## 5 Results
Figure 2: Multi-parameter synthetic example when using a low-frequency source signal: (**a**) the true S- wave velocity model for the calculation of the observed data, (**b**) the initial S- wave velocity model, and (**c**) the inverted S- wave velocity model. The CPML frame is marked by a thin black line. Figure 4: Model fitting when using a low-frequency source signal: (**a**) vertical profiles of the P- wave velocity model, (**b**) vertical profiles of the S- wave velocity model, and (**c**) vertical profiles of the density model. The true model is plotted with the grey line, the initial model is represented by the dashed black line and vertical profile at \(x=25\) m of the inverted models is the plotted blue line. Figure 3: Multi-parameter synthetic example when using a low-frequency source signal: (**a**) the true density model for the calculation of the observed data, (**b**) the initial density model, and (**c**) the inverted density model. The CPML frame is marked by a thin black line. Therefore, it can be said that in this study by considering a broad bandwidth signal as the source wavelet, the capability of the multi-parameter pseudo-viscoelastic FWI of the shallow-seismic wavefield is tested in the case of using a vibroseis source, too. A reflector is then added to the bottom of the true models (Figures 6a, 7a and 8a) at the depth of 15 m. A 1D model is also used for the initial and background of the true models (Figures 6b, 7b and 8b). Multi-parameter inversion is conducted for the parameters discretized at a 2D cartesian grid with the same grid spacing and the total propagation time as were used in the previous example. The high cut frequency filter, up to 100 Hz is applied progressively in the multi-scale strategy. In order to reduce the computational time, the number of receivers was reduced to 66 and the total of shots used in this test is 17. This test takes about 11 hours, and 317 iteration steps are calculated by using the same system as used in the previous test. In this example, the inverted S- wave velocity model (Figure 7c), is still better reconstructed than the P- wave velocity (Figure 6c) and the density (8c) models. The high-velocity layer is reconstructed sharper and more accurate compared to the inverted S- wave velocity model in the previous test. As can be seen in the vertical profile obtained for this model in Figure 9b, the velocity value of the high-velocity layer matches the value of the true high-velocity layer robustly. The velocity value of the low-velocity zone is obtained precisely too. There is an improvement in the results of inversion of the P- wave velocity and density models. As the artefacts in the low-velocity zone are decreased. In the presence of the reflector at the bottom of the model, the structure beneath the high-velocity layer is resolved with higher quality and resolution. In other words, the artefacts at the dipper parts of the models are significantly decreased too. Similar to the previous example, the final synthetic data nicely fits the observed data (Figure 10a). According to the zoomed comparison of the initial and inverted data for trace 36 (Figure 10b), misfit of the inverted and observed data is low. Figure 5: Fitting of the data in the shot at \(x=9\) m when using a low-frequency source signal. (**a**) Comparison of the vertical velocity observed and inverted seismograms. (**b**) Comparison of the normalized seismograms calculated for the initial, inverted, and observed data for trace 36. Figure 6: Multi-parameter synthetic example when using a high-frequency source signal: (**a**) the true P- wave velocity model for the calculation of the observed data, (**b**) the initial P- wave velocity model, and (**c**) the inverted P- wave velocity model. The CPML frame is marked by a thin black line. Figure 7: Multi-parameter synthetic example when using a high-frequency source signal: (**a**) the true S- wave velocity model for the calculation of the observed data, (**b**) the initial S- wave velocity model, and (**c**) the inverted S- wave velocity model.