Abstract-We used kernel density estimation (KDE) methods to build a priori probability density functions (pdfs) for the vector of features that are used to classify unexploded ordnance items given electromagnetic-induction sensor data. This a priori information is then used to develop a new suite of estimation and classification algorithms. As opposed to the commonly used maximumlikelihood parameter estimation methods, here we employ a maximum a posteriori (MAP) estimation algorithm that makes use of KDE-generated pdfs. Similarly, we use KDE priors to develop a suite of classification schemes operating in both "feature" space as well as "signal/data" space. In terms of feature-based methods, we construct a support vector machine classifier and its extension to support M -ary classification. The KDE pdfs are also used to synthesize a MAP feature-based classifier. To address the numerical challenges associated with the optimal data-space Bayesian classifier, we have used several approximation techniques, including Laplacian approximation and generalized likelihood ratio tests employing the priors. Using both simulations and real field data, we observe a significant improvement in classification performance due to the use of the KDE-based prior models.
A B S T R A C TUsing a subset of the SEG Advanced Modeling Program Phase I controlled-source electromagnetic data, we apply our standard controlled-source electromagnetic interpretation workflows to delineate a simulated hydrocarbon reservoir. Experience learned from characterizing such a complicated model offers us an opportunity to refine our workflows to achieve better interpretation quality. The exercise proceeded in a blind test style, where the interpreting geophysicists did not know the true resistivity model until the end of the project. Rather, the interpreters were provided a traditional controlled-source electromagnetic data package, including electric field measurements, interpreted seismic horizons, and well log data. Based on petrophysical analysis, a background resistivity model was established first. Then, the interpreters started with feasibility studies to establish the recoverability of the prospect and carefully stepped through 1D, 2.5D, and 3D inversions with seismic and well log data integrated at each stage. A high-resistivity zone is identified with 1D analysis and further characterized with 2.5D inversions. Its lateral distribution is confirmed with a 3D anisotropic inversion. The importance of integrating all available geophysical and petrophysical data to derive more accurate interpretation is demonstrated.
The physics-based classification of unexploded ordnance (UXO) from electromagnetic induction (EMI) data is an exercise in nonlinear data inversion in which model parameters are extracted from a dataset by way of a physical model. Gradientdescent-based algorithms like Levenberg-Marquart (LM) suffer from local minima entrapment, but deliver rapid, accurate estimates when initialized near the global minima. Global optimizers, like particle swarm optimization (PSO) are less susceptible to this limitation. Here we consider an approach for parameter estimation based on a hybridization of PSO and LevenbergMarquart. For purposes of initializing the LM procedure, we demonstrate that PSO applied to a reduced form of the physical model reaches a reliable initialization in one tenth the time of a coarse search of parameter space. Monte Carlo testing of the approach shows PSO initialized Levenberg-Marquardt estimation converging to the best-fit solution every time, as opposed to a randomly but reasonably initialized estimation. PSO as a stand alone approach provides less fit solutions on average than the PSO/Levenberg-Marquardt hybrid within the same computation time. We demonstrate these observations using both the simple, dipole model for the UXO problem as well as an enhanced form of this model capable of better capturing signal structure for large UXO-type objects.
We used kernel density estimation to build a-priori probability distributions on the vector of features used to characterize unexploded ordnance from electromagnetic induction sensor data. This priori information is then used in a Bayesian framework to develop a new suite of estimation and classification algorithms. Based on this prior information several classification algorithms are developed in feature and signal space. Results using real field data show more robust estimation and significant improvement in classification performance for signal space classifiers comparing to conventional Gaussian approximation to the density of the features.
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