1
Partners in Environmental Technology Technical Symposium & Workshop, Washington, D.C., December 2-4, 2008 Nicolas Lhomme, Fridon Shubitidze and Stephen D. Billings Sky Research, Inc Leonard R. Pasion (P.I.), Lin-Ping Song and Douglas W. Oldenburg Univ. of British Columbia, Vancouver, B.C., Canada SERDP MM1637: Selecting Optimal Models for Inverting EMI Data A Comparison of Different Models applied to Geonics EM63 data at Camp Sibert, AL Processing of data with overlapping anomalies Cell 297: Significant anomaly overlap Cell 515: Small amount of anomaly overlap 1. Normalized Surface Magnetic Sources (NSMS) Model 2. The Point Dipole Model Polarizations ITC Sibert Cell 515 ITC Information-Theoretical Criteria for Detecting Object Number 1) Assuming model parameters: 2) Introducing a likelihood function: 3) Choosing a penalty function: Principle of ITC without inversion The probability density f of the data D given the η-th model θ η 4) Minimizing a criterion : Data covariance matrix based approach [Wax and Kailath, IEEE-ASSP, 33(2), 1985] Eigenvectors Estimate minimum number of dipolar polarizations that represent the data maximally Noise level Eigenvalues Sibert Cell 297 Inverting Data Simultaneously for Two targets. Investigating the effect of non-dipolar data components on the spread of estimated dipole polarizations Figure of Merits to assess data quality and the degree of reliability of inversion results: EM-63 data at Fort McClellan, AL FOM features • SNF = max(1, SNR/30) so that SNF max if SNR > 30 dB • GC = Grid Coverage (spatial coverage, amplitude sampling) • Zpred = depth predicted by inversion • CC = correlation coefficient (observed / predicted data) • CCW = corr. coeff. of weighted data (data are weighted by their standard deviation, which depends on the estimated noise) • GOF = goodness of fit • DZI = depth resolution (subsurface scan for target location) • DZF = depth variance (among converged models) • MedResid = Median of residual (should be 0) Combination of FOM parameters can be used to: -Identify anomalies that should not be inverted (SNF, GC) -Identify failed inversion: either because non-UXO-like object, or implementation issues -Define reliability of inversion result (input for classification) -Predict depth error Noise-free synthetic data produced by the method of auxiliary sources Numerical Standardized Excitation Approach (Shubitidze et al, IEEE-TGRS, 43, 1736, 2005) The library can be built over a wide frequency band then transformed into the time domain. 40 cm θ = 0 θ = 180 Orange dots indicate recovered dipole locations • Noise-free synthetic datasets created using the SEA • SEA data inverted for the three elements of the dipole polarization tensor. • Two depths: 40cm (‘+’ symbols) and 75 cm (‘x’ symbols) below the Tx/Rx measurement plane • 13 Orientations: 0 (nose up) to 180 degrees (nose down) at 15 o increments • Data inverted for the 3 elements of the diagonalized polarization tensor The SEA modeling technique is able to model heterogenerous metallic targets. • The spread of the estimated dipole polarizations were smaller than expected. For the 81 mm mortar, the spread of dipole polarizations due to inaccurate position and orientation is greater than the spread due to the inaccuracy of the dipole model. Polarizations estimated from SEA data were compared to polarizations derived from in-air measurements: • Dipole polarizations derived from SEA data have correct behaviour at all times for the steel cylinder and 40 mm projectile. • The mortars have correct early time behaviour (up to about 5 ms), but does not have the correct late time behavior. This is likely because to the RSS for the mortars were created using solid bodies of revolution, instead of thin-walled shells. ATC 40 mm ATC 60 mm Mortar Steel Cylinder ATC 81 mm Mortar • The location of the estimated dipole for the mortar corresponds to the steel body of the mortar. It appears that the steel part of the mortar provides the majority of the response, and that response is well represented by a dipole model A closer look at the 81 mm mortar inversions A Relationship between the Total Normalized NSMS and the Dipole Polarization MM1637 PROJECT OVERVIEW: • Practical and cost-effective strategies for remediation require reliable algorithms for discrimination • Discrimination depends upon the ability to estimate parameters. The success of this procedure requires: 1. A careful choice of the forward model, and 2. An understanding of how data quality impacts parameter estimates of the chosen forward model. The goal of this research is to delineate the circumstances for which a particular type of forward model should be chosen. Methodologies will be developed that would allow a user to more efficiently extract meaningful parameters from data. Objectives: • Determine the conditions for which a more complex model might yield superior information compared to dipole models • Determine which parameterizations of the dipole model are most useful for discrimination • Develop practical diagnostic procedures to assess which data anomalies are of high enough quality to warrant inversion and which inversion procedure should be used • Develop inversion strategies and software to simultaneously invert for multiple items. Transmitter L 1 : Axial Polarization L 2 =L 3 : Transverse Polarization Transmitter • The secondary field is modeled by a distribution of charges or dipoles on a surface surrounding the target. Objectives: Develop inversion strategies to simultaneously invert for multiple items. Determine when multi-peak anomaly and overlapping anomalies should be processed as a single target or as a pair of targets. If the multi-peak anomaly should be processed as a pair of targets, then we need to decide if the anomaly should be inverted as two separate anomalies, simultaneously, or not at all. Above: Recovered polarizations when inverting 200 simulated EM63 data anomalies. Appropriate sensor noise levels were used. A position error of 1cm and a sensor orientation error of 1 degree were used. Tx • Polarization parameters recovered from data inversion • Polarizations fit with the parameterization: • Cooperative Inversion was also applied to dataset. Depth for non- linear inversion constrained by magnetometry data depth estimates. • A template match algorithm was also applied. For the template match, we solved for the location and orientation of a 4.2 inch mortar that would best fit the data. A dig- list based on misfit was created. Excavated Target Excavated Target Observed Data (t1) Observed Data (t1) Predicted Residual Single Target Inversion Predicted Residual Two Target Inversion Predicted Residual Single Target Inversion Predicted Residual Two Target Inversion Target 1 Target 2 Polarizations of excavated target derived from in air TEMTADS measurements. Polarizations of base plate The Geonics EM63 data acquired at Camp Sibert were of high enough quality to support multi-target inversions. Multi-target inversions of Cell 515 and cell 297 suggest that a base plate was also present in each cell. L(t) = k t - β exp(-t/γ) • Data collected for the SERDP Discrimination Pilot project • 4.2 inch mortars • Data collected in cued interrogation mode. • 216 total anomalies acquired. 66 anomalies used as ground truth. Objective: Determine conditions under which a more complex model might yield superior information compared to dipole models. As part of this investigation, we are using numerical modeling of targets to determine the amount of spread in estimated polarizations due to non-dipolar components in the data. Template Method FAR = 0.009 AUC = 0.995 Method 2: Invert for Location, and Surface Dipole Distribution on a sphere The sum of the 3 dipole polarizations is equivalent to the total NSMS. One interpretation is that the total NSMS (derived from data acquired at the surface) is an "average" of the dipole polarizations. Method 1: Invert for Location, Orientation, and Surface Dipole Distribution on a spheroid • Location, orientation and dipole distribution determined via differential evolution optimization • Recovered Q(t) then fit with • A template match method was implemented where the recovered Q(t) was compared to the Q determined from training data. k t - β exp(-t/γ) Recovered normalized surface source were computed by Fridon Shubitidze Inversion of SEA data for polarization tensor elements 3. Data Features • Data based features do not involve estimating target location and orientation. They are features calculated directly from the data: for example, data amplitudes, data energy, and decay characteristics (e.g. time constant, power law exponent) of soundings. • For summarizing decay characteristics, we fit the largest magnitude sounding in each anomaly with the function f(t) = kt - β exp(-t/γ). • Good performance (FAR=0.121, AUC=0.948) is achieved by using the decay characteristics (β,γ) k k • Step One: Estimate the depth. • Step Two: Invert for location and dipole distribution. The estimate in Step One is used to constrain the depth (+/- 5 cm) • The total NSMS is used for discrimination: Depths used in inversion UXO Base Plates Non OE Scrap Groundtruth NSMS Depth Number of Scrap Partial Mortars Shrapnel UXO Base Plates Non OE Scrap Partial Mortars Shrapnel Pd_disc Pd_disc The performance is excellent. This may be due to: 1. There is no need to calculate orientation 2. The depth estimate used to constrain the NSMS inversion matched the ground truth depths β vs. γ Number of Scrap Pd_disc UXO Number of Scrap Pd_disc Predicted depth error using FOM (m) Depth error from ground truth (m) Number of Scrap Decay Parameters Size Parameters β 1 vs. γ 1 β 2 vs. γ 2 β 3 vs. γ 3 k 1 vs. (k 2 , k 3 ) k 1 vs. Δk UXO NON-UXO Polarizations 1
