GNGTS 2013 - Atti del 32° Convegno Nazionale

Tab. 1 shows two different velocity distribution models, one with decreasing velocities and the other with a deep high velocity layer. Both models have small and large velocity contrasts, to further test the accuracy of the inversion. The layer thicknesses are also different, with values generally increasing with depth. In both forward modeling and inversion, only the TE case is simulated (with a 70 cm constant offset) since it is the usual acquisition configuration for GPR surveys. This is another test for the method, since with such GPR system the two models have different travel paths and reflection coefficients. In particular, the different thicknesses of the shallow layer in the two models give 19.3° and 9.9° incident angles at the first interface, respectively. Tab. 1 – Parameters of the two 1-D velocity models used in forward modeling. Model 1 Model 2 Layer h i [m] v i [cm/ns] h i [m] v i [cm/ns] 1 1.0 25.0 2.0 16.0 2 3.0 24.0 5.0 17.0 3 5.0 19.0 1.0 24.5 4 2.0 18.5 3.0 25.0 5 6.0 17.0 6.0 15.5 6 9.0 16.0 9.0 15.0 The forward and inverse processes are completely independent. The peak amplitudes, including their polarity, and the traveltimes required as input for the inversion, were taken from the synthetic GPR traces, while the velocities of the shallow layer of each model, the peak value of the initial wavelet and the offset are supposed to be known. Typical measurement uncertainties were added to each input parameter to estimate the error propagation, with the confidence of the velocity in the first layer being the most important factor in determining the uncertainties of the results. The results of the inversion are consistent with the initial models parameters, as shown in Tab. 2. One important aspect is the general increase of the estimated error with depth, which is due to the iterative nature of the inversion program. Nevertheless, while the estimated errors can grow quite large, especially in the deeper layers and depending mainly on the initial measurement uncertainties used, the mean values are nonetheless very close to the initial values used in the forward modeling (Tab. 1). Tab. 2 – Results of the inversion of the traces obtained from the models in Tab. 1, with the EM wave velocities in the shallow layer of the two models fixed as input parameters of the inversion procedure. The mean values in each layer are consistent with the initial models, while the main influence on the errors estimation is the uncertainty related to the velocities in the first layer. Model 1 Model 2 Layer h i [m] v i [cm/ns] h i [m] v i [cm/ns] 1 1.00 ± 0.05 25.00 ± 0.20 2.00 ± 0.05 16.00 ± 0.20 2 3.00 ± 0.16 24.01 ± 0.20 5.00 ± 0.20 17.01 ± 0.21 3 5.00 ± 0.39 18.98 ± 0.24 1.01 ± 0.58 24.56 ± 0.55 4 2.00 ± 0.69 18.47 ± 0.25 3.00 ± 1.26 25.06 ± 0.59 5 5.99 ± 1.41 16.96 ± 0.32 5.98 ± 2.25 15.44 ± 1.19 6 8.98 ± 2.91 15.97 ± 0.40 8.96 ± 5.63 14.93 ± 1.25 115 GNGTS 2013 S essione 3.2