Laurens Beran

Magnetic models of unexploded ordnance

Magnetometry is widely used for the characterization of areas contaminated by unexploded ordnance (UXO). To successfully discriminate hazardous UXO from nonhazardous clutter requires accurate models of the ordnance response. This paper develops an ordnance library with 15 different items using total-field magnetic data collected over a test stand. The induced and remanent magnetizations were obtained by varying the three-dimensional orientation of each item and measuring the magnetic field on a horizontal plane in the dipolar regime. Replicate measurements using multiple specimens of the same ordnance returned very similar induced magnetizations. The fitted moments were used to estimate the detection depths for different sensor noise floors. A prolate spheroid with a 3.5 aspect ratio was used to provide a good approximation to the detection depths for many of the ordnance items. Assuming a 1-nT noise floor, these orientation-dependent detection depths ranged from 10 to 17 times of the objects diameter

Selecting a Discrimination Algorithm for Unexploded Ordnance Remediation

We review the algorithms that have been used to discriminate between hazardous unexploded ordnance (UXO) and harmless clutter. Statistical classifiers use model parameters estimated from geophysical data to formulate a decision rule. This rule tries to discriminate between UXO and clutter using the available information. In contrast, library-based discrimination algorithms make decisions using a predefined library of signatures for expected UXO types. Given the variety of algorithms that are available for UXO discrimination, we describe two metrics for evaluating discrimination performance - the area under the receiver operating characteristic and the false-alarm rate. We propose a bootstrapping algorithm for estimating these metrics when limited data are available. Last, we demonstrate this approach on real electromagnetic and magnetic data sets.

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 ...

Robust Inversion of Time-domain Electromagnetic Data: Application to Unexploded Ordnance Discrimination

We invert time-domain electromagnetic data for the purpose of discriminating between buried unexploded ordnance (UXO) and non-hazardous metallic clutter. The observed secondary magnetic field radiated by a conductor is forward modeled as a linear combination of decaying, orthogonal dipoles. We show via a perturbation analysis that errors in the measurement of sensor position propagate to non-normal errors on the observed data. A least squares (L2) inversion assumes normal errors on the data, so non-normal errors have the potential to bias dipole parameter estimates. In contrast, robust norms are designed to downweight the effect of outlying (noisy) data and so can provide useful parameter estimates when there is a non-normal component to the noise. When positional errors are modeled as independent Gaussian perturbations, we find that weighted least squares and robust inversions have comparable performance. Both inversion techniques estimate data uncertainties from observed data, and this has the effect of making the least squares inversion robust to outliers. However, when simulated errors are correlated, robust inversion with a bisquare norm provides a marked improvement over L2 inversion. Application of robust inversion to real data sets from Camp Sibert, Alabama produced an incremental improvement to the initial L2 inversion, identifying outlying ordnance items and improving discrimination performance.

Estimation of Cole‐Cole parameters from time‐domain electromagnetic data

The occurrence of negative transients in central loop time domain electromagnetic soundings is a well-documented phenomenon in the geophysical literature. While early papers speculated that this effect could be caused by particular conductivity distributions or magnetic effects, Weidelt (1982) showed that for a coincident loop system with a step-off primary field, the measured secondary field must be non-negative over nonpolarizable ground, regardless of the subsurface distribution of conductivity. Observed negative transients can therefore only be attributed to polarization effects; that is, the conductivity of the ground is time-varying.

Incorporating Uncertainty in Unexploded Ordnance Discrimination

We examine representations of feature vector uncertainty in the context of unexploded ordnance (UXO) discrimination with electromagnetic data. We compare a local uncertainty estimate derived from the curvature of the misfit function with global estimates of the model posterior probability density (PPD) obtained with Markov chain sampling. For well-posed experiments (i.e., with high SNR and adequate spatial coverage), the two methods of uncertainty appraisal agree. However, when the inverse problem is ill posed, we find out that the PPD can be multimodal. To incorporate these uncertainties in discrimination, we first develop an extension of discriminant analysis which integrates over the posterior distribution of the model. When dealing with multimodal PPDs, we show that an effective solution is to input all modes of the PPD-corresponding to all models at local minima of the misfit-into discrimination and, then, to classify on the basis of the model which is most likely a UXO.

Requirements for unexploded ordnance detection and discrimination in the marine environment using magnetic and electromagnetic sensors

The topic of marine unexploded ordnance (UXO) mapping is becoming one of the most significant technology challenges of environmental characterization and remediation. For obscured object detection and characterization, magnetic and electromagnetic methods have been the primary sensor modalities used in terrestrial applications. However, while some marine systems have been developed and deployed, detection performance has been generally poor, particularly against small targets, and limited discrimination ability has been demonstrated. In this paper, we will review both the detection and discrimination requirements for magnetic and electromagnetic induction (EMI) sensor modalities and will discuss some systems either under development or at a conceptual stage. The paper focuses on data requirements and does not address the engineering required to effectively deploy the sensors.

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.

UXO and UXO Sensor Technology

Advanced electromagnetic induction sensors have been developed under the SERDP and ESTCP Munitions Response program to find and identify buried unexploded ordnance. These sensors consist of multiple transmit and receive coil configurations that collect sufficient data for inverting the time decaying, dipole polarizations of a buried metallic object. These polarizations can be used to identify the object as UXO or metallic debris. These sensor platforms have been deployed in both dynamic survey modes to locate and identify and stationary “cued” modes to just identify at target locations. ESTCP has sponsored a number of Live Site Demonstrations and these systems have been found to be very effective in finding UXO. An approach has been developed for advanced EMI survey data that applies a model based detection filter to locate metallic targets and a dipole inversion to identify the targets as UXO or clutter based on the inverted polarizations. Analysis of the Live Site data has found a significant fraction of the target locations have multiple target signals present. To address this, an N-dipole inversion is being applied to all target locations. This inversion inverts for a specified (N) number of targets. Fit results are returned for N = 1, 2, and 3 possible targets at each location. The problem arises that quite often all of the multi-target fits represent the data equally well. We will present these results and some strategies taken to insure that all possible targets of interest are selected from the multiple fit results. Work is also in progress to try and evaluate when the local target density is too high for valid analysis.

Risk assessment for unexploded ordnance remediation

We develop and compare methods for assessing the risk that unexploded ordnance (UXO) have been missed following prioritized digging. A random compliance sampling approach has been suggested for UXO risk assessment, and we extend this approach to account for the bias in prioritized digging, thereby reducing the number of excavations required to test for outlying UXO. We then discuss and compare methods for identification of outliers to the distribution of UXO via generative models of the receiver operating characteristic (ROC). Next, we consider how seeded items emplaced for quality control can be used to increase confidence in the classification process, and we model this process by constraining the ROC model. Finally, we turn to the problem of identifying novel, or unique, UXO with prioritized validation digs. We propose a metric that combines features of the geophysical model estimated for each detected target to identify novel UXO. The metric requires no prior information about the UXO present at a site.