Frequency‐domain modelling and inversion of electromagnetic data for 2D permittivity and conductivity imaging: An application to the Institut Fresnel experimental dataset

Abstract

The need for quantitative imaging of the near subsurface leads to the development of inversion algorithms to infer ground properties from recorded data. The aim of this study is to validate an inversion method recently developed for the simultaneous imaging of dielectric permittivity and electrical conductivity from 2D ground-penetrating radar measurements. The validation is performed using electromagnetic data collected in a well-controlled laboratory environment. In this experiment, the knowledge of the targets enables a quality control of the inversion results. In addition, the free space environment and the measurement of the incident field simplify the choice of a starting model for the inversion, as well as the calibration of the data with respect to the source signature and to the geometrical spread. To perform accurate and efficient forward simulations, we use a frequency-domain finite-difference scheme whose stencil coefficients can be optimized for each simulated frequency. As the objects of interest are locally concentrated at the centre of the acquisition array, it is possible to restrict the computation domain to a small region enclosing the targets using an integral representation of the analytical incident field coming from the sources and of the scattered field that we analytically propagate towards the receivers. An analysis of the numerical errors done on synthetic data shows that this strategy provides an error level that is low enough not to perturb the inversion, while dramatically decreasing the computational cost compared to a full-domain simulation. The monoparameter reconstruction of a purely dielectric target recovers permittivity values in very good agreement with the expected ones, as well as a very satisfying data fit. We also validate our strategy for multiparameter inversion on targets involving both a purely dielectric cylinder and a purely metallic copper tube, although the optimization cannot recover the exact conductivity of copper.