GNGTS 2017 - 36° Convegno Nazionale

626 GNGTS 2017 S essione 3.2 An additional problem is related to the representation of the data, which are provided by the GPR along a rectangular abscissa-depth time grid (B-scan). This is not much troublesome and can be solved by a suitable wrapping of the solution. In this study, after zero-timing the data, we take one half of the recorded time depth up to the reflection from the opposite point of the circumference of the column with respect to the position of the antenna. In this way, we approximately retain the data up to the return trip time from the antenna to the centre of the circular cross section of the column (Masini et al. , 2010). A more substantial problem about the data processing remains, and in particular about the development a focusing algorithm suitable for the imaging task. In this respect, migration algorithms usually exploited in GPR data processing are implicitly based on the hypothesis of a flat surface, and on the hypothesis of a straight observation line along it (Persico, 2014). Here, we adopt a linear inverse scattering algorithm based on the Born approximation and accounting for the geometry of the scenario as well as for the measurement configuration. A 2D geometry is assumed and the pertinent incident fields and Green’s function are considered for the case of a homogeneous scenario. In particular, the incident field and the Green’s function are expressed by the Hankel function of the second kind and of zero order. The imaging problem is recast as the inversion of the following integral relationship: (1) where s E is the scattered field at the measurement position r → (source-observation point) and χ �� ��� �������� ��������� ����� �� ��� ������� �� ��� ������� ��������� �� ��� �������� is the contrast function, which is the unknown of the problem expressed as the relative difference between the permittivity of the targets and that of the surrounding medium. k is the wavenumber within the column. In Eq. (1), several unessential factors outside the integrand are neglected. The estimation of the reference permittivity [and consequently of the wavenumber to be put into Eq. (1)], is provided by the flat reflection attributable to the opposite side of the columns, which occurs at a known depth. Of course, it would be improper to make use of diffraction hyperbolas, because the curvature of the columns surface distort them. The scattered field data are found in an approximate way from the GPR data after zero timing and a background removal plus a cut time up to the alleged centre of the columns as above said. Then, the data are transformed in frequency domain and inverted by means of an inversion approach working under a multi-monostatic/multi-frequency configuration. The data have been gathered with a Ris Hi mode system manufactured by IDS equipped Fig. 1 - The test site constituted by two columns (left). Internal composition of the column considered for the experiments (right).