Ground Penetrating Radar
Ground penetrating radar (GPR) is used in civil engineering, archaeology, and many other areas. GPR antennas are moved over the surface of the inspected soil or structure, while emitting and receiving electromagnetic (EM) waves. In order to extract accurate and useful information from the received EM field, it is important to have as much a priori information as possible . Such information includes a good understanding of the electromagnetic properties of the involved media and used antennas . However, the knowledge about these properties is inevitably stochastic in its nature.
Many researchers have studied the EM behaviour of GPR antennas, by using different techniques that can be classified in two main categories: frequency domain (FD)  and time domain (TD) - techniques. A stochastic analysis of the transient response of a GPR antenna has been presented in -. In  the unknown current along the wire above the lossy-half space is governed by the space-time Hallen integral equation. The deterministic solution is featured by GB-IBEM method. The stochastic response is obtained with respect to uncertain antenna position (height) and uncertain ground conductivity. The work done in  and  present the stochastic current response for the wire buried in the lossy ground which may be found useful not only in GPR purposes but in other areas, for example in the design of lighting protection for electrical settlements.
As a counterpoise to time domain analysis, the stochastic analysis of frequency domain response is presented in the present paper. Stochastic Collocation (SC) method is combined with a direct EM solver to assess the variability of the current induced on a GPR dipole antenna, due to the uncertain nature of the soil and antenna height. The dipole is assumed to be thin and is placed above a lossy half-space, with its axis parallel to the air-soil interface: such simple geometry is especially convenient for testing new computational approaches and methods. The formulation of the problem, implemented in our deterministic EM solver, is based on a FD solution of Pocklington's integro-differential equation, by means of Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) ; the transient response is then obtained via inverse Fast Fourier's transform .
The paper is organized as follows. Section 2 outlines the employed FD integral equation approach and related numerical solution (Sub-section 2.1); the theoretical basis of the Stochastic Collocation method are also presented (Sub-section 2.2). Section 3 brings computational examples, while in Section 4 general conclusions are given.
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For information concerning COST Action TU1208 and TU1208 GPR Association, please take contact with the Chair of the Action and President of the Association, Prof. Lara Pajewski. From 4 April 2013 to 3 October 2017, this website was supported by COST, European Cooperation in Science and Technology - COST is supported by the EU RTD Framework Programme Horizon2020. TU1208 Members are deeply grateful to COST for funding and supporting COST Action TU1208. As of 4 October 2017, this website is supported by TU1208 GPR Association, a non-profit association stemming from COST Action TU1208.