Geodesic
The two-dimensional GPR modeling for near-surface investigation using the Dirichlet--Neumann boundary condition combination
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 385-399.

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We have developed an algorithm to simulate a Ground Penetrating Radar (GPR) survey responses in the two-dimensional (2D) geological media using a finite element numerical method (FEM). The scalar transverse electric mode of Maxwell's wave equation was simulated utilizing a combination of the Dirichlet and the Neumann boundary conditions. Immediately, the program designed was used to analyze various survey situations, observing such effects as antenna frequencies selection, pipes and buried tanks locations and karst cavities detection in limestone. Several pipes configurations were studied, mainly those filled with fresh water, salt water, oil and air. Thus, all these tests permitted us to conclude that the target size and conductivity change the hyperbolic pattern of the GPR response, and, the shape of the tails gives a measure of velocity and depth. In this form, we have shown how efficient GPR is to map the underground conditions and their benefits to environmental and hydrogeological studies. The results obtained allow us to perform all kinds of the 2D models using smaller meshes, which traduce in faster calculations, and, in this form, to select optimal parameters and conditions to provide more information, which can potentially help us to develop better field surveys and, consequently, to obtain better interpretations. 
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     title = {The two-dimensional {GPR} modeling for near-surface investigation using the {Dirichlet--Neumann} boundary condition combination},
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J. DA Silva; A. Carrasquilla; V. Priimenko. The two-dimensional GPR modeling for near-surface investigation using the Dirichlet--Neumann boundary condition combination. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 385-399. http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a5/

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