Fridon Shubitidze

Application of the method of auxiliary sources to the wide-band electromagnetic induction problem

The Method of Auxiliary Sources (MAS) is formulated and applied to solution of wide-band electromagnetic induction problems involving highly conducting and possibly permeable metallic objects. Improved remote sensing discrimination of buried unexploded ordnance (UXO) motivates the study. The method uses elementary auxiliary magnetic charges and magnetic current elements to produce the unknown field. Auxiliary sources are located on virtual surfaces that usually conform to but do not coincide with the real surface of the object. Once the source coefficients are determined, the-secondary field can easily be found. The method involves no confrontations with source or Greens function singularities. It is capable of treating penetrable as well as nonpenetrable objects. Because the solution is composed of fields that automatically satisfy the governing equations, by construction, all approximation resides only in the enforcement of boundary conditions at matching (collocation) points. Accuracy in satisfying the boundary conditions can be evaluated explicitly using noncollocation points over the surface. This in turn allows one to identify problem areas on the surface and make intelligent adjustments of the source distributions, to improve solutions at minimal cost. A general 3D formulation is presented, and a version specialized to treat bodies of revolution is applied in the specific test cases discussed.

Fast data-derived fundamental spheroidal excitation models with application to UXO discrimination

Current idealized forward models for electromagnetic induction (EMI) response can be defeated by the characteristic material and geometrical heterogeneity of realistic unexploded ordnance (UXO). A new, physically complete modeling system was developed that includes all effects of these heterogeneities and their interactions within the object, in both near and far fields. The model is fast enough for implementation in inversion processing algorithms. A method is demonstrated for extracting the model parameters by straightforward processing of data from a defined measurement protocol. Depending on the EMI sensor used for measurements, the process of inferring model parameters is more or less ill-posed. More complete data can alleviate the problem. For a given set of data, special numerical treatment is introduced to take the best advantage of the data and obtain reliable model parameters. The resulting fast model is implemented in a pattern matching treatment of measurements by which signals from a UXO are identified within a series of those from unknown targets. Preliminary results show that this fast model is promising for use in processing of this kind. The inherent difficulties of target identification are examined, and solutions for resolving these difficulties are discussed.

Simulation of electromagnetic induction scattering from targets with negligible to moderate penetration by primary fields

The problem of numerical modeling of electromagnetic induction (EMI) responses by metallic objects is complicated by the fact that transmitted fields may penetrate the target, but will often only do so slightly. The effect cannot be ignored, yet it is often grossly impractical to discretize the entire surface or volume of a target in space increments only on the order of a fraction of the skin depth. To deal with this problem, we retain a simple integral equation formulation in scalar potential for the region outside the target, where magnetic fields are quasi-static and irrotational. Within the target we apply only the divergence relation, /spl nabla//spl middot/H = 0. When the skin depth is small relative to the radius of curvature of the target (e.g., <0.1), we use the thin skin depth approximation (TSA), /spl part/H/sub n///spl part/n as /spl sim/-ikH/sub n/, just inside the targets surface, where k is the electromagnetic wavenumber inside the metal and n is the normal direction on the surface and pointing inside of metallic object. Examination of analytical solutions for the sphere suggests the parameter range in which this approximation might perform well and suggests ways of improving accuracy over an extended range. The fundamental TSA formulation appears to be relatively robust. Analysis indicates that it is insensitive to variation over the targets surface of primary field orientation relative to that surface, and that it is only dependent on the targets magnetic permeability through induction number. Implementing the TSA numerically, within the above divergence relation, allows us to express all quantities in terms of tangential magnetic field components and their tangential derivatives over the target surface. In principle, this closes the system completely in terms of the exterior scalar potential. Broad-band numerical simulations based on the TSA compare favorably with analytical and other numerical solutions.

Fast and accurate calculation of physically complete EMI response by a heterogeneous metallic object

In this paper, the coupling and close-proximity effects arising between highly conducting and permeable metallic objects are exposed and analyzed, for the electromagnetic induction (EMI) frequency range (from tens of hertz up to several hundreds of kilohertz). To understand the physics of the interaction phenomena, a numerical technique is applied, consisting of the full method of auxiliary sources (MAS) at low frequencies and a combination of the MAS with thin-skin approximation (TSA) at high frequencies. Both numerical MAS-MAS/TSA and experimental studies have shown that the scattered field from a heterogeneous target generated as a simple superposition of independent responses from each part can be very different from the field determined from whole object with full internal interaction. A new numerical technique for fast and accurate representation of EMI responses for heterogeneous objects is pursued here, applicable to any three-dimensional heterogeneous object placed in an arbitrary time-varying EMI field. First, any primary magnetic field input is decomposed into the spheroidal modes over a fictitious surface surrounding the object. Then, for each input spheroidal mode, the full EMI problem including all interaction is solved using the MAS-MAS/TSA technique, and each modal response is reproduced using a compact reduced set of sources (RSS). Finally, the total response from the given target for any other excitation can be synthesized simply by calculating that primary fields constituent spheroidal modes and combining their stored responses. Several numerical examples are designed to show how an objects electromagnetic parameters, geometry, distance between objects, antenna positions, and orientations relative to the object affect the coupling. Comparisons between numerical and measured data for a machined composite object and for an actual unexploded ordnance demonstrate the superior accuracy and applicability of the MAS-MAS/TSA RSS model over simple dipole approximations, for certain classes of heterogeneous objects.

Investigation of broadband electromagnetic induction scattering by highly conductive, permeable, arbitrarily shaped 3-D objects

Operating as low as tens of hertz and as high as hundreds of kilohertz, new broadband electromagnetic induction (EMI) sensors have shown promise for classification of unseen buried metallic objects. The three-dimensional (3-D) and bodies-of-revolution (BOR) numerical studies reported here are designed to explain key scattering sensitivities that may either be useful in or may limit object classification capability. The target is excited either by a spatially uniform oscillating primary magnetic field or by the oscillating field from a loop antenna. The problem is formulated in terms of Poisons equation for scalar potential outside the object, where conductivity and electric field values are low and consequent conduction currents are generally negligible. The Helmholtz equation for vector potential applies inside the highly conducting and permeable object. In both regions, the electromagnetic phenomena of interest are magneto-quasi-static (MQS). The simulation algorithm uses the method of auxiliary sources (MAS), with auxiliary magnetic charges and auxiliary magnetic current elements distributed on auxiliary surfaces. These surfaces generally conform to but do not coincide with physical surfaces, providing extraordinarily efficient and accurate 3-D solutions. Comparisons to available analytical solutions and experimental data validate the solutions. The simulations and data illuminate broadband MQS scattering phenomenology for both magnetic and nonmagnetic metallic objects. Distinctive sensitivities are shown and signature effects analyzed relative to the scatterers shape and aspect ratio, orientation, sharp points and edges, finite wall thickness in hollow bodies, and compound structure in which a geometrically complex body consists of a number of distinct sections, e.g., fins.

Simultaneous Identification of Multiple Unexploded Ordnance Using Electromagnetic Induction Sensors

The simultaneous detection and identification of multiple targets using electromagnetic induction (EMI) time-domain sensors remains a challenge due to the fast decay of the magnetic field with sensor-target distance. For example, the signal from a weak yet shallow target or clutter item can overshadow that from a much larger yet deeper unexploded ordnance (UXO), potentially resulting in erroneous localization and/or identification. We propose, in this paper, a method based on the Gauss-Newton algorithm for the inversion of multiple targets within the field of view of sensors operating at EMI frequencies (tens of hertz to a few hundred kilohertz). In order to minimize the number of unknowns to invert for, the polarizability tensor is written as a time-independent orientation matrix multiplied by a time-dependent diagonal intrinsic polarizability tensor. Similarly, position is supposed to be time independent so that both position and orientation angles are inverted only once using all time channels collected by the instrument. Moreover, using the dipole approximation, we are able to compute the Jacobian in closed form for instruments with either square or circular primary field coils, thus contributing to the speed of the algorithm. Validating results are shown based on the measurement data collected with two EMI sensors on various types of UXO.

An improved accuracy version of the method of auxiliary sources for computational electromagnetics

The method of auxiliary sources (MAS) is normally applicable to electromagnetic problems involving structures of significant thickness, so that an adequately large distance between source and collocation points is guaranteed. For thin or open geometries the accuracy of the method is depleted, due to numerical instabilities caused by the highly singular terms of the dyadic Greens function (DGF). In this paper a modified MAS (MMAS) is developed to circumvent this particular difficulty. Higher order terms of the DGF are numerically calculated by introducing a canonical grid, where derivatives can be accurately computed via a discrete scheme, unlike standard MAS, where the DGF analytical, problematic expression is invoked instead. This procedure is equivalent to the involvement of auxiliary currents and charges in the solution, instead of the elementary source fields used in standard MAS.

A Man-Portable Vector Sensor for Identification of Unexploded Ordnance

The identification and discrimination of unexploded ordnance using low-frequency electromagnetic induction is an expensive and difficult process, typically beset by low data diversity and high positioning uncertainty. In this paper, we present the Man-Portable Vector (MPV) sensor, a new time-domain instrument designed to remedy these shortcomings by measuring all three vector components of the secondary magnetic field at five distinct points around each transmitter location. The MPV also has a laser positioning system that can give its location with millimeter precision. After describing the instrument in detail, we study its performance in various sets of measurements, using the tensor dipole model to analyze the data. We find that the sensor can detect deeply buried targets and identify some standard ordnance items. It can also resolve separate targets in cases where two objects share the field of view and produce overlapping signals. A new incarnation of the MPV, the MPV-II, is in an advanced stage of development.

Theoretical analysis and range of validity of TSA formulation for application to UXO discrimination

Operating in the magnetoquasistatic regime (a few hertz to perhaps a few 100 kHz), electromagnetic induction (EMI) sensing has recently emerged as one of the most promising avenues for discrimination of subsurface metallic objects, e.g., unexploded ordnance. The technique of thin-skin approximation (TSA) was devised to deal with numerical problems caused by the rapid decay of fields beneath the scatterers surface. The rather nonintuitively broad applicability and specific error patterns of the TSA formulation are explained here by theoretical analysis based on analytical solutions and approximate Monte Carlo simulation. In the limiting case of infinitesimal skin depth (EMI perfect reflection), the scatterer aspect ratio (AR) is inferred without regard to metal type. Alternatively, the AR of some homogeneous magnetic objects is inferred from the pattern of transverse to axial response ratio over the entire EMI ultrawideband. Use of the method in inversions for electromagnetic parameters reveals fundamental nonuniqueness problems and shows their basis, which is not dependent on the method of forward solution.

Magnetic nanoparticles with high specific absorption rate of electromagnetic energy at low field strength for hyperthermia therapy

Magnetic nanoparticles (MNPs), referred to as the Dartmouth MNPs, which exhibit high specific absorption rate at low applied field strength have been developed for hyperthermia therapy applications. The MNPs consist of small (2-5 nm) single crystals of gamma-Fe2O3 with saccharide chains implanted in their crystalline structure, forming 20-40 nm flower-like aggregates with a hydrodynamic diameter of 110-120 nm. The MNPs form stable (>12 months) colloidal solutions in water and exhibit no hysteresis under an applied quasistatic magnetic field, and produce a significant amount of heat at field strengths as low as 100 Oe at 99-164 kHz. The MNP heating mechanisms under an alternating magnetic field (AMF) are discussed and analyzed quantitatively based on (a) the calculated multi-scale MNP interactions obtained using a three dimensional numerical model called the method of auxiliary sources, (b) measured MNP frequency spectra, and (c) quantified MNP friction losses based on magneto-viscous theory. The frequency responses and hysteresis curves of the Dartmouth MNPs are measured and compared to the modeled data. The specific absorption rate of the particles is measured at various AMF strengths and frequencies, and compared to commercially available MNPs. The comparisons demonstrate the superior heating properties of the Dartmouth MNPs at low field strengths (<250 Oe). This may extend MNP hyperthermia therapy to deeper tumors that were previously non-viable targets, potentially enabling the treatment of some of the most difficult cancers, such as pancreatic and rectal cancers, without damaging normal tissue.