Detection of complex point targets with distributed assets in a MIMO radar system

The report explores the problem of detecting complex point target models in a MIMO radar system. A complex point target is a mathematical and statistical model for a radar target that is not resolved in space, but exhibits varying complex reflectivity across the different bistatic view angles. The complex reflectivity can be modeled as a complex stochastic process whose index set is the set of all the bistatic view angles, and the parameters of the stochastic process follow from an analysis of a target model comprising a number of ideal point scatterers randomly located within some radius of the targets center of mass. The proposed complex point targets may be applicable to statistical inference in multistatic or MIMO radar system. Six different target models are summarized here – three 2-dimensional (Gaussian, Uniform Square, and Uniform Circle) and three 3-dimensional (Gaussian, Uniform Cube, and Uniform Sphere). They are assumed to have different distributions on the location of the point scatterers within the target. We develop data models for the received signals from such targets in the MIMO radar system with distributed assets and partially correlated signals, and consider the resulting detection problem which reduces to the familiar Gauss-Gauss detection problem. We illustrate that the target parameter and transmit signal have an influence on the detector performance through target extent and the SNR respectively. A series of the receiver operator characteristic (ROC) curves are generated to notice the impact on the detector for varying SNR. Kullback–Leibler (KL) divergence is applied to obtain the approximate mean difference between density functions the scatterers assume inside the target models to show the change in the performance of the detector with target extent of the point scatterers.

Hydrogeochemical controls on uranium in aquifers of the Jacobsville Sandstone

The occurrence of elevated uranium (U) in sandstone aquifers was investigated in the Upper Peninsula of Michigan, focusing on aquifers of the Jacobsville Sandstone. The hydrogeochemical controls on groundwater U concentrations were characterized using a combination of water sampling and spectral gamma-ray logging of sandstone cliffs and residential water wells. 235U/238U isotope ratios were consistent with naturally occurring U. Approximately 25% of the 270 wells tested had U concentrations above the U.S. Environmental Protection Agency Maximum Contaminant Level (MCL) of 30 μg/L, with elevated U generally occurring in localized clusters. Water wells were logged to determine whether groundwater U anomalies could be explained by the heterogeneous distribution of U in the sandstone. Not all wells with relative U enrichment in the sandstone produced water with U above the MCL, indicating that the effect of U enrichment in the sandstone may be modified by other hydrogeochemical factors. Well water had high redox, indicating U is in its highly soluble (VI) valence. Equilibrium modeling indicated that aqueous U is complexed with carbonates. In general, wells with elevated U concentrations had low 235U/238U activity ratios. However, in some areas U concentrations and 235U/238U activity ratios were simultaneously high, possibly indicating differences in rock-water interactions. Limited groundwater age dating suggested that residence time may also help explain variations in well water U concentrations. Low levels of U enrichment (4 to 30 ppm) in the Jacobsville sandstone may make wells in its oxidized aquifers at risk for U concentrations above the MCL. On average, U concentrations were highest in heavy mineral and clay layers and rip up conglomerates. Uranium concentrations above 4 ppm also occurred in siltstones, sandstones and conglomerates. Uranium enrichment was likely controlled by deposition processes, sorption to clays, and groundwater flow, which was controlled by permeability variations in the sandstone. Low levels of U enrichment were found at deltaic, lacustrine and alluvial fan deposits and were not isolated to specific depositional environments.