Fast evaluation of zero‐offset Green's function for layered media with application to ground‐penetrating radar

Abstract

We propose an efficient integration path for the fast evaluation of the three‐dimensional spatial‐domain Green's function for electromagnetic wave propagation in layered media for the particular case of zero‐offset, source‐receiver proximal ground‐penetrating radar (GPR) applications. The integration path is deformed in the complex plane of the integration variable kρ so that the oscillations of the dominant exponential term in the spectral Green's function are minimized. The contour does not need to be closed back on the real kρ axis as the complex integrand rapidly damps. The accuracy and efficiency of the technique have been confirmed by comparison with traditional elliptic integration contours. The proposed algorithm appears to be promising development for fast, full‐wave modeling and inversion of GPR data.

Short-Term Scientific Missions on electromagnetic modelling and inversion techniques for Ground Penetrating Radar - COST Action TU1208

“…During the first STSM, research activities focused on incorporating the asymptotic forward electromagnetic model developed by Pinel et al [17] in the multilayer Green function code developed at UCL [18]. Numerical tests were made and compared with former measurements lead at UCL [19] to validate the implementation: a case of three layers (two interfaces) was considered, in which only the upper interface is rough.…”

Application of Coupled-Wave Wentzel-Kramers-Brillouin Approximation to Ground Penetrating Radar

“…Thus, for a given vertical permittivity distribution ε(z), the calculation of the essential Green function component, corresponding to the signal due to partial subsurface reflections, requires numerical localization of the poles, summation of the corresponding residues, and substitution of the kernel ( ; , ) into the integral ( ; , 0). Let us finally comment that usually modification of the integration path is performed in order to achieve faster integration (and consequently accelerate forward-modelling calculations) -for example, [23] is a proper reference on this topic. In our case, this procedure allows one to reduce the integral to a sum of residues (33), completely avoiding numerical quadrature.…”

The electromagnetic response in a layered vertical transverse isotropic medium: A new look at an old problem

“…The vertical distance between the source and receivers can be minimized by increasing the bandwidth of the integral. A rule of thumb for how to choose the upper bound of the integral for a given vertical distance h between the source and receivers is given by the following relation (similar to the expression used in Lambot et al, 2007):…”