[1] A sequential, geostatistical inverse approach was developed for electrical resistivity tomography (ERT). Unlike most ERT inverse approaches, this new approach allows inclusion of our prior knowledge of general geological structures of an area and point electrical resistivity measurements to constrain the estimate of the electrical resistivity field. This approach also permits sequential inclusion of different data sets, mimicking the ERT data collection scheme commonly employed in the field survey. Furthermore, using the conditional variance concept, the inverse model quantifies uncertainty of the estimate caused by spatial variability and measurement errors. Using this approach, numerical experiments were conducted to demonstrate the effects of bedding orientation on ERT surveys and to show both the usefulness and uncertainty associated with the inverse approach for delineating the electrical resistivity distribution using down-hole ERT arrays. A statistical analysis was subsequently undertaken to explore the effects of spatial variability of the electrical resistivity-moisture relation on the interpretation of the change in water content in the vadose zone, using the change in electrical resistivity. Core samples were collected from a field site to investigate the spatial variability of the electrical resistivity-moisture relation. Numerical experiments were subsequently conducted to illustrate how the spatially varying relations affect the level of uncertainty in the interpretation of change of moisture content based on the estimated change in electrical resistivity. Other possible complications are also discussed.

Abstract-Compromised-node and denial-of-service are two key attacks in wireless sensor networks (WSNs). In this paper, we study data delivery mechanisms that can with high probability circumvent black holes formed by these attacks. We argue that classic multipath routing approaches are vulnerable to such attacks, mainly due to their deterministic nature. So once the adversary acquires the routing algorithm, it can compute the same routes known to the source, hence making all information sent over these routes vulnerable to its attacks. In this paper, we develop mechanisms that generate randomized multi-path routes. Under our designs, the routes taken by the "shares" of different packets change over time. So even if the routing algorithm becomes known to the adversary, the adversary still cannot pinpoint the routes traversed by each packet. Besides randomness, the generated routes are also highly dispersive and energyefficient, making them quite capable of circumventing black holes. We analytically investigate the security and energy performance of the proposed schemes. We also formulate an optimization problem to minimize the end-to-end energy consumption under given security constraints. Extensive simulations are conducted to verify the validity of our mechanisms.Index Terms-Randomized multi-path routing, wireless sensor network, secure data delivery.

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