical applications where conductivity can vary over many orders of magnitude. We present four new, relatively simple nonlinear estimators that can be used for rapid electromagnetic modeling. The first, termed the static localized nonlinear approximation, is designed specifically to correct the magnitude of the electric field internal to the scatterer. The second, termed the localized nonlinear approximation, improves the estimate of the phase of the scattered field and includes some of the cross‐polarization effects due to full wave scattering. Two further new estimators, based on the Rytov transformation (the localized nonlinear Rytov and the static localized nonlinear Rytov approximations) are designed to further improve the estimation of the phase of the scattered field, especially at high frequency and for larger size scatterers. Although these approximations are nonlinear functions in conductivity, they are generally much faster to compute than the full forward problem, and are almost as efficient as the Born or Rytov approximations. Moreover, the enhanced accuracy of the new estimators has made us optimistic about their application to low‐frequency three‐dimensional inverse problems in electromagnetics. The approximations developed in this paper will also be applicable to fields such as quantum mechanics, optics, ultrasonics, and seismology.

An inverse electromagnetic induction problem

An analytical procedure is presented to determine the surface current density required to produce a specified form of the electric field at a given depth in a conducting half-space. It is demonstrated that the system could be implemented with a discrete array of concentric loop currents. Attention is confined to azimuthal symmetry and to low frequencies where displacement currents in the upper free space region are negligible. >

The electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding: reconstruction of the permittivity and conductivity

He, S. and S. Ström, The electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding: Reconstruction of the permittivity and conductivity, Journal of Computational and Applied Mathematics 42 (1992) 137-155. We consider the electromagnetic inverse problem for a point source above an inhomogeneous dissipative slab of permittivity ∈( z) and conductivity σ( z), where z is the depth. Two inversion algorithms based on the invariant imbedding equations derived in previous work are used to reconstruct both the permittivity and the conductivity. Both algorithms use two-sided reflection data and one of them also uses transmission data. Results are presented for clean and noisy data.

The use of finite elements and neural networks for the solution of inverse electromagnetic problems

A method that combines a neural network (NN) and the finite-element method is introduced for solving inverse electromagnetic field problems. This forms the basis for design synthesis. A two-layered NN with one-pass training is used in this scheme. It uses the information from the finite-element analysis for training and is very efficient and stable. The one-pass training of the NN leads to a time efficient scheme. The finite-element method is used to produce the training patterns and to analyze the optimized solution, and the neural network is used to optimize the parameters. With the use of the trained NN for optimization, the solution time for design optimization is reduced. An example of its use in the optimization of a permanent-magnet rotor configuration is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>