Lin-Ping Song

Unexploded ordnance discrimination using magnetic and electromagnetic sensors: Case study from a former military site

In a study at a military range with the objective to discriminate potentially hazardous 4.2-inch mortars from nonhazardous shrapnel, range, and cultural debris, six different discrimination techniques were tested using data from an array of magnetometers, a time-domain electromagnetic induction (EMI) cart, an array of time-domain sensors, and a time-domain EMI cart with a wider measurement bandwidth. Discrimination was achieved using rule-based or statistical classification of feature vectors extracted from dipole or polarization tensor models fit to detected anomalies. For magnetics, the ranking by moment yielded better discrimination results than that of apparent remanence from relatively large remanent magnetizations of several of the seeded items. The magnetometer results produced very accurate depths and fewer failed fits attributable to noisy data or model insuffi-ciency. The EMI-based methods were more effective than the magnetometer for intrinsic discrimination ability. The higher signal-to-noise ...

Computing Transient Electromagnetic Responses of a Metallic Object Using a Spheroidal Excitation Approach

The model-based spheroidal excitation approach is extended to accurately compute the transient electromagnetic response of a highly conducting and permeable object. The complete formulation is presented in the convolution form. The method is applicable to data from various sensors that measure the transient field or voltage in either the on- or off-time regime and for an arbitrary transmitter waveform. The technique is tested against state-of-the-art time-domain electromagnetic induction sensor data. The results show good agreements between modeled and measured data. In addition, numerical studies demonstrate the importance of accounting for the transmitter waveform.

Nonlinear Inversion for Multiple Objects in Transient Electromagnetic Induction Sensing of Unexploded Ordnance: Technique and Applications

We develop an inversion technique to process overlapping data that arise from closely spaced targets. In contrast to a usual single-object inversion model, a multiobject problem is more challenging because of the increased number of parameters to be found and because of the additional nonlinearity and nonuniqueness. Our solution strategy is to break down the full problem into a sequence of smaller problems so that optimization is conducted in a lower dimensional model space. In the numerical implementation, a set of nonlinear model parameters, e.g., the locations of the underlying sources, is sought while the set of linear model parameters, i.e., their polarization tensors, are updated accordingly in a nested manner. This is an explicit separable nonlinear optimization technique that we cast. We employ a joint diagonalization to find an average principal direction among multiple magnetic polarizability tensors. Since the principal directions are more sensitive to the inaccuracies in the estimated polarization tensor, we suggest a subsequent procedure to optimize the two sets of parameters: orientation and principal polarizations of objects. For initialization, we propose a selected multistart nonlinear algorithm for source localizations that paves an efficient way to find a good initial guess of model parameters and makes the nonlinear inversion effectively automated. We report the new applications of the technique to the test-stand and field data acquired with next-generation sensor systems of the TEMTADS and MetalMapper and study the issue of the spatial resolution of overlapping anomalies through inversions and using the metric defined as the total uncertainty of the polarizabilities.

Transient electromagnetic inversion for multiple targets

In UXO contaminated sites, there are often cases in which two or more targets are likely close together and the electromagnetic induction sensors record overlapping signals contributed from each individual target. It is important to develop inversion techniques that have the ability to recover parameters for each object so that effective discrimination can be performed. The multi-object inversion problem is numerically challenging because of the increased number of parameters to be found and because of the additional nonlinearity and non-uniqueness. An inversion algorithm is easily trapped in a local minimum of the objective function that is being minimized. To tackle these problems we exploit the fact that, based on an equivalent magnetic dipole model, the measured electromagnetic induction signals are nonlinear functions of locations and orientations of equivalent dipoles and linear functions of their polarizations. Based on these conditions, we separate model parameters into nonlinear parts (source locations and orientations) and linear parts (source polarizations) and proceed sequentially. We propose a selected multi-start nonlinear procedure to first localize multiple sources and then get the estimated polarization tensor matrix for each item through a subsequent or a nested linear inverse problem. It follows that the orientations of the objects are estimated from the computed tensor matrix. The resultant parameter set is input to a complete nonlinear inversion where all of the dipole parameters are estimated. The overall process can be automated and thus efficiently carried out both in terms of human interaction and numerical computation time. We validate the technique using synthetic and field data.

Adaptive Focusing for Source Localization in EMI Sensing of Metallic Objects: A Preliminary Assessment

This paper considers a technique to deal with the problem of detecting and localizing objects in the data processing of electromagnetic induction (EMI) sensing. The technique is formulated using the concept of source power, which in our case is defined as the averaged sum of squared elements of a dipolar polarizabiltiy tensor over a measured time window for a transient electromagnetic (TEM) system. Under the valid dipole approximation to an EMI target, the source is point-like and therefore should occupy a small volume in space. This is the fundamental basis of the energy focusing technique for localizing a source. To achieve a focusing effect on a specified source, a focusing operator is constructed by minimizing the total output power subject to a unity response constraint for that assumed source. A closed-form expression is derived for source power as a function of a source location and can be used blindly without knowledge of the number of objects. The source power is related to data via a data covariance matrix, which in practice is computed with enough data samples. The experiments were conducted with the simulated and real data collected by a standard Geonics EM-63 system. The results, which we regard as a proof-of-concept, show that the focusing technique, under adequate signal-to-noise ratio (SNR), is able to accurately localize sources and is promising in EMI array processing.

Transient Electromagnetic Scattering of a Metallic Object Buried in Underwater Sediments

In this paper, we study the electromagnetic scattering of a conducting and permeable sphere buried in sea sediments. Instead of taking a uniform conducting medium in the previous work, we model marine environments as a layered medium that consists of the air, the sea, and the sediment. We adopt an integral equation technique to compute time-harmonic solutions for background and scattered fields under fundamental source excitations, i.e., vertical and horizontal magnetic dipoles. The corresponding transient scattering responses to causal step waveform are computed through the digital sine transform. The derived fundamental solutions provide convenient formulas tailored for three-layer medium modeling. The numerical experiments demonstrate that the scattered responses computed in the different backgrounds are approaching almost to the same decays at late times. However, the background fields can significantly mask the scattered responses. Subtracting assumed uniform background responses from “measured” total fields in the three-layered medium cannot provide a correct scattering response in the interested time range, i.e., 0.1-25 ms. To remove the background fields, we propose a conceptual gradiometer system that has receiver cubes installed radially symmetric with respect to a transmitting antenna. The results demonstrate that the suitable differential combinations are able to yield the scattering responses that well agree with those of a free space as the layered background fields in these combined receivers are equal and their influence are automatically canceled out.

Temporal Orthogonal Projection Inversion for EMI Sensing of UXO

We present a new approach for inverting time-domain electromagnetic data to recover the location and magnetic dipole polarizations of a limited number of buried objects. We form the multichannel electromagnetic induction (EMI) sensor data as a spatial-temporal response matrix (STRM). The rows of the STRM correspond to measurements sampled at different time channels from one sensor and the columns correspond to measurements sampled at the same time channel from different sensors. The singular value decomposition of the STRM produces the left and right singular vectors that are related to the sensor and the temporal spaces, respectively. If the effective rank of the STRM is r, then the first r singular vectors span signal subspaces (SS), and the remaining singular vectors span the noise subspaces. The original data are projected onto the SS, and the temporal orthogonal projection inversion (TOPI) uses these data in a nonlinear inverse problem to solve for source locations of the objects. The polarizations of the targets are then obtained by solving a linear optimization problem in the original data domain. We present theoretical and numerical analyses to investigate the singular value system of the STRM and the sensitivity of the TOPI to the size of an SS. Only a few subspace vectors are required to generate locations of the objects. The results are insensitive to the exact choice of rank, and this differs from usual methods that involve selecting the number of time channels to be used in the inversion and carefully estimating associated uncertainties. The proposed approach is evaluated using the synthetic and real multistatic EMI data.

Space-time MUSIC imaging of EMI sensing data and a subspace partition study

Abstract To localize sources in electromagnetic induction (EMI) sensing, we propose a space-time MUltiple SIgnal Classification (MUSIC) imaging approach. Under the EMI physical model, the approach is established upon a receiver array-based spatial and temporal response matrix. In contrast to the multi-static response matrix-based MUSIC imaging approach that requires a sufficient number of receivers and transmitters, the new imaging scheme relaxes the condition on a large number of transmitters and thus becomes applicable to a wide range of EMI sensing systems. We also investigate the issue of forming a noise subspace that is essential to the MUSIC performance. Our theoretic analysis indicates that the choice of an underestimated noise subspace is appropriate for the imaging. Thus it implies, when doing a subspace partition required in the MUSIC, that a difficult task of exactly distinguishing signal from noise eigenvalues can be eased greatly in a practical eigenvalue distribution map. The technique is evaluated through the synthetic and real data. The results show that the space-time MUSIC can be used to detect sources with an EMI system consisting of multiple receivers but a few transmitters. As predicted from the theoretical analysis, the tests show that the MUSIC-source locations are robust to under-estimates of the dimension of the noise subspace.

Transient VRM Response From a Large Circular Loop Over a Conductive and Magnetically Viscous Half-Space

To effectively characterize the impact of viscous remanent magnetization (VRM) on the transient electromagnetic response, we present a set of analytical expressions for the vertical and radial VRM responses generated by a large circular loop over a magnetically viscous half-space. For a step-off excitation, Néel relaxation theory is used to express the VRM within the half-space as the product of a static on-time magnetization and a time-dependent aftereffect function. Through heuristic and empirical approximations to the elliptic integral of the second kind, we are able to convert Hankel integral-based expressions for static fields into simplified analytical expressions. These were validated with a numerical 1-D forward modeling code. Analytical expressions show that VRM responses are largest near the transmitter wire, and that at the center of a large loop, the strength of the VRM response is inversely proportional to the loop’s radius. We also present an estimate of the crossover time from which the VRM signal starts to dominate the transient response. We found that later crossover times were observed near the centers of large loops and that crossover times were much earlier near the transmitter wire. Also, the magnetic flux density has an earlier crossover time compared with its time derivative. To lower or remove the VRM response in an anticipated survey, our analytical expressions can be used straightforwardly to choose an appropriate loop size, identify the VRM response time window, and select an optimal set of time channels.

Sensor Placement via Optimal Experiment Design in EMI Sensing of Metallic Objects

This work, under the optimal experimental design framework, investigates the sensor placement problem that aims to guide electromagnetic induction (EMI) sensing of multiple objects. We use the linearized model covariance matrix as a measure of estimation error to present a sequential experimental design (SED) technique. The technique recursively minimizes data misfit to update model parameters and maximizes an information gain function for a future survey relative to previous surveys. The fundamental process of the SED seeks to increase weighted sensitivities to targets when placing sensors. The synthetic and field experiments demonstrate that SED can be used to guide the sensing process for an effective interrogation. It also can serve as a theoretic basis to improve empirical survey operation. We further study the sensitivity of the SED to the number of objects within the sensing range. The tests suggest that an appropriately overrepresented model about expected anomalies might be a feasible choice.